PEARL Model Overview </>

The PEARL (ProjEcting Age, multmoRbidity, and poLypharmacy) model is an agent-based simulation model of HIV care in the United States. The model leverages the power of the North American AIDS Cohort Collaboration on Research and Design (NA-ACCORD) data set. Data on ~200,000 HIV-infected individuals are provided by over 200 sites across North America. This size of this dataset allows us to treat 15 sub-populations independently. The PEARL model characterizes population by sex (male and female), race (white, black, and hispanic), and risk (men who have sex with men, intravenous drug users, and heterosexual HIV risk).

Table 1: Sub-Populations Used in the PEARL Model

Population	Race	Risk	Sex	Code
Black Heterosexual Women	Black	HET	Female	het_black_female
Black Heterosexual Men	Black	HET	Male	het_black_male
Hispanic Heterosexual Women	Hispanic	HET	Female	het_hisp_female
Hispanic Heterosexual Men	Hispanic	HET	Male	het_hisp_male
White Heterosexual Women	White	HET	Female	het_white_female
White Heterosexual Men	White	HET	Male	het_white_male
Black Women Who Use Intravenous Drugs	Black	IDU	Female	idu_black_female
Black Men Who Use Intravenous Drugs	Black	IDU	Male	idu_black_male
Hispanic Women Who Use Intravenous Drugs	Hispanic	IDU	Female	idu_hisp_female
Hispanic Men Who Use Intravenous Drugs	Hispanic	IDU	Male	idu_hisp_male
White Women Who Use Intravenous Drugs	White	IDU	Female	idu_white_female
White Men Who Use Intravenous Drugs	White	IDU	Male	idu_white_male
Black Men Who Have Sex With Men	Black	MSM	Male	msm_black_male
Hispanic Men Who Have Sex With Men	Hispanic	MSM	Male	msm_hisp_male
White Men Who Have Sex With Men	White	MSM	Male	msm_white_male

The PEARL model runs in discrete time steps representing one year. The simulations begin in year 2009 by creating an initial population of HIV-infected individuals receiving or disengaged from ART in the US. The size of this population and the distribution of their ages, ART initiation years, and CD4 count at ART initiation is estimated based on data available from NA-ACCORD and the Centers for Disease Control and Prevention (CDC). At the beginning of each simulated year (2010 – 2035), a population of those newly diagnosed with HIV enter the model, and a specific proportion (modeled as an increasing function of time) of these individuals link to HIV care and start ART. The population size, age, and CD4 count distributions at ART initiation are estimated from CDC’s and NA-ACCORD’s data. Individuals on ART experience a likelihood of mortality and disengagement from care over time. Upon disengagement, individuals experience an increase in probability of mortality and a gradual reduction in CD4 count. Time-varying CD4 count is updated for all individuals in the model depending on their HIV care status (i.e., increasing among those in care and decreasing among those out of care). All simulation parameters have been estimated from CDC’s and NA-ACCORD’s data for year 2010 to 2022. Simulated outcomes, in terms of age distribution of population in HIV care, are cross-validated against NA-ACCORD’s data during this period. Model projections are made from year 2023 to 2035.

Clarification on terminology: Given the complexities involved in defining, parametrizing and calibrating all steps of the HIV care continuum for the 15 sub-groups, we have limited the scope of the PEARL model to population of HIV infected individuals who have ever been and/or are currently on ART. Following this definition, the simulated population is divided into two groups including “ART users” (those currently on ART) and “ART non-users” (those previously on ART who disengaged from treatment and are currently off ART). Furthermore, the usage of term “HIV care” in this text is closely related to previous or current instances of “ART usage”, and does not include prior steps to ART initiation such as diagnosed, linked to care, retained, etc. We further underscore the difference in terminology used to refer to “population on ART” (those receiving ART in a given period of time, aka ART users), and “population initiating ART” (those starting ART for the first time, aka first time ART initiators) throughout the text.

Initial Population in Year 2009 </>

Population Size </>

The size of the initial sub-populations using ART in 2009 is estimated from CDC surveillance data through the Medical Monitoring Project (MMP).

First, the estimated number of persons living with HIV infection in 2009 for each sex and risk group combination is taken from table 14a in the 2013 HIV Surveillance Report. We then use table 17a in the 2010 HIV Surveillance Report to calculate the proportion of each risk/sex group by race. We multiply these two numbers to get an estimate of the total number of persons in each sub-population who are living with HIV.

Finally, we multiply the estimated number living with HIV by estimated proportion of that sub-population to be receiving ART treatment. These estimates come from different sources depending on the sub-population.

Table 2: Total ART Users in 2009

Population	# With HIV Per Risk/Sex	Proportion By Race	# By Sub-Population	Proportion On ART	Total On ART In 2009	ART Source
het_black_female	148,349	0.613	90,981	0.514	46,764	CDC MMWR, February 7, 2014, Table 3
het_black_male	65,857	0.632	41,608	0.421	17,516	CDC MMWR, February 7, 2014, Table 3
het_hisp_female	148,349	0.191	28,342	0.498	14,114	CDC MMWR, October 10, 2014, Table 3
het_hisp_male	65,857	0.212	13,940	0.459	6,398	CDC MMWR, October 10, 2014, Table 3
het_white_female	148,349	0.167	24,742	0.551	13,632	Correspondence with Luke Shouse, CDC
het_white_male	65,857	0.131	8,635	0.37	3,194	Correspondence with Luke Shouse, CDC
idu_black_female	53,717	0.528	28,350	0.498	14,118	CDC MMWR, February 7, 2014, Table 3
idu_black_male	134,962	0.429	57,881	0.34	19,679	CDC MMWR, February 7, 2014, Table 3
idu_hisp_female	53,717	0.199	10,711	0.341	3,652	CDC MMWR, October 10, 2014, Table 3
idu_hisp_male	134,962	0.270	36,391	0.31	11,281	CDC MMWR, October 10, 2014, Table 3
idu_white_female	53,717	0.245	13,152	0.55	7,233	Correspondence with Luke Shouse, CDC
idu_white_male	134,962	0.275	37,145	0.455	16,900	Correspondence with Luke Shouse, CDC
msm_black_male	414,232	0.293	12,1240	0.471	57,104	CDC MMWR, September 26, 2014, Table 3
msm_hisp_male	414,232	0.201	83,125	0.492	40,897	CDC MMWR, September 26, 2014, Table 3
msm_white_male	414,232	0.474	196,500	0.496	97,464	CDC MMWR, September 26, 2014, Table 3

Age Distribution </>

The age distribution of each sub-population was modeled using a two-component mixed normal distribution (resulting in the best fit among alternative models), as follows:

\[f(x|\lambda_1, \mu_1, \sigma_1, \mu_2, \sigma_2) = \lambda_1 g(x|\mu_1, \sigma_1) + (1 - \lambda_1)g(x|\mu_2, \sigma_2)\]

where

\[g(x|\mu, \sigma) = \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}\]

is just the normal distribution. Here $x$ is age of those on ART in year 2009, $\lambda_1$ is the mixing proportion, and the $\mu$’s and $\sigma$’s are the means and standard deviations of the bimodal distribution. These parameters (Table 3) were obtained by fitting to the NA-ACCORD population of ART users in 2009. The normalmixEM2comp function of the mixtools package for R was used to fit the distributions. When initializing a simulation run, the ages of the 2009 population were drawn from a distribution with the same parameters after being truncated at ages 18 and 85.

Table 3: Coefficients for Age of Initial Population

group	lambda1	mu1	mu2	sigma1	sigma2
het_black_female	0.11	31.31	44.53	5.26	9.76
het_black_male	0.43	48.02	48.99	6.97	11.89
het_hisp_female	0.20	32.38	45.75	5.31	9.39
het_hisp_male	0.50	39.17	51.70	7.82	10.45
het_white_female	0.77	42.16	52.61	8.59	10.80
het_white_male	0.14	48.06	49.63	3.87	10.72
idu_black_female	0.17	42.62	50.18	8.31	6.49
idu_black_male	0.05	39.35	53.93	7.71	6.31
idu_hisp_female	0.08	29.98	48.81	2.85	7.09
idu_hisp_male	0.11	32.55	50.31	3.80	7.48
idu_white_female	0.07	33.64	45.92	4.28	8.24
idu_white_male	0.02	26.15	47.11	2.44	8.10
msm_black_male	0.12	25.68	45.00	3.34	9.41
msm_hisp_male	0.92	40.44	56.80	8.69	11.01
msm_white_male	0.15	46.26	46.92	3.40	10.54

Figure 1a: HET Black Female

Figure 1b: HET White Female

Figure 1c: HET Hispanic Female

Figure 1d: HET Black Male

Figure 1e: HET White Male

Figure 1f: HET Hispanic Male

Figure 1g: IDU Black Female

Figure 1h: IDU White Female

Figure 1i: IDU Hispanic Female

Figure 1j: IDU Black Male

Figure 1k: IDU White Male

Figure 1l: IDU Hispanic Male

Figure 1m: MSM Black Male

Figure 1n: MSM White Male

Figure 1o: MSM Hispanic Male

Year of ART Initiation </>

To estimate the original year of ART initiation among the simulated population, we applied available data from the NA-ACCORD population on ART in year 2009. To this end, each sub-population was broken into the seven age categories, including <20, [20,30), [30,40), [40,50), [50,60), [60,70), $\geq$70. Within each category, we then estimated the proportion initiating ART in each year between 2000 and 2009 as shown in Table 4. Those initiating ART prior to 2000 were counted in the 2000 category. If there were no data from a given population in a certain age category, the proportions from the white MSM population were used as indicated by dashes in the following tables. We use the 2009 NA-ACCORD population to inform the ART initiation year of our starting population.

Table 4a: HET Female

Race	Age Category	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009
black	<20	0.17	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.50	0.33
black	[20,30)	0.03	0.02	0.02	0.03	0.03	0.10	0.14	0.15	0.22	0.26
black	[30,40)	0.17	0.05	0.05	0.08	0.09	0.09	0.12	0.10	0.13	0.12
black	[40,50)	0.27	0.07	0.05	0.07	0.07	0.08	0.08	0.10	0.10	0.10
black	[50,60)	0.28	0.07	0.05	0.08	0.08	0.08	0.08	0.09	0.11	0.09
black	[60,70)	0.30	0.07	0.04	0.07	0.09	0.07	0.05	0.06	0.15	0.11
black	>=70	0.37	0.09	0.09	0.06	0.06	0.11	0.09	0.03	0.09	0.03
hisp	<20	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.50	0.50
hisp	[20,30)	0.06	0.04	0.06	0.03	0.06	0.15	0.06	0.09	0.25	0.20
hisp	[30,40)	0.18	0.05	0.04	0.09	0.11	0.11	0.11	0.09	0.11	0.11
hisp	[40,50)	0.28	0.05	0.05	0.07	0.10	0.08	0.10	0.06	0.10	0.10
hisp	[50,60)	0.32	0.08	0.05	0.06	0.08	0.10	0.07	0.07	0.08	0.08
hisp	[60,70)	0.35	0.12	0.05	0.07	0.07	0.02	0.02	0.07	0.11	0.12
hisp	>=70	1.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
white	<20	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.50	0.50
white	[20,30)	0.04	0.04	0.02	0.00	0.10	0.17	0.10	0.10	0.17	0.25
white	[30,40)	0.26	0.04	0.07	0.07	0.10	0.07	0.07	0.09	0.08	0.14
white	[40,50)	0.42	0.05	0.06	0.04	0.09	0.05	0.07	0.07	0.08	0.08
white	[50,60)	0.47	0.03	0.05	0.03	0.06	0.07	0.03	0.07	0.09	0.11
white	[60,70)	0.47	0.05	0.07	0.08	0.08	0.02	0.03	0.07	0.08	0.05
white	>=70	0.25	0.17	0.17	0.08	0.08	0.00	0.08	0.00	0.08	0.08

Table 4b: HET Male

Race	Age Category	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009
black	<20	0.50	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.50	0.00
black	[20,30)	0.02	0.03	0.02	0.02	0.03	0.13	0.11	0.17	0.18	0.26
black	[30,40)	0.12	0.05	0.03	0.05	0.10	0.09	0.12	0.11	0.17	0.17
black	[40,50)	0.26	0.07	0.05	0.07	0.07	0.09	0.08	0.08	0.10	0.13
black	[50,60)	0.36	0.06	0.05	0.07	0.07	0.07	0.08	0.08	0.08	0.08
black	[60,70)	0.40	0.09	0.07	0.05	0.09	0.07	0.06	0.07	0.05	0.06
black	>=70	0.55	0.08	0.06	0.07	0.02	0.01	0.08	0.05	0.06	0.03
hisp	<20	–	–	–	–	–	–	–	–	–	–
hisp	[20,30)	0.01	0.01	0.03	0.01	0.04	0.06	0.11	0.14	0.26	0.32
hisp	[30,40)	0.11	0.05	0.06	0.06	0.10	0.10	0.10	0.10	0.19	0.13
hisp	[40,50)	0.26	0.05	0.04	0.09	0.08	0.11	0.08	0.08	0.10	0.09
hisp	[50,60)	0.38	0.05	0.04	0.06	0.06	0.07	0.05	0.09	0.12	0.07
hisp	[60,70)	0.46	0.08	0.05	0.09	0.04	0.08	0.10	0.04	0.04	0.02
hisp	>=70	0.52	0.12	0.04	0.04	0.08	0.00	0.04	0.00	0.12	0.04
white	<20	–	–	–	–	–	–	–	–	–	–
white	[20,30)	0.00	0.00	0.00	0.00	0.15	0.23	0.00	0.00	0.31	0.31
white	[30,40)	0.18	0.01	0.04	0.03	0.08	0.06	0.09	0.16	0.22	0.13
white	[40,50)	0.37	0.04	0.06	0.06	0.10	0.05	0.08	0.07	0.09	0.09
white	[50,60)	0.40	0.06	0.08	0.06	0.09	0.06	0.05	0.06	0.08	0.06
white	[60,70)	0.49	0.04	0.04	0.11	0.05	0.07	0.05	0.04	0.08	0.02
white	>=70	0.50	0.12	0.08	0.00	0.08	0.00	0.04	0.08	0.04	0.04

Table 4c: IDU Female

Race	Age Category	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009
black	<20	–	–	–	–	–	–	–	–	–	–
black	[20,30)	0.00	0.00	0.00	0.00	0.00	0.17	0.17	0.50	0.00	0.17
black	[30,40)	0.14	0.07	0.10	0.12	0.00	0.10	0.10	0.12	0.14	0.12
black	[40,50)	0.33	0.07	0.05	0.07	0.06	0.09	0.05	0.09	0.12	0.08
black	[50,60)	0.42	0.09	0.03	0.05	0.05	0.06	0.09	0.07	0.06	0.08
black	[60,70)	0.31	0.00	0.06	0.12	0.06	0.12	0.03	0.06	0.09	0.12
black	>=70	–	–	–	–	–	–	–	–	–	–
hisp	<20	–	–	–	–	–	–	–	–	–	–
hisp	[20,30)	0.00	0.00	0.00	0.00	0.20	0.00	0.00	0.60	0.00	0.20
hisp	[30,40)	0.20	0.00	0.20	0.00	0.07	0.00	0.13	0.00	0.20	0.20
hisp	[40,50)	0.24	0.06	0.02	0.10	0.06	0.12	0.08	0.18	0.10	0.06
hisp	[50,60)	0.39	0.04	0.04	0.13	0.04	0.07	0.04	0.07	0.09	0.09
hisp	[60,70)	0.33	0.00	0.17	0.00	0.00	0.00	0.00	0.00	0.17	0.33
hisp	>=70	0.00	0.00	0.00	0.00	1.00	0.00	0.00	0.00	0.00	0.00
white	<20	–	–	–	–	–	–	–	–	–	–
white	[20,30)	0.20	0.00	0.00	0.00	0.00	0.10	0.00	0.20	0.00	0.50
white	[30,40)	0.23	0.03	0.10	0.06	0.11	0.10	0.01	0.08	0.21	0.07
white	[40,50)	0.34	0.05	0.06	0.09	0.12	0.06	0.09	0.04	0.07	0.08
white	[50,60)	0.40	0.07	0.07	0.08	0.07	0.05	0.04	0.04	0.11	0.08
white	[60,70)	0.36	0.00	0.00	0.18	0.00	0.00	0.18	0.00	0.18	0.09
white	>=70	0.50	0.00	0.00	0.00	0.00	0.00	0.00	0.50	0.00	0.00

Table 4d: IDU Male

Race	Age Category	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009
black	<20	–	–	–	–	–	–	–	–	–	–
black	[20,30)	0.11	0.00	0.11	0.00	0.00	0.00	0.11	0.22	0.22	0.22
black	[30,40)	0.19	0.00	0.06	0.04	0.15	0.06	0.09	0.13	0.13	0.15
black	[40,50)	0.36	0.06	0.05	0.09	0.05	0.08	0.08	0.08	0.07	0.07
black	[50,60)	0.51	0.05	0.06	0.06	0.06	0.04	0.06	0.06	0.05	0.05
black	[60,70)	0.61	0.06	0.02	0.04	0.05	0.03	0.05	0.04	0.03	0.07
black	>=70	0.62	0.00	0.00	0.06	0.06	0.06	0.12	0.06	0.00	0.00
hisp	<20	–	–	–	–	–	–	–	–	–	–
hisp	[20,30)	0.00	0.00	0.00	0.00	0.07	0.00	0.14	0.29	0.29	0.21
hisp	[30,40)	0.14	0.03	0.06	0.03	0.07	0.19	0.08	0.10	0.15	0.14
hisp	[40,50)	0.34	0.05	0.03	0.06	0.06	0.08	0.09	0.13	0.10	0.07
hisp	[50,60)	0.48	0.06	0.05	0.04	0.06	0.04	0.05	0.10	0.06	0.06
hisp	[60,70)	0.52	0.04	0.06	0.06	0.08	0.08	0.00	0.06	0.06	0.02
hisp	>=70	0.67	0.00	0.00	0.00	0.00	0.00	0.00	0.33	0.00	0.00
white	<20	–	–	–	–	–	–	–	–	–	–
white	[20,30)	0.00	0.02	0.02	0.00	0.00	0.13	0.13	0.15	0.26	0.30
white	[30,40)	0.15	0.06	0.04	0.04	0.07	0.08	0.10	0.19	0.13	0.14
white	[40,50)	0.42	0.06	0.04	0.06	0.07	0.08	0.07	0.07	0.07	0.08
white	[50,60)	0.51	0.07	0.05	0.06	0.05	0.04	0.05	0.05	0.07	0.05
white	[60,70)	0.68	0.00	0.05	0.07	0.06	0.06	0.01	0.02	0.01	0.05
white	>=70	0.50	0.25	0.25	0.00	0.00	0.00	0.00	0.00	0.00	0.00

Table 4e: MSM

Race	Age Category	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009
black	<20	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	1.00
black	[20,30)	0.01	0.01	0.02	0.02	0.05	0.07	0.08	0.14	0.26	0.34
black	[30,40)	0.17	0.05	0.06	0.06	0.08	0.07	0.10	0.12	0.14	0.16
black	[40,50)	0.38	0.06	0.05	0.07	0.06	0.06	0.07	0.07	0.09	0.08
black	[50,60)	0.47	0.07	0.05	0.07	0.06	0.05	0.06	0.06	0.04	0.07
black	[60,70)	0.59	0.06	0.07	0.05	0.05	0.04	0.03	0.03	0.05	0.04
black	>=70	0.56	0.03	0.12	0.00	0.03	0.12	0.00	0.03	0.06	0.03
hisp	<20	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.25	0.75
hisp	[20,30)	0.00	0.00	0.01	0.02	0.04	0.07	0.10	0.16	0.21	0.39
hisp	[30,40)	0.13	0.03	0.04	0.06	0.09	0.09	0.11	0.12	0.14	0.19
hisp	[40,50)	0.28	0.07	0.06	0.07	0.06	0.09	0.08	0.09	0.10	0.11
hisp	[50,60)	0.41	0.08	0.05	0.04	0.07	0.05	0.07	0.09	0.09	0.05
hisp	[60,70)	0.56	0.06	0.05	0.07	0.04	0.02	0.04	0.02	0.07	0.06
hisp	>=70	0.61	0.00	0.04	0.09	0.00	0.09	0.09	0.00	0.04	0.04
white	<20	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	1.00
white	[20,30)	0.01	0.02	0.01	0.02	0.04	0.06	0.09	0.16	0.24	0.35
white	[30,40)	0.14	0.04	0.04	0.05	0.08	0.08	0.10	0.13	0.15	0.18
white	[40,50)	0.39	0.05	0.04	0.06	0.06	0.06	0.08	0.07	0.08	0.09
white	[50,60)	0.51	0.05	0.04	0.05	0.06	0.05	0.06	0.06	0.07	0.05
white	[60,70)	0.60	0.06	0.05	0.05	0.04	0.03	0.05	0.05	0.03	0.04
white	>=70	0.64	0.05	0.03	0.05	0.09	0.05	0.03	0.03	0.02	0.01

CD4 Count at ART Initiation </>

To estimate the CD4 count at first ART initiation among simulated population in year 2009, we applied available data from the NA-ACCORD population on ART in year 2009. To this end, each sub-population was split into original ART initiation years between [2000, 2009] as estimated in the previous step. A normal distribution was fit to describe the \(\sqrt{\mathrm{CD4}}\) count at ART initiation in each year. Within each sub-population, a linear regression model was applied to describe changes in the normal distribution parameters (\(\mu\) mean and \(\sigma\) standard deviation) over time, such that

\[\mu(\mathrm{year}) = \mu_0 + \beta_\mu \cdot \mathrm{year}\]

and

\[\sigma(\mathrm{year}) = \sigma_0 + \beta_\sigma \cdot \mathrm{year}\]

The linear regression was fit using the glm function of the stats package in base R. Table 5 presents the value of the fitted coefficients.

Table 5: Initial Population CD4 Count at ART Initiation Coefficients

group	meanint	meanslp	stdint	stdslp
het_black_female	-388.48	0.20	108.83	-0.05
idu_black_male	-20.03	0.02	117.09	-0.06
idu_hisp_male	110.09	-0.05	-54.13	0.03
msm_black_male	-450.86	0.23	183.12	-0.09
idu_white_male	-239.51	0.13	152.97	-0.07
het_hisp_female	-127.64	0.07	-37.09	0.02
het_black_male	14.98	0.00	151.32	-0.07
het_hisp_male	50.88	-0.02	132.09	-0.06
msm_hisp_male	-506.13	0.26	243.24	-0.12
idu_black_female	-261.53	0.14	194.90	-0.09
msm_white_male	-339.98	0.18	375.69	-0.18
het_white_male	-584.30	0.30	155.80	-0.07
idu_hisp_female	-222.97	0.12	602.42	-0.30
het_white_female	-320.81	0.17	302.93	-0.15
idu_white_female	-294.14	0.15	-583.75	0.29

When drawing CD4 values, we truncate the normal distribution at $0$ and $\sqrt{2000}$. The trajectory of the means and standard deviations is shown in the following plots:

Figure 2a: HET Female

Figure 2b: HET Male

Figure 2c: IDU Female

Figure 2d: IDU Male

Figure 2e: MSM

Initial Population not Using ART in Year 2009 </>

In addition to an initial population of people on ART in 2009 the simulation is seeded with an initial population of those who had previously been on ART but are currently disengaged from care (and experience a likelihood of ART re-engagement in year 2010 and afterward). The size of this population is generated by estimating the number of those linking to care but not initiating ART from 2006 to 2009 as outlined in the following section. The age and CD4 count distributions for this population is assumed to be identical to the initial ART using population.

Population Initiating ART From 2010 - 2030 </>

Population Size </>

New HIV diagnosis: In order to predict the number of new people linking to HIV care and starting ART in a given year, we begin with data on the number of new HIV diagnoses per year as estimated by the CDC’s Medical Monitoring Project (MMP) as shown in Table 6. Dates before 2016 came from Table 1 of the 2015 HIV Surveillance Report, while data 2016 and after came from Table 1 of the 2018 HIV Surveillance Report.

Table 6: Number of New HIV Diagnoses by Year

Various candidate models were proposed in order to predict the number of new HIV diagnoses from 2006 to 2030. Predicted HIV diagnoses prior to 2010 are used later in the initial 2009 population creation. After removing models with inadequate fit (based on AIC values), the data were fit using a Poisson model, a gamma model and a natural cubic spline model with a single knot. Of these models, those resulting in unrealistic projections (>50% increase in new diagnosis from 2020 – 2030) were also removed. The Poisson and gamma fits were accomplished using the glm function of the stats package in base R, while the spline fit was generated using the lm and ns functions of the base R packages stats and splines, respectively. To incorporate additional uncertainties in annual estimates, the 95% prediction intervals around each fit were calculated. These prediction intervals were combined to generate an annual range for the number of new diagnosis in each year for a given subgroup (black, white and Hispanic). The annual ranges are estimated from the largest upper prediction interval and the lowest lower prediction interval of existing models as shown in panel 2 of Figure 3. For each simulation run, a random number between 0 and 1 is drawn that defines the number of new diagnoses in that simulation. Figure 3 shows the full ranges used to generate the number of new diagnoses.

Figure 3a: HET Female

Figure 3b: HET Male

Figure 3c: IDU Female

Figure 3d: IDU Male

Figure 3e: MSM

Linkage to HIV care and ART initiation: We estimated percentage of people in each sub-population linking to HIV care in the first 4 months after HIV diagnosis for each year between 2010 – 2015 from the CDC. To project future trends from 2016 to 2030, we applied a linear regression and capped at 95% linkage as shown in Figure 4. The linear regression was accomplished using the ols function of the statsmodels package for Python. Among remaining cases, we further assumed that 40% link to care over the next three years after initial diagnosis. To estimate the population starting ART, we assumed that 70% of those linking to care begin ART immediately in years prior to 2011. This percentage rises to 85% in 2011 and up to 97% thereafter.

Figure 4a: HET Female

Figure 4b: HET Male

Figure 4c: IDU Female

Figure 4d: IDU Male

Figure 4e: MSM

Age Distribution </>

The age distributions of the populations initiating ART in each year are modeled as a two component mixed normal distribution:

\[f(x|\lambda_1, \mu_1, \sigma_1, \mu_2, \sigma_2) = \lambda_1 g(x|\mu_1, \sigma_1) + (1 - \lambda_1)g(x|\mu_2, \sigma_2)\]

where

\[g(x|\mu, \sigma) = \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}\]

is the usual normal distribution. Here $x$ represents age at ART initiation, $\lambda_1$ is the mixing proportion, and the $\mu$’s and $\sigma$’s are the means and standard deviations of the bimodal distribution. A fit was found for each ART initiation year, from 2010 to 2022, and each sub-population using data from NA-ACCORD using the normalmixEM function of the mixtools package for R. Due to lack of available data, some years had to be collapsed together according to the following rules:

Age Distribution Data Collapse Rules

Heterosexual Hispanic Female:

• 2015-2017

• 2018-2022

Heterosexual Hispanic Male :

• 2016-2017

• 2018-2022

Heterosexual White Female:

• 2015-2016

• 2017-2018

• 2019-2022

Heterosexual White Male:

• 2016-2017

• 2018-2019

• 2020-2022

IDU Black Female:

• 2010-2013

• 2014-2022

IDU Black Male:

• 2015-2016

• 2017-2018

• 2019-2022

IDU Hisp Female:

• 2010-2022

IDU Hisp Male:

• 2010-2011

• 2012-2013

• 2014-2015

• 2016-2022

IDU White Female:

• 2010-2011

• 2012-2014

• 2015-2022

IDU White Male:

• 2018-2019

• 2020-2022

To estimate changes in age distribution of ART initiators over time, we modeled changes in the five parameters of the distribution as a linear function of calendar year (Figure 5). For this purpose, each parameter was fit to a linear regression using the glm function of the stats package in base R (blue dots in Figure 5). Given the sharp rate of change through the linear fit and lack of available data to support predictions from 2018 onward, the predicted values in year 2018 were used as an upper/lower bound to develop a prediction range for future years (shaded areas in Figure 5). Values for \(\lambda\_1\) were truncated between 0 and 1 and all variables are truncated at 0. These models were applied to generate the value of 5 parameters describing the bimodal normal distribution of age at ART initiation in each year. The distribution was further truncated at ages 18 and 85.

Figure 5a: HET Black Female

Figure 5b: HET Black Male

Figure 5c: HET Hispanic Female

Figure 5d: HET Hispanic Male

Figure 5e: HET White Female

Figure 5f: HET White Male

Figure 5g: IDU Black Female

Figure 5h: IDU Black Male

Figure 5i: IDU Hispanic Female

Figure 5j: IDU Hispanic Male

Figure 5k: IDU White Female

Figure 5l: IDU White Male

Figure 5m: MSM Black Male

Figure 5n: MSM Hispanic Male

Figure 5o: MSM White Male

CD4 Count at ART Initiation </>

Using data from NA-ACCORD, we categorized each sub-populations 8 categories based on ART initiation year (2010 – 2022). A normal distribution was fit to square root of CD4 count values for each sub-group and in each year. Within each sub-population, a linear regression model was applied to describe changes in the normal distribution parameters ($\mu$ mean and $\sigma$ standard deviation) over time, such that:

\[\mu(\mathrm{year}) = \mu_0 + \beta_\mu \cdot \mathrm{year}\]

and

\[\sigma(\mathrm{year}) = \sigma_0 + \beta_\sigma \cdot \mathrm{year}\]

Some sub-populations had to be collapsed by year in order to generate enough data for the regression according to the following rules:

CD4 Count Data Collapse Rules

Collapse subgroups:

• All HET men

• All IDU women

• All HET women

• All IDU women

• All IDU women:

  • 2011-2012

  • 2014-2016

  • 2017-2022

• All IDU men

  • 2020-2022

The fits were estimated using the glm function of the stats package in base R. Table 7 presents the value of the fitted coefficients and the trend is shown in Figure 6.

Table 7: ART Initiator Population CD4 Count Coefficients

group	meanint	meanslp	stdint	stdslp
het_hisp_male	-481.12	0.25	-136.09	0.07
het_black_male	-481.12	0.25	-136.09	0.07
het_white_male	-481.12	0.25	-136.09	0.07
idu_black_male	-876.43	0.44	-97.37	0.05
idu_hisp_male	-876.43	0.44	-97.37	0.05
idu_white_male	-876.43	0.44	-97.37	0.05
msm_black_male	-424.13	0.22	-187.66	0.10
msm_hisp_male	-459.66	0.24	-38.47	0.02
msm_white_male	-427.41	0.22	-187.30	0.10
het_black_female	-544.65	0.28	-198.66	0.10
het_white_female	-544.65	0.28	-198.66	0.10
het_hisp_female	-544.65	0.28	-198.66	0.10
idu_black_female	-1121.86	0.57	-59.33	0.03
idu_hisp_female	-1121.86	0.57	-59.33	0.03
idu_white_female	-1121.86	0.57	-59.33	0.03

When drawing CD4 values, we truncate the normal distribution at $0$ and $\sqrt{2000}$. Additionally, the predicted values in year 2018 were used as an upper/lower bound to develop a prediction range for future year.

Figure 6a: HET Female

Figure 6b: HET Male

Figure 6c: IDU Female

Figure 6d: IDU Male

Figure 6e: Black MSM

Figure 6e: Hispanic MSM

Figure 6e: White MSM

Annual Population Dynamics </>

Disengagement From HIV Care </>

The NA-ACCORD dataset was restricted to the years 2009 – 2022 and each patient was represented by a data point for each year they were alive and under observation in NA-ACCORD. A patient was defined to be disengaged if ≥2 years had elapsed without a CD4 or viral load lab result and the year of disengagement was set to the first year without a lab. Using this data, a logistic regression was used to model the probability of disengagement as a function of calendar year ($\mathrm{year}$), square root of CD4 count at ART initiation (\(\mathrm{sqrt\_init\_cd4}\)), ART initiation period (\(\mathrm{art\_period}\)), and age ($\mathrm{age}$). ART initiation period was coded as a binary variable such that \(\mathrm{art\_period} = 1\) if ART was initiated after 2010 and 0 otherwise. Age is modeled as a restricted quadratic spline with 4 knots. The knots were placed at the 0.05, 0.35, 0.65, and 0.95 quantiles of the $\mathrm{age}$ variable (Table 8). The knot variables are defined such that

\[\mathrm{age}\_1 = \begin{cases} \frac{(\mathrm{age} - k_1)^2 - (\mathrm{age} - k_4)^2}{k_4 - k_1}, & \mathrm{age} \ge k_4\\ \frac{(\mathrm{age} - k_1)^2} {k_4 - k_1}, & k_4 \gt \mathrm{age} \ge k_1\\ 0, & \mathrm{else} \end{cases}\] \[\mathrm{age}\_2 = \begin{cases} \frac{(\mathrm{age} - k_2)^2 - (\mathrm{age} - k_4)^2}{k_4 - k_1}, & \mathrm{age} \ge k_4\\ \frac{(\mathrm{age} - k_2)^2} {k_4 - k_1}, & k_4 \gt \mathrm{age} \ge k_2\\ 0, & \mathrm{else} \end{cases}\] \[\mathrm{age}\_3 = \begin{cases} \frac{(\mathrm{age} - k_3)^2 - (\mathrm{age} - k_4)^2}{k_4 - k_1}, & \mathrm{age} \ge k_4\\ \frac{(\mathrm{age} - k_3)^2} {k_4 - k_1}, & k_4 \gt \mathrm{age} \ge k_3\\ 0, & \mathrm{else} \end{cases}\]

Table 8: Disengagement Spline Knot Locations

subgroup	knot_1	knot_2	knot_3	knot_4
het_black_female	28	42	51	65
het_black_male	31	47	56	69
het_hisp_female	29	41	50	65
het_hisp_male	30	44	53	69
het_white_female	28	44	53	67
het_white_male	32	48	57	71
idu_black_female	38	50	57	67
idu_black_male	40	55	61	70
idu_hisp_female	33	46	53	64
idu_hisp_male	31	47	55	67
idu_white_female	31	44	52	63
idu_white_male	30	46	54	66
msm_black_male	24	35	49	64
msm_hisp_male	26	38	47	62
msm_white_male	29	46	54	68

The resulting regression equation is

\[\begin{aligned} \mathrm{logit}(p) = \beta\_0 &+ \beta\_\mathrm{year} \cdot\mathrm{year} + \beta\_\mathrm{sqrt\\init\\cd4} \cdot\mathrm{sqrt\\init\\cd4} + \beta\_\mathrm{art\\period} \cdot \mathrm{art\\period} \\ &+ \beta\_\mathrm{age} \cdot\mathrm{age} + \beta\_\mathrm{age\\1} \cdot\mathrm{age\\1} + \beta\_\mathrm{age\\2} \cdot\mathrm{age\\2} + \beta\_\mathrm{age\\3} \cdot\mathrm{age\\3} \end{aligned}\]

where

\[\mathrm{logit}(p) = \log \frac{p}{1 - p}\]

is the logit function and $p$ is the probability of disengagement from HIV care.

The coefficients were estimated using a generalized estimating equation (GEE) with a logit link and an exchangeable correlation structure using the geeglm function of the geepack software package for R. The estimated regression coefficients are shown in Table 9 and the covariance matrices is shown in Table 10.

Table 9: Disengagement Coefficient Estimates

group	intercept	age	_age	__age	___age	year	sqrtcd4n	haart_period
het_black_male	99.84	-0.01	-0.01	-0.08	0.15	-0.05	0.00	0.20
het_black_female	96.30	-0.01	-0.03	0.04	0.00	-0.05	0.01	0.10
het_hisp_male	35.60	-0.01	-0.03	0.04	0.01	-0.02	0.02	-0.02
het_hisp_female	117.63	-0.04	0.14	-0.29	0.19	-0.06	-0.01	0.29
het_white_male	56.28	-0.03	0.03	-0.16	0.14	-0.03	0.01	0.10
het_white_female	74.75	-0.02	-0.02	0.04	-0.01	-0.04	0.00	0.02
idu_black_male	87.38	-0.03	0.03	-0.27	0.40	-0.04	0.00	0.53
idu_black_female	67.06	-0.01	-0.03	0.19	-0.27	-0.03	0.00	0.45
idu_hisp_male	26.06	-0.02	-0.01	0.03	-0.13	-0.01	-0.01	0.10
idu_hisp_female	-99.03	-0.02	0.03	-0.29	0.37	0.05	-0.01	-0.48
idu_white_male	20.63	0.01	-0.05	0.05	-0.16	-0.01	0.01	0.14
idu_white_female	21.77	0.01	-0.11	0.32	-0.22	-0.01	0.01	-0.32
msm_black_male	36.98	0.07	-0.22	0.25	-0.03	-0.02	0.01	0.07
msm_hisp_male	15.99	0.07	-0.18	0.26	-0.10	-0.01	0.01	-0.03
msm_white_male	31.14	0.00	-0.06	0.12	-0.07	-0.02	0.01	0.00

Table 10 Variance and Covariance

group	varname	intercept	age	_age	__age	___age	year	sqrtcd4n	haart_period
het_black_female	intercept	185.271075	0.007836522	-0.00112997	0.019492126	-0.026039776	-0.092245869	0.002741405	0.284554514
het_black_female	age	0.007836522	1.25E-04	-2.73E-04	5.23E-04	-3.26E-04	-5.78E-06	3.79E-06	3.04E-05
het_black_female	_age	-0.00112997	-2.73E-04	7.05E-04	-0.001582584	0.001197041	4.43E-06	-3.21E-06	1.99E-05
het_black_female	__age	0.019492126	5.23E-04	-0.001582584	0.004277036	-0.004021257	-1.68E-05	-1.04E-06	-7.38E-05
het_black_female	___age	-0.026039776	-3.26E-04	0.001197041	-0.004021257	0.004779601	1.71E-05	4.76E-06	7.99E-05
het_black_female	year	-0.092245869	-5.78E-06	4.43E-06	-1.68E-05	1.71E-05	4.60E-05	-1.53E-06	-1.42E-04
het_black_female	sqrtcd4n	0.002741405	3.79E-06	-3.21E-06	-1.04E-06	4.76E-06	-1.53E-06	1.31E-05	-3.72E-05
het_black_female	haart_period	0.284554514	3.04E-05	1.99E-05	-7.38E-05	7.99E-05	-1.42E-04	-3.72E-05	0.003311122
het_black_male	intercept	219.8332737	-0.003800992	0.013663238	0.042994107	-0.101107108	-0.109208728	-0.001681469	0.356953658
het_black_male	age	-0.003800992	1.12E-04	-2.22E-04	4.68E-04	-3.37E-04	2.45E-08	1.79E-06	7.80E-05
het_black_male	_age	0.013663238	-2.22E-04	5.17E-04	-0.001297461	0.001117953	-3.29E-06	-2.81E-06	-6.36E-05
het_black_male	__age	0.042994107	4.68E-04	-0.001297461	0.004185503	-0.004662877	-2.84E-05	1.23E-07	2.46E-04
het_black_male	___age	-0.101107108	-3.37E-04	0.001117953	-0.004662877	0.006636827	5.51E-05	3.07E-06	-3.14E-04
het_black_male	year	-0.109208728	2.45E-08	-3.29E-06	-2.84E-05	5.51E-05	5.43E-05	7.17E-07	-1.79E-04
het_black_male	sqrtcd4n	-0.001681469	1.79E-06	-2.81E-06	1.23E-07	3.07E-06	7.17E-07	1.33E-05	-3.70E-05
het_black_male	haart_period	0.356953658	7.80E-05	-6.36E-05	2.46E-04	-3.14E-04	-1.79E-04	-3.70E-05	0.003917841
het_hisp_female	intercept	845.8712519	0.022060761	0.029632616	-0.145485142	0.261762632	-0.42085395	0.001447187	0.853297485
het_hisp_female	age	0.022060761	7.46E-04	-0.001756704	0.002917353	-0.001424294	-2.24E-05	1.27E-05	1.27E-04
het_hisp_female	_age	0.029632616	-0.001756704	0.004799058	-0.009097784	0.005529795	1.09E-05	-7.96E-06	1.16E-04
het_hisp_female	__age	-0.145485142	0.002917353	-0.009097784	0.019808449	-0.014881799	3.12E-05	-7.77E-06	-8.65E-04
het_hisp_female	___age	0.261762632	-0.001424294	0.005529795	-0.014881799	0.014748728	-1.11E-04	1.70E-05	0.001118864
het_hisp_female	year	-0.42085395	-2.24E-05	1.09E-05	3.12E-05	-1.11E-04	2.10E-04	-1.33E-06	-4.28E-04
het_hisp_female	sqrtcd4n	0.001447187	1.27E-05	-7.96E-06	-7.77E-06	1.70E-05	-1.33E-06	4.83E-05	-5.55E-05
het_hisp_female	haart_period	0.853297485	1.27E-04	1.16E-04	-8.65E-04	0.001118864	-4.28E-04	-5.55E-05	0.011886905
het_hisp_male	intercept	740.3173022	0.02787669	0.001286347	0.132014325	-0.262730952	-0.368474736	-0.007852919	1.049815354
het_hisp_male	age	0.02787669	4.03E-04	-9.26E-04	0.001743292	-0.001019167	-2.03E-05	7.22E-06	1.63E-04
het_hisp_male	_age	0.001286347	-9.26E-04	0.002492909	-0.005458677	0.003861525	1.35E-05	-2.05E-05	-2.97E-05
het_hisp_male	__age	0.132014325	0.001743292	-0.005458677	0.014447999	-0.01283614	-9.13E-05	3.62E-05	-2.28E-04
het_hisp_male	___age	-0.262730952	-0.001019167	0.003861525	-0.01283614	0.014420576	1.45E-04	-2.98E-05	3.87E-04
het_hisp_male	year	-0.368474736	-2.03E-05	1.35E-05	-9.13E-05	1.45E-04	1.84E-04	3.52E-06	-5.26E-04
het_hisp_male	sqrtcd4n	-0.007852919	7.22E-06	-2.05E-05	3.62E-05	-2.98E-05	3.52E-06	4.34E-05	-1.09E-04
het_hisp_male	haart_period	1.049815354	1.63E-04	-2.97E-05	-2.28E-04	3.87E-04	-0.000525765	-0.000109101	0.011389478
het_white_female	intercept	654.3233874	0.007762047	0.049619856	-0.058638006	-3.33E-04	-0.325455559	0.001299009	1.155309545
het_white_female	age	0.007762047	4.00E-04	-8.04E-04	0.001663796	-0.001135938	-9.99E-06	1.25E-05	2.74E-04
het_white_female	_age	0.049619856	-8.04E-04	0.001883184	-0.004589327	0.003762243	-1.30E-05	-8.77E-06	-1.48E-04
het_white_female	__age	-0.058638006	0.001663796	-0.004589327	0.014129341	-0.014897406	6.13E-06	-4.09E-06	-1.41E-04
het_white_female	___age	-3.33E-04	-0.001135938	0.003762243	-0.014897406	0.020073382	1.51E-05	1.43E-05	5.94E-04
het_white_female	year	-0.325455559	-9.99E-06	-1.30E-05	6.13E-06	1.51E-05	1.62E-04	-1.26E-06	-5.80E-04
het_white_female	sqrtcd4n	0.001299009	1.25E-05	-8.77E-06	-4.09E-06	1.43E-05	-1.26E-06	4.62E-05	-1.27E-04
het_white_female	haart_period	1.155309544	2.74E-04	-1.48E-04	-1.41E-04	5.94E-04	-5.80E-04	-1.27E-04	0.012967097
het_white_male	intercept	713.6727774	0.013555743	0.007645773	0.146567513	-0.328952296	-0.354955502	0.003842253	1.128869518
het_white_male	age	0.013555743	3.33E-04	-7.00E-04	0.001527218	-0.001130891	-1.24E-05	1.31E-05	3.89E-04
het_white_male	_age	0.007645773	-7.00E-04	0.001780393	-0.004664282	0.004123648	7.33E-06	-1.30E-05	-2.41E-04
het_white_male	__age	0.146567513	0.001527218	-0.004664282	0.015480648	-0.017296718	-9.58E-05	2.27E-05	-2.63E-04
het_white_male	___age	-0.328952296	-0.001130891	0.004123648	-0.017296718	0.024403704	1.80E-04	-2.84E-05	6.61E-04
het_white_male	year	-0.354955502	-1.24E-05	7.33E-06	-9.58E-05	1.80E-04	1.77E-04	-2.55E-06	-5.70E-04
het_white_male	sqrtcd4n	0.003842253	1.31E-05	-1.30E-05	2.27E-05	-2.84E-05	-2.55E-06	5.09E-05	-9.00E-05
het_white_male	haart_period	1.128869518	3.89E-04	-2.41E-04	-2.63E-04	6.61E-04	-5.70E-04	-9.00E-05	0.013566181
idu_black_female	intercept	2096.233051	-0.098940686	0.5938993	-1.551873166	1.986007683	-1.040674113	0.030376871	2.480864945
idu_black_female	age	-0.098940686	0.001147934	-0.002467392	0.005186504	-0.003692398	2.69E-05	2.03E-05	0.001090253
idu_black_female	_age	0.5938993	-0.002467392	0.006638436	-0.016980648	0.014955653	-2.50E-04	-2.83E-05	-9.12E-04
idu_black_female	__age	-1.551873166	0.005186504	-0.016980648	0.053988459	-0.060338806	6.79E-04	3.56E-05	-2.52E-04
idu_black_female	___age	1.986007683	-0.003692398	0.014955653	-0.060338806	0.088340606	-9.24E-04	6.37E-05	0.001691034
idu_black_female	year	-1.040674113	2.69E-05	-2.50E-04	6.79E-04	-9.24E-04	5.17E-04	-1.65E-05	-0.001256089
idu_black_female	sqrtcd4n	0.030376871	2.03E-05	-2.83E-05	3.56E-05	6.37E-05	-1.65E-05	1.28E-04	-5.78E-04
idu_black_female	haart_period	2.480864945	0.001090253	-9.12E-04	-2.52E-04	0.001691034	-0.001256089	-5.78E-04	0.042875289
idu_black_male	intercept	897.2968632	-0.064000065	0.143588783	0.270373501	-0.531521829	-0.444789038	-5.59E-05	1.439990739
idu_black_male	age	-0.064000065	1.71E-04	-3.43E-04	0.001033269	-9.96E-04	2.83E-05	8.05E-06	3.13E-04
idu_black_male	_age	0.143588783	-3.43E-04	9.43E-04	-0.003807912	0.004366243	-6.50E-05	-2.31E-05	-7.49E-05
idu_black_male	__age	0.270373501	0.001033269	-0.003807912	0.02382312	-0.035678079	-1.52E-04	7.47E-05	6.12E-04
idu_black_male	___age	-0.531521829	-9.96E-04	0.004366243	-0.035678079	0.06529744	2.81E-04	-4.42E-05	-0.001102303
idu_black_male	year	-0.444789038	2.83E-05	-6.50E-05	-1.52E-04	2.81E-04	2.21E-04	-4.16E-07	-7.24E-04
idu_black_male	sqrtcd4n	-5.59E-05	8.05E-06	-2.31E-05	7.47E-05	-4.42E-05	-4.16E-07	4.32E-05	-2.02E-04
idu_black_male	haart_period	1.439990739	3.13E-04	-7.49E-05	6.12E-04	-0.001102303	-7.24E-04	-2.02E-04	0.016495406
idu_hisp_female	intercept	10303.62837	2.93148134	-3.634019384	3.924816885	1.824005448	-5.179937022	0.237727822	18.66993272
idu_hisp_female	age	2.93148134	0.006181422	-0.011318588	0.021592835	-0.011866228	-0.001566012	1.39E-05	0.006559636
idu_hisp_female	_age	-3.634019385	-0.011318588	0.023657791	-0.052703708	0.035993078	0.001999176	1.98E-05	-0.00856183
idu_hisp_female	__age	3.924816885	0.021592835	-0.052703708	0.148621693	-0.133089097	-0.002309008	5.12E-05	0.010279091
idu_hisp_female	___age	1.824005447	-0.011866228	0.035993078	-0.133089097	0.153228848	-7.18E-04	-1.01E-04	0.003898479
idu_hisp_female	year	-5.179937022	-0.001566012	0.001999176	-0.002309008	-7.18E-04	0.002605734	-1.21E-04	-0.009415165
idu_hisp_female	sqrtcd4n	0.237727822	1.39E-05	1.98E-05	5.12E-05	-1.01E-04	-1.21E-04	3.11E-04	-1.53E-04
idu_hisp_female	haart_period	18.66993272	0.006559636	-0.00856183	0.010279091	0.003898479	-0.009415165	-1.53E-04	0.157836669
idu_hisp_male	intercept	1050.706389	0.003443364	-0.030011124	0.422739961	-0.447761722	-0.522622756	0.035896928	1.713012712
idu_hisp_male	age	0.003443364	5.68E-04	-0.001056991	0.002380021	-0.001854311	-1.13E-05	2.05E-05	5.80E-04
idu_hisp_male	_age	-0.030011124	-0.001056991	0.002297511	-0.006236331	0.005830005	3.20E-05	-3.90E-05	-5.94E-04
idu_hisp_male	__age	0.422739961	0.002380021	-0.006236331	0.023031557	-0.02884396	-2.47E-04	8.60E-05	0.001499508
idu_hisp_male	___age	-0.447761722	-0.001854311	0.005830005	-0.02884396	0.047628639	2.50E-04	-1.87E-05	-0.001678896
idu_hisp_male	year	-0.522622756	-1.13E-05	3.20E-05	-2.47E-04	2.50E-04	2.60E-04	-1.87E-05	-8.63E-04
idu_hisp_male	sqrtcd4n	0.035896928	2.05E-05	-3.90E-05	8.60E-05	-1.87E-05	-1.87E-05	7.57E-05	-2.59E-04
idu_hisp_male	haart_period	1.713012712	5.80E-04	-5.94E-04	0.001499508	-0.001678896	-8.63E-04	-2.59E-04	0.021125133
idu_white_female	intercept	2499.803078	0.212015328	-0.185026074	0.618285671	-0.57323304	-1.247012381	0.079762419	4.96571129
idu_white_female	age	0.212015328	0.0016972	-0.003363702	0.006660172	-0.004656974	-1.33E-04	2.73E-05	0.001005909
idu_white_female	_age	-0.185026074	-0.003363702	0.008079744	-0.019509631	0.017087133	1.45E-04	-3.05E-05	-5.74E-04
idu_white_female	__age	0.618285671	0.006660172	-0.019509631	0.059563343	-0.066647369	-4.09E-04	2.76E-05	7.08E-04
idu_white_female	___age	-0.57323304	-0.004656974	0.017087133	-0.066647369	0.093905921	3.52E-04	1.55E-04	-0.003054944
idu_white_female	year	-1.247012382	-1.33E-04	1.45E-04	-4.09E-04	3.52E-04	6.23E-04	-4.16E-05	-0.002491198
idu_white_female	sqrtcd4n	0.079762419	2.73E-05	-3.05E-05	2.76E-05	1.55E-04	-4.16E-05	1.70E-04	-6.73E-05
idu_white_female	haart_period	4.965711291	0.001005909	-5.74E-04	7.08E-04	-0.003054944	-0.002491198	-6.73E-05	0.050911691
idu_white_male	intercept	422.4689226	-0.011817005	0.062160748	-0.121173229	0.134891904	-0.209810006	-0.004497995	0.815994573
idu_white_male	age	-0.011817005	2.71E-04	-5.13E-04	0.001187788	-9.85E-04	1.51E-06	3.04E-06	1.04E-04
idu_white_male	_age	0.062160748	-5.13E-04	0.0011508	-0.003239405	0.003233182	-2.31E-05	3.83E-06	1.95E-04
idu_white_male	__age	-0.12117323	0.001187788	-0.003239405	0.012378766	-0.016523074	4.33E-05	-3.78E-05	-0.001007757
idu_white_male	___age	0.134891904	-9.85E-04	0.003233182	-0.016523074	0.029717938	-5.38E-05	5.39E-05	0.001306192
idu_white_male	year	-0.209810006	1.51E-06	-2.31E-05	4.33E-05	-5.38E-05	1.04E-04	1.87E-06	-4.08E-04
idu_white_male	sqrtcd4n	-0.004497995	3.04E-06	3.83E-06	-3.78E-05	5.39E-05	1.87E-06	3.63E-05	-1.59E-04
idu_white_male	haart_period	0.815994573	1.04E-04	1.95E-04	-0.001007757	0.001306192	-4.08E-04	-1.59E-04	0.010028371
msm_black_male	intercept	109.1186038	0.01504293	-0.029173896	0.041740205	-0.003210434	-0.054442697	0.001064732	0.220413383
msm_black_male	age	0.01504293	1.41E-04	-3.71E-04	5.10E-04	-2.09E-04	-9.31E-06	2.00E-06	2.51E-05
msm_black_male	_age	-0.029173896	-3.71E-04	0.001100476	-0.001655193	8.79E-04	1.91E-05	-3.26E-06	7.21E-05
msm_black_male	__age	0.041740205	5.10E-04	-0.001655193	0.002699339	-0.001794198	-2.70E-05	3.76E-06	-1.37E-04
msm_black_male	___age	-0.003210434	-2.09E-04	8.79E-04	-0.001794198	0.002044894	4.06E-06	-2.35E-06	9.67E-05
msm_black_male	year	-0.054442697	-9.31E-06	1.91E-05	-2.70E-05	4.06E-06	2.72E-05	-6.14E-07	-1.10E-04
msm_black_male	sqrtcd4n	0.001064732	2.00E-06	-3.26E-06	3.76E-06	-2.35E-06	-6.14E-07	7.36E-06	-2.46E-05
msm_black_male	haart_period	0.220413383	2.51E-05	7.21E-05	-1.37E-04	9.67E-05	-1.10E-04	-2.46E-05	0.002257966
msm_hisp_male	intercept	184.0856325	0.014529451	-0.018705699	0.046544573	-0.028929336	-0.09174528	0.004540654	0.339868118
msm_hisp_male	age	0.014529451	2.17E-04	-5.01E-04	8.47E-04	-4.47E-04	-1.03E-05	1.18E-06	1.01E-04
msm_hisp_male	_age	-0.018705699	-5.01E-04	0.001321852	-0.002543229	0.001647847	1.61E-05	1.68E-06	-7.27E-05
msm_hisp_male	__age	0.046544573	8.47E-04	-0.002543229	0.005693712	-0.004611725	-3.42E-05	-7.16E-06	7.69E-05
msm_hisp_male	___age	-0.028929336	-4.47E-04	0.001647847	-0.004611725	0.004961619	2.00E-05	5.93E-06	-1.19E-05
msm_hisp_male	year	-0.09174528	-1.03E-05	1.61E-05	-3.42E-05	2.00E-05	4.58E-05	-2.40E-06	-1.71E-04
msm_hisp_male	sqrtcd4n	0.004540654	1.18E-06	1.68E-06	-7.16E-06	5.93E-06	-2.40E-06	1.49E-05	-4.99E-05
msm_hisp_male	haart_period	0.339868118	1.01E-04	-7.27E-05	7.69E-05	-1.19E-05	-1.71E-04	-4.99E-05	0.003509684
msm_white_male	intercept	61.52477965	0.00219027	-0.001110188	0.023805685	-0.034730747	-0.030621775	5.32E-04	0.109100492
msm_white_male	age	0.00219027	3.78E-05	-7.32E-05	1.72E-04	-1.29E-04	-1.69E-06	6.89E-07	2.70E-05
msm_white_male	_age	-0.001110188	-7.32E-05	1.64E-04	-4.53E-04	3.93E-04	1.65E-06	-6.49E-07	-9.62E-06
msm_white_male	__age	0.023805685	1.72E-04	-4.53E-04	0.001640293	-0.001811147	-1.43E-05	1.26E-06	1.22E-05
msm_white_male	___age	-0.034730747	-1.29E-04	3.93E-04	-0.001811147	0.002448887	1.91E-05	-1.06E-06	-2.21E-05
msm_white_male	year	-0.030621775	-1.69E-06	1.65E-06	-1.43E-05	1.91E-05	1.53E-05	-3.22E-07	-5.48E-05
msm_white_male	sqrtcd4n	5.32E-04	6.89E-07	-6.49E-07	1.26E-06	-1.06E-06	-3.22E-07	5.23E-06	-1.59E-05
msm_white_male	haart_period	0.109100492	2.70E-05	-9.62E-06	1.22E-05	-2.21E-05	-5.48E-05	-1.59E-05	0.001289467

Reengagement With HIV Care </>

In order to model reengagement in care, we aggregated all sub-populations in the NA-ACCORD and assessed at the number of years spent out of care, estimated between 1 to 7 years. The probability of spending a certain number of years out of care was fit to a normalized Poisson distribution such that the probability of staying disengaged for more than 7 years was zero (Figure 7). The fit was accomplished using the curve_fit and poisson functions of the scipy package for Python. Upon disengagement, this distribution is applied to generate the number of years that a simulated person will spend off ART before reengaging back with treatment.

Figure 7: Number of Years Spent Out of Care

Table 11: Probability of Reengaging

years	probability	prob_0.8	prob_0.9	prob_1.1	prob_1.2
1	0.338	0.420	0.377	0.304	0.273
2	0.367	0.364	0.368	0.362	0.354
3	0.199	0.158	0.179	0.216	0.230
4	0.072	0.046	0.058	0.086	0.100
5	0.019	0.010	0.014	0.026	0.032
6	0.004	0.002	0.003	0.006	0.008
7	0.001	0.000	0.000	0.001	0.002
8	0.000	0.000	0.000	0.000	0.000
9	0.000	0.000	0.000	0.000	0.000
10	0.000	0.000	0.000	0.000	0.000
11	0.000	0.000	0.000	0.000	0.000
12	0.000	0.000	0.000	0.000	0.000

When simulated agents are lost to follow up, a number of years out of care is drawn from this distribution and the person will stay lost to follow up until they have spent the correct number of years out of care, they die, or the simulation ends.

CD4 Dynamics In Care </>

A linear regression was used to model the time varying CD4 count of those on ART. To this end, the square root of the time-varying CD4 count (\(\mathrm{sqrt\_cd4n}\)) was modeled as a linear function of age (modeled with a 4-knot restricted cubic spline), CD4 at ART initiation (modeled with a 4-knot restricted cubic spline), number of years since ART initiation (modeled with a 4-knot restricted cubic spline), and interaction terms between CD4 count at ART initiation and number of years since ART initiation.

Age is modeled as a restricted quadratic spline with 4 knots:

\[\mathrm{age}\_1 = \begin{cases} \frac{(\mathrm{age} - k_1)^2 - (\mathrm{age} - k_4)^2}{k_4 - k_1}, & \mathrm{age} \ge k_4\\ \frac{(\mathrm{age} - k_1)^2} {k_4 - k_1}, & k_4 \gt \mathrm{age} \ge k_1\\ 0, & \mathrm{else} \end{cases}\] \[\mathrm{age}\_2 = \begin{cases} \frac{(\mathrm{age} - k_2)^2 - (\mathrm{age} - k_4)^2}{k_4 - k_1}, & \mathrm{age} \ge k_4\\ \frac{(\mathrm{age} - k_2)^2} {k_4 - k_1}, & k_4 \gt \mathrm{age} \ge k_2\\ 0, & \mathrm{else} \end{cases}\] \[\mathrm{age}\_3 = \begin{cases} \frac{(\mathrm{age} - k_3)^2 - (\mathrm{age} - k_4)^2}{k_4 - k_1}, & \mathrm{age} \ge k_4\\ \frac{(\mathrm{age} - k_3)^2} {k_4 - k_1}, & k_4 \gt \mathrm{age} \ge k_3\\ 0, & \mathrm{else} \end{cases}\]

CD4 at ART initiation is modeled as a restricted quadratic spline with 4 knots:

\[\mathrm{cd4\_art}\_1 = \begin{cases} \frac{(\mathrm{cd4\_art} - k_1)^2 - (\mathrm{cd4\_art} - k_4)^2}{k_4 - k_1}, & \mathrm{cd4\_art} \ge k_4\\ \frac{(\mathrm{cd4\_art} - k_1)^2} {k_4 - k_1}, & k_4 \gt \mathrm{cd4\_art} \ge k_1\\ 0, & \mathrm{else} \end{cases}\] \[\mathrm{cd4\_art}\_2 = \begin{cases} \frac{(\mathrm{cd4\_art} - k_2)^2 - (\mathrm{cd4\_art} - k_4)^2}{k_4 - k_1}, & \mathrm{cd4\_art} \ge k_4\\ \frac{(\mathrm{cd4\_art} - k_2)^2} {k_4 - k_1}, & k_4 \gt \mathrm{cd4\_art} \ge k_2\\ 0, & \mathrm{else} \end{cases}\] \[\mathrm{cd4\_art}\_3 = \begin{cases} \frac{(\mathrm{cd4\_art} - k_3)^2 - (\mathrm{cd4\_art} - k_4)^2}{k_4 - k_1}, & \mathrm{cd4\_art} \ge k_4\\ \frac{(\mathrm{cd4\_art} - k_3)^2} {k_4 - k_1}, & k_4 \gt \mathrm{cd4\_art} \ge k_3\\ 0, & \mathrm{else} \end{cases}\]

The number of years since ART initiation is modeled as a restricted quadratic spline with 4 knots:

\[\mathrm{yrs\_art}\_1 = \begin{cases} \frac{(\mathrm{yrs\_art} - k_1)^2 - (\mathrm{yrs\_art} - k_4)^2}{k_4 - k_1}, & \mathrm{yrs\_art} \ge k_4\\ \frac{(\mathrm{yrs\_art} - k_1)^2} {k_4 - k_1}, & k_4 \gt \mathrm{yrs\_art} \ge k_1\\ 0, & \mathrm{else} \end{cases}\] \[\mathrm{yrs\_art}\_2 = \begin{cases} \frac{(\mathrm{yrs\_art} - k_2)^2 - (\mathrm{yrs\_art} - k_4)^2}{k_4 - k_1}, & \mathrm{yrs\_art} \ge k_4\\ \frac{(\mathrm{yrs\_art} - k_2)^2} {k_4 - k_1}, & k_4 \gt \mathrm{yrs\_art} \ge k_2\\ 0, & \mathrm{else} \end{cases}\] \[\mathrm{yrs\_art}\_3 = \begin{cases} \frac{(\mathrm{yrs\_art} - k_3)^2 - (\mathrm{yrs\_art} - k_4)^2}{k_4 - k_1}, & \mathrm{yrs\_art} \ge k_4\\ \frac{(\mathrm{yrs\_art} - k_3)^2} {k_4 - k_1}, & k_4 \gt \mathrm{yrs\_art} \ge k_3\\ 0, & \mathrm{else} \end{cases}\]

The same knot locations were used for each population at $k_1=1$, $k_2=4$, $k_3=7$, and $k_4=13$. The final regression equation resulting from this choice of regressors are as follow:

\[\begin{split} \mathrm{sqrt\_cd4} = \beta_0 &+ \beta_\mathrm{age} \cdot\mathrm{age} + \beta_\mathrm{age\_1} \cdot\mathrm{age\_1} + \beta_\mathrm{age\_2} \cdot\mathrm{age\_2} + \beta_\mathrm{age\_3} \cdot\mathrm{age\_3}\\[2ex] &+ \beta_\mathrm{cd4} \cdot\mathrm{cd4} + \beta_\mathrm{cd4\_1} \cdot\mathrm{cd4\_1} + \beta_\mathrm{cd4\_2} \cdot\mathrm{cd4\_2} + \beta_\mathrm{cd4\_3} \cdot\mathrm{cd4\_3}\\[2ex] &+ \beta_\mathrm{yrs\_art} \cdot\mathrm{yrs\_art} + \beta_\mathrm{yrs\_art\_1} \cdot\mathrm{yrs\_art\_1} + \beta_\mathrm{yrs\_art\_2} \cdot\mathrm{yrs\_art\_2} + \beta_\mathrm{yrs\_art\_3} \cdot\mathrm{yrs\_art\_3}\\[2ex] &+ \beta_\mathrm{cd4\_1\_yrs\_1} \cdot \mathrm{cd4\_1} \cdot \mathrm{yrs\_art\_1} + \beta_\mathrm{cd4\_1\_yrs\_2} \cdot \mathrm{cd4\_1} \cdot \mathrm{yrs\_art\_2}+ \beta_\mathrm{cd4\_1\_yrs\_3} \cdot \mathrm{cd4\_1} \cdot \mathrm{yrs\_art\_3}\\[2ex] &+ \beta_\mathrm{cd4\_2\_yrs\_1} \cdot \mathrm{cd4\_2} \cdot \mathrm{yrs\_art\_1} + \beta_\mathrm{cd4\_2\_yrs\_2} \cdot \mathrm{cd4\_2} \cdot \mathrm{yrs\_art\_2}+ \beta_\mathrm{cd4\_2\_yrs\_3} \cdot \mathrm{cd4\_2} \cdot \mathrm{yrs\_art\_3}\\[2ex] &+ \beta_\mathrm{cd4\_3\_yrs\_1} \cdot \mathrm{cd4\_3} \cdot \mathrm{yrs\_art\_1} + \beta_\mathrm{cd4\_3\_yrs\_2} \cdot \mathrm{cd4\_3} \cdot \mathrm{yrs\_art\_2}+ \beta_\mathrm{cd4\_3\_yrs\_3} \cdot \mathrm{cd4\_3} \cdot \mathrm{yrs\_art\_3} \end{split}\]

The coefficients were estimated using a generalized estimating equation (GEE) with an identity link function and an exchangeable correlation structure. The NA-ACCORD population was filtered to those that never left care during study follow-up. Patients who initiated ART before 2000 and who were missing CD4 count data at ART initiation were dropped from analysis. Each remaining patient was assigned a single data point per year for the full range of years 2009 – 2022 and the CD4 count was taken to be the median CD4 count by calendar year. The resulted coefficient estimates are shown in Table 12 and the covariance matrices are shown in Table 16

Table 12: CD4 Increase Coefficient Estimates

group	(Intercept)	rcs(age, 4)age	rcs(age, 4)age’	rcs(age, 4)age’’	rcs(cd4n_ini, 4)cd4n_ini	rcs(cd4n_ini, 4)cd4n_ini’	rcs(cd4n_ini, 4)cd4n_ini’’	rcs(cd4n_ini, 4)cd4n_ini’’:rcs(time_from_h1yy, 4)time_from_h1yy	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’’	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’’	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’’	rcs(time_from_h1yy, 4)time_from_h1yy	rcs(time_from_h1yy, 4)time_from_h1yy’	rcs(time_from_h1yy, 4)time_from_h1yy’’
het_black_female	10.67	-0.05	0.40	-1.45	0.04	-0.01	-0.01	-0.06	0.31	-0.64	0.03	-0.13	0.27	-0.01	0.04	-0.07	2.46	-7.84	14.15
het_black_male	10.65	-0.03	0.11	-0.60	0.04	-0.05	0.07	-0.06	0.22	-0.37	0.03	-0.12	0.20	-0.01	0.03	-0.04	1.73	-4.87	7.80
het_hisp_female	15.97	-0.14	0.77	-2.45	0.02	0.03	-0.11	-0.03	0.06	-0.08	0.01	-0.02	0.02	0.00	0.01	-0.01	1.60	-3.52	5.80
het_hisp_male	13.71	-0.08	0.14	-0.41	0.03	0.04	-0.08	-0.07	0.35	-0.74	0.04	-0.22	0.45	-0.01	0.03	-0.06	1.60	-5.00	8.70
het_white_female	12.17	-0.03	0.15	-0.75	0.03	-0.02	0.00	0.03	-0.20	0.33	-0.01	0.07	-0.12	0.00	-0.01	0.02	1.23	-2.07	3.18
het_white_male	15.11	-0.11	0.25	-1.27	0.04	-0.05	0.06	-0.05	0.11	-0.22	0.03	-0.07	0.13	-0.01	0.02	-0.03	1.76	-4.49	9.44
idu_black_female	6.57	0.10	0.00	-0.37	0.03	-0.03	0.03	-0.08	0.10	-0.20	0.03	-0.04	0.06	-0.01	0.01	0.00	1.42	-1.13	0.85
idu_black_male	14.24	-0.10	0.31	-1.69	0.02	0.05	-0.14	0.03	-0.09	0.20	-0.01	0.04	-0.09	0.00	0.00	0.00	1.00	-1.18	2.40
idu_hisp_female	21.21	-0.28	0.35	-0.87	0.03	0.00	-0.07	0.14	-1.37	2.45	-0.05	0.48	-0.86	0.01	-0.09	0.17	0.29	6.40	-14.28
idu_hisp_male	13.92	-0.11	0.20	-0.80	0.04	-0.04	0.08	-0.06	0.17	-0.32	0.02	-0.07	0.13	-0.01	0.01	-0.01	1.25	-0.60	-0.59
idu_white_female	13.28	-0.11	0.51	-2.01	0.04	-0.03	0.01	-0.07	0.20	-0.45	0.03	-0.09	0.20	-0.01	0.03	-0.08	1.56	-4.82	12.48
idu_white_male	13.46	-0.11	0.23	-1.24	0.04	-0.06	0.09	-0.02	0.12	-0.32	0.01	-0.04	0.11	0.00	0.01	-0.02	1.37	-2.32	4.03
msm_black_male	12.06	-0.07	0.20	-0.53	0.04	-0.02	0.00	-0.03	0.19	-0.42	0.01	-0.08	0.18	-0.01	0.02	-0.05	1.81	-6.05	11.77
msm_hisp_male	12.00	-0.06	0.08	-0.29	0.04	-0.04	0.07	-0.02	0.11	-0.23	0.01	-0.05	0.10	0.00	0.02	-0.04	1.81	-5.44	10.64
msm_white_male	12.79	-0.05	0.08	-0.48	0.04	-0.03	0.04	-0.02	0.09	-0.23	0.01	-0.03	0.08	0.00	0.01	-0.02	1.48	-2.90	5.89

Table 13: Age Spline Knot Locations

subgroup	knot_1	knot_2	knot_3	knot_4
het_black_female	29.00	42.00	51	66
het_black_male	32.00	48.00	56	69
het_hisp_female	29.00	40.00	49	65
het_hisp_male	31.00	44.00	53	68
het_white_female	29.00	44.00	53	67
het_white_male	34.00	49.00	58	72
idu_black_female	38.00	50.00	57	67
idu_black_male	41.00	54.05	61	69
idu_hisp_female	34.65	48.00	56	66
idu_hisp_male	34.00	47.00	55	67
idu_white_female	33.00	45.00	52	65
idu_white_male	31.00	46.00	54	66
msm_black_male	25.00	36.00	48	63
msm_hisp_male	26.00	38.00	47	62
msm_white_male	30.00	46.00	54	68

Table 14: CD4 Spline Knot Locations

subgroup	knot_1	knot_2	knot_3	knot_4
het_black_female	12	183.0	335	719.3
het_black_male	9	136.0	303	657.0
het_hisp_female	20	207.0	359	784.0
het_hisp_male	8	89.0	239	579.0
het_white_female	22	215.0	360	763.0
het_white_male	9	119.0	317	671.6
idu_black_female	8	184.0	317	715.0
idu_black_male	12	154.0	329	761.0
idu_hisp_female	24	206.1	363	651.0
idu_hisp_male	31	189.0	353	653.0
idu_white_female	29	201.0	361	690.0
idu_white_male	16	177.0	329	716.0
msm_black_male	13	199.0	370	765.0
msm_hisp_male	22	207.0	373	758.4
msm_white_male	30	240.0	397	790.0

Table 15: Age Spline Knot Locations

subgroup	knot_1	knot_2	knot_3	knot_4
het_black_female	1	4	8	15
het_black_male	1	4	9	16
het_hisp_female	1	4	8	15
het_hisp_male	1	4	8	16
het_white_female	1	4	9	16
het_white_male	1	5	9	17
idu_black_female	1	6	10	17
idu_black_male	1	6	10	17
idu_hisp_female	1	3	7	13
idu_hisp_male	1	5	9	16
idu_white_female	1	5	8	15
idu_white_male	1	5	9	16
msm_black_male	1	4	7	16
msm_hisp_male	1	4	7	15
msm_white_male	1	5	9	16

Table 16: CD4 Increase Covariance Matrices

group	varname	(Intercept)	rcs(age, 4)age	rcs(age, 4)age’	rcs(age, 4)age’’	rcs(cd4n_ini, 4)cd4n_ini	rcs(cd4n_ini, 4)cd4n_ini’	rcs(cd4n_ini, 4)cd4n_ini’’	rcs(time_from_h1yy, 4)time_from_h1yy	rcs(time_from_h1yy, 4)time_from_h1yy’	rcs(time_from_h1yy, 4)time_from_h1yy’’	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’’	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’’	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’’
het_black_female	(Intercept)	0.945246509	-0.021234239	0.057339439	-0.178161473	-0.001592247	0.005511022	-0.012257957	-0.04481439	0.146252756	-0.272918774	0.000351007	-0.001231117	0.002735874	-0.00113566	0.004076262	-0.009138423	0.002112031	-0.007643653	0.017212017
het_black_female	rcs(age, 4)age	-0.021234239	0.000599454	-0.001728817	0.005497105	5.92E-06	-8.13E-06	9.84E-06	-6.80E-06	0.00089194	-0.001756471	-1.22E-07	-2.54E-06	8.04E-06	-6.21E-06	3.11E-05	-7.66E-05	1.25E-05	-6.02E-05	0.000145779
het_black_female	rcs(age, 4)age’	0.057339439	-0.001728817	0.006246235	-0.021475055	-1.31E-05	2.14E-05	-3.31E-05	-0.00010192	-0.002895695	0.005826867	-3.56E-07	1.05E-05	-3.08E-05	2.48E-05	-0.00012416	0.000306428	-5.06E-05	0.00024595	-0.000599393
het_black_female	rcs(age, 4)age’’	-0.178161473	0.005497105	-0.021475055	0.077170859	3.31E-05	-4.66E-05	6.34E-05	0.000215588	0.00884281	-0.017840626	2.24E-06	-3.70E-05	0.000106534	-8.32E-05	0.000425333	-0.001056503	0.000168387	-0.000841515	0.002066785
het_black_female	rcs(cd4n_ini, 4)cd4n_ini	-0.001592247	5.92E-06	-1.31E-05	3.31E-05	1.34E-05	-5.78E-05	0.000136495	0.000344337	-0.001326612	0.002498236	-3.33E-06	1.44E-05	-3.39E-05	1.29E-05	-5.60E-05	0.00013223	-2.44E-05	0.000105875	-0.000249973
het_black_female	rcs(cd4n_ini, 4)cd4n_ini’	0.005511022	-8.13E-06	2.14E-05	-4.66E-05	-5.78E-05	0.000271593	-0.000655298	-0.001308663	0.005050464	-0.009517634	1.44E-05	-6.69E-05	0.000160829	-5.60E-05	0.000261255	-0.000628544	0.000105849	-0.000493977	0.00118887
het_black_female	rcs(cd4n_ini, 4)cd4n_ini’’	-0.012257957	9.84E-06	-3.31E-05	6.34E-05	0.000136495	-0.000655298	0.00159152	0.002989357	-0.011538104	0.021747503	-3.38E-05	0.000160797	-0.000389134	0.00013217	-0.000628208	0.001519932	-0.000249727	0.001187893	-0.002875001
het_black_female	rcs(time_from_h1yy, 4)time_from_h1yy	-0.04481439	-6.80E-06	-0.00010192	0.000215588	0.000344337	-0.001308663	0.002989357	0.026825428	-0.132383834	0.258675987	-0.000202664	0.000771517	-0.001763223	0.001001723	-0.003821538	0.008742103	-0.001957753	0.007474226	-0.017103996
het_black_female	rcs(time_from_h1yy, 4)time_from_h1yy’	0.146252756	0.00089194	-0.002895695	0.00884281	-0.001326612	0.005050464	-0.011538104	-0.132383834	0.862644548	-1.777086869	0.001002014	-0.00382255	0.00874374	-0.006546039	0.025106534	-0.057545186	0.01350365	-0.051869229	0.118951018
het_black_female	rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.272918774	-0.001756471	0.005826867	-0.017840626	0.002498236	-0.009517634	0.021747503	0.258675987	-1.777086869	3.706869575	-0.00195807	0.007472713	-0.017096636	0.013497456	-0.051832405	0.118856615	-0.02820944	0.108547777	-0.249084635
het_black_female	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy	0.000351007	-1.22E-07	-3.56E-07	2.24E-06	-3.33E-06	1.44E-05	-3.38E-05	-0.000202664	0.001002014	-0.00195807	1.96E-06	-8.50E-06	2.01E-05	-9.63E-06	4.17E-05	-9.84E-05	1.88E-05	-8.12E-05	0.000191735
het_black_female	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy	-0.001231117	-2.54E-06	1.05E-05	-3.70E-05	1.44E-05	-6.69E-05	0.000160797	0.000771517	-0.00382255	0.007472713	-8.50E-06	3.98E-05	-9.57E-05	4.17E-05	-0.000194844	0.00046952	-8.12E-05	0.000379575	-0.000914903
het_black_female	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy	0.002735874	8.04E-06	-3.08E-05	0.000106534	-3.39E-05	0.000160829	-0.000389134	-0.001763223	0.00874374	-0.017096636	2.01E-05	-9.57E-05	0.000231901	-9.84E-05	0.000469454	-0.001138379	0.000191646	-0.000914744	0.002219006
het_black_female	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.00113566	-6.21E-06	2.48E-05	-8.32E-05	1.29E-05	-5.60E-05	0.00013217	0.001001723	-0.006546039	0.013497456	-9.63E-06	4.17E-05	-9.84E-05	6.24E-05	-0.000270548	0.000639545	-0.000128538	0.000557751	-0.001318905
het_black_female	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’	0.004076262	3.11E-05	-0.00012416	0.000425333	-5.60E-05	0.000261255	-0.000628208	-0.003821538	0.025106534	-0.051832405	4.17E-05	-0.000194844	0.000469454	-0.000270548	0.001271677	-0.003071227	0.000557754	-0.002625605	0.006345264
het_black_female	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.009138423	-7.66E-05	0.000306428	-0.001056503	0.00013223	-0.000628544	0.001519932	0.008742103	-0.057545186	0.118856615	-9.84E-05	0.00046952	-0.001138379	0.000639545	-0.003071227	0.007468855	-0.001318928	0.00634533	-0.015443936
het_black_female	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.002112031	1.25E-05	-5.06E-05	0.000168387	-2.44E-05	0.000105849	-0.000249727	-0.001957753	0.01350365	-0.02820944	1.88E-05	-8.12E-05	0.000191646	-0.000128538	0.000557754	-0.001318928	0.000268738	-0.001168115	0.002763949
het_black_female	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.007643653	-6.02E-05	0.00024595	-0.000841515	0.000105875	-0.000493977	0.001187893	0.007474226	-0.051869229	0.108547777	-8.12E-05	0.000379575	-0.000914744	0.000557751	-0.002625605	0.00634533	-0.001168115	0.005515092	-0.013341831
het_black_female	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.017212017	0.000145779	-0.000599393	0.002066785	-0.000249973	0.00118887	-0.002875001	-0.017103996	0.118951018	-0.249084635	0.000191735	-0.000914903	0.002219006	-0.001318905	0.006345264	-0.015443936	0.002763949	-0.013341831	0.032512122
het_black_male	(Intercept)	0.930349892	-0.019187795	0.041202289	-0.174061707	-0.001840601	0.008143175	-0.014975348	-0.043395794	0.150386876	-0.251289692	0.000433578	-0.002022006	0.00375066	-0.001600853	0.008079541	-0.015246795	0.002681522	-0.013846384	0.026254056
het_black_male	rcs(age, 4)age	-0.019187795	0.000488209	-0.001108958	0.004789707	6.35E-06	-1.27E-05	1.76E-05	1.55E-05	0.000797777	-0.001633349	-5.01E-07	4.85E-07	-3.54E-08	-3.70E-06	1.03E-05	-1.68E-05	8.90E-06	-2.22E-05	3.42E-05
het_black_male	rcs(age, 4)age’	0.041202289	-0.001108958	0.003291914	-0.015769404	-1.48E-05	2.94E-05	-4.15E-05	-0.000261866	-0.001674972	0.003662925	1.18E-06	1.31E-07	-2.67E-06	7.11E-06	-1.45E-05	1.99E-05	-1.85E-05	3.37E-05	-4.11E-05
het_black_male	rcs(age, 4)age’’	-0.174061707	0.004789707	-0.015769404	0.081740396	6.09E-05	-0.000109077	0.000144856	0.001355359	0.006525474	-0.015235628	-6.13E-06	-9.51E-07	1.30E-05	-2.58E-05	3.63E-05	-2.35E-05	7.22E-05	-0.000102701	7.19E-05
het_black_male	rcs(cd4n_ini, 4)cd4n_ini	-0.001840601	6.35E-06	-1.48E-05	6.09E-05	2.04E-05	-0.000112394	0.000215625	0.000414553	-0.001739016	0.003014395	-5.07E-06	2.75E-05	-5.26E-05	2.15E-05	-0.000117463	0.000225443	-3.74E-05	0.000204869	-0.000393468
het_black_male	rcs(cd4n_ini, 4)cd4n_ini’	0.008143175	-1.27E-05	2.94E-05	-0.000109077	-0.000112394	0.000668326	-0.001302921	-0.001998223	0.008468994	-0.014701927	2.75E-05	-0.000159966	0.000310819	-0.000117232	0.000687815	-0.001340823	0.000204487	-0.001203433	0.002348128
het_black_male	rcs(cd4n_ini, 4)cd4n_ini’’	-0.014975348	1.76E-05	-4.15E-05	0.000144856	0.000215625	-0.001302921	0.002549788	0.003736784	-0.015876648	0.027572451	-5.26E-05	0.000310695	-0.000605896	0.000224797	-0.001339535	0.002621754	-0.000392366	0.002345768	-0.004595812
het_black_male	rcs(time_from_h1yy, 4)time_from_h1yy	-0.043395794	1.55E-05	-0.000261866	0.001355359	0.000414553	-0.001998223	0.003736784	0.021369439	-0.102880603	0.181250929	-0.000203543	0.000988365	-0.001852511	0.00098825	-0.004824213	0.009058817	-0.001742721	0.008514914	-0.015993834
het_black_male	rcs(time_from_h1yy, 4)time_from_h1yy’	0.150386876	0.000797777	-0.001674972	0.006525473	-0.001739016	0.008468994	-0.015876648	-0.102880603	0.609947322	-1.121379198	0.000987308	-0.004817983	0.009044785	-0.005860119	0.028695699	-0.053946394	0.01077489	-0.052772314	0.099217419
het_black_male	rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.251289692	-0.001633349	0.003662925	-0.015235628	0.003014395	-0.014701927	0.027572451	0.181250929	-1.121379198	2.087553788	-0.001740809	0.008502666	-0.015966124	0.010772094	-0.052764966	0.099202734	-0.020050028	0.09820981	-0.184643364
het_black_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy	0.000433578	-5.01E-07	1.18E-06	-6.13E-06	-5.07E-06	2.75E-05	-5.26E-05	-0.000203543	0.000987308	-0.001740809	2.56E-06	-1.41E-05	2.72E-05	-1.26E-05	6.98E-05	-0.000134619	2.22E-05	-0.000123716	0.00023855
het_black_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy	-0.002022006	4.85E-07	1.31E-07	-9.51E-07	2.75E-05	-0.000159966	0.000310695	0.000988365	-0.004817983	0.008502666	-1.41E-05	8.41E-05	-0.000164233	6.98E-05	-0.000419043	0.000821197	-0.000123632	0.000743893	-0.001458699
het_black_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy	0.00375066	-3.54E-08	-2.67E-06	1.30E-05	-5.26E-05	0.000310819	-0.000605896	-0.001852511	0.009044785	-0.015966124	2.72E-05	-0.000164233	0.000322013	-0.000134462	0.00082078	-0.001615453	0.000238275	-0.001457931	0.002871397
het_black_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.001600853	-3.70E-06	7.11E-06	-2.58E-05	2.15E-05	-0.000117232	0.000224797	0.00098825	-0.005860119	0.010772094	-1.26E-05	6.98E-05	-0.000134462	7.68E-05	-0.000433491	0.000838349	-0.000142037	0.000804533	-0.001556753
het_black_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’	0.008079541	1.03E-05	-1.45E-05	3.63E-05	-0.000117463	0.000687815	-0.001339535	-0.004824213	0.028695699	-0.052764966	6.98E-05	-0.000419043	0.00082078	-0.000433491	0.002660851	-0.005239906	0.000804548	-0.004959001	0.009772736
het_black_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.015246795	-1.68E-05	1.99E-05	-2.35E-05	0.000225443	-0.001340823	0.002621754	0.009058817	-0.053946394	0.099202734	-0.000134619	0.000821197	-0.001615453	0.000838349	-0.005239906	0.010368196	-0.00155678	0.009772788	-0.019352489
het_black_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.002681522	8.90E-06	-1.85E-05	7.22E-05	-3.74E-05	0.000204487	-0.000392366	-0.001742721	0.01077489	-0.020050028	2.22E-05	-0.000123632	0.000238275	-0.000142037	0.000804548	-0.00155678	0.000266323	-0.001513074	0.002929159
het_black_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.013846384	-2.22E-05	3.37E-05	-0.000102701	0.000204869	-0.001203433	0.002345768	0.008514914	-0.052772314	0.09820981	-0.000123716	0.000743893	-0.001457931	0.000804533	-0.004959001	0.009772788	-0.001513074	0.009367442	-0.018472949
het_black_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.026254056	3.42E-05	-4.11E-05	7.19E-05	-0.000393468	0.002348128	-0.004595812	-0.015993834	0.099217419	-0.184643364	0.00023855	-0.001458699	0.002871397	-0.001556753	0.009772736	-0.019352489	0.002929159	-0.018472949	0.036606857
het_hisp_female	(Intercept)	4.601714247	-0.100546917	0.330178438	-0.89568551	-0.00820612	0.028352683	-0.065664477	-0.346888677	1.425756849	-2.685194864	0.002185509	-0.007236891	0.016496576	-0.008018604	0.023883815	-0.052034961	0.014564567	-0.040996691	0.086829796
het_hisp_female	rcs(age, 4)age	-0.100546917	0.00292686	-0.01032742	0.028640477	2.74E-05	-1.48E-05	-3.32E-05	0.002728946	-0.015682363	0.030688032	-1.47E-05	2.02E-05	-2.05E-05	6.16E-05	-1.69E-05	-0.000128222	-0.000107386	-5.85E-05	0.000505942
het_hisp_female	rcs(age, 4)age’	0.330178438	-0.01032742	0.046118061	-0.136787313	-8.49E-05	0.000114533	-0.000116205	-0.009544086	0.052850145	-0.102180274	5.00E-05	-4.29E-05	-1.25E-05	-0.000222854	-3.57E-05	0.000766647	0.000382397	0.000405753	-0.002419933
het_hisp_female	rcs(age, 4)age’’	-0.89568551	0.028640477	-0.136787313	0.418009057	0.000217441	-0.000349536	0.000470044	0.02343291	-0.13902898	0.266061831	-0.000129404	7.62E-05	0.000152114	0.00062308	0.00011026	-0.0021981	-0.001058075	-0.001153275	0.00682513
het_hisp_female	rcs(cd4n_ini, 4)cd4n_ini	-0.00820612	2.74E-05	-8.49E-05	0.000217441	5.99E-05	-0.000262613	0.00065355	0.001706384	-0.006050258	0.011144904	-1.38E-05	6.09E-05	-0.000152019	5.03E-05	-0.000223214	0.000557773	-9.30E-05	0.00041302	-0.001031917
het_hisp_female	rcs(cd4n_ini, 4)cd4n_ini’	0.028352683	-1.48E-05	0.000114533	-0.000349536	-0.000262613	0.001290441	-0.003313573	-0.006511383	0.023087825	-0.042491772	6.08E-05	-0.000304025	0.000786012	-0.000223604	0.001128449	-0.002922212	0.000414336	-0.002093773	0.005422701
het_hisp_female	rcs(cd4n_ini, 4)cd4n_ini’’	-0.065664477	-3.32E-05	-0.000116205	0.000470044	0.00065355	-0.003313573	0.008586116	0.015622691	-0.055363613	0.101854783	-0.000151817	0.000785838	-0.002052618	0.000559153	-0.002923302	0.007649228	-0.001036407	0.005426413	-0.014201909
het_hisp_female	rcs(time_from_h1yy, 4)time_from_h1yy	-0.346888677	0.002728946	-0.009544086	0.02343291	0.001706384	-0.006511383	0.015622691	0.133016303	-0.584451241	1.128644681	-0.000879571	0.003388603	-0.008148841	0.003911502	-0.015215596	0.036676705	-0.007561834	0.029445729	-0.070990722
het_hisp_female	rcs(time_from_h1yy, 4)time_from_h1yy’	1.425756849	-0.015682363	0.052850145	-0.13902898	-0.006050258	0.023087825	-0.055363613	-0.584451241	3.344107427	-6.875270416	0.003922817	-0.015242571	0.036729318	-0.022672334	0.089379726	-0.216307017	0.046623849	-0.18402324	0.445525561
het_hisp_female	rcs(time_from_h1yy, 4)time_from_h1yy’’	-2.685194864	0.030688032	-0.102180274	0.266061831	0.011144904	-0.042491772	0.101854783	1.128644681	-6.875270416	14.40605336	-0.00758633	0.029508255	-0.071124376	0.046634955	-0.1840257	0.445516811	-0.097690608	0.385854449	-0.934451507
het_hisp_female	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy	0.002185509	-1.47E-05	5.00E-05	-0.000129404	-1.38E-05	6.08E-05	-0.000151817	-0.000879571	0.003922817	-0.00758633	7.34E-06	-3.28E-05	8.21E-05	-3.33E-05	0.000150199	-0.000376347	6.45E-05	-0.000291045	0.000729257
het_hisp_female	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy	-0.007236891	2.02E-05	-4.29E-05	7.62E-05	6.09E-05	-0.000304025	0.000785838	0.003388603	-0.015242571	0.029508255	-3.28E-05	0.000165507	-0.000428	0.000150315	-0.000762822	0.001973486	-0.000291382	0.001478277	-0.003823747
het_hisp_female	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy	0.016496576	-2.05E-05	-1.25E-05	0.000152114	-0.000152019	0.000786012	-0.002052618	-0.008148841	0.036729318	-0.071124376	8.21E-05	-0.000428	0.001117653	-0.000376742	0.001973921	-0.005156708	0.000730402	-0.003824896	0.009990513
het_hisp_female	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.008018604	6.16E-05	-0.000222854	0.00062308	5.03E-05	-0.000223604	0.000559153	0.003911502	-0.022672334	0.046634955	-3.33E-05	0.000150315	-0.000376742	0.000196924	-0.000901361	0.002267341	-0.000404886	0.001854234	-0.004665158
het_hisp_female	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’	0.023883815	-1.69E-05	-3.57E-05	0.00011026	-0.000223214	0.001128449	-0.002923302	-0.015215596	0.089379726	-0.1840257	0.000150199	-0.000762822	0.001973921	-0.000901361	0.004631569	-0.012013866	0.001854411	-0.009525534	0.024707727
het_hisp_female	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.052034961	-0.000128222	0.000766647	-0.0021981	0.000557773	-0.002922212	0.007649228	0.036676705	-0.216307017	0.445516811	-0.000376347	0.001973486	-0.005156708	0.002267341	-0.012013866	0.031467749	-0.004665745	0.024707905	-0.064715095
het_hisp_female	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.014564567	-0.000107386	0.000382397	-0.001058075	-9.30E-05	0.000414336	-0.001036407	-0.007561834	0.046623849	-0.097690608	6.45E-05	-0.000291382	0.000730402	-0.000404886	0.001854411	-0.004665745	0.000846988	-0.003879585	0.009762359
het_hisp_female	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.040996691	-5.85E-05	0.000405753	-0.001153275	0.00041302	-0.002093773	0.005426413	0.029445729	-0.18402324	0.385854449	-0.000291045	0.001478277	-0.003824896	0.001854234	-0.009525534	0.024707905	-0.003879585	0.01991397	-0.051649574
het_hisp_female	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.086829796	0.000505942	-0.002419933	0.00682513	-0.001031917	0.005422701	-0.014201909	-0.070990722	0.445525561	-0.934451507	0.000729257	-0.003823747	0.009990513	-0.004665158	0.024707727	-0.064715095	0.009762359	-0.051649574	0.135268812
het_hisp_male	(Intercept)	2.709933555	-0.064740678	0.184444489	-0.582021792	-0.005869062	0.045722216	-0.074362994	-0.084335019	0.506400315	-1.047521951	0.001407894	-0.01235579	0.020593568	-0.006117877	0.048072329	-0.079303557	0.011335895	-0.082826701	0.13545393
het_hisp_male	rcs(age, 4)age	-0.064740678	0.001864469	-0.005536102	0.017786914	6.66E-06	-0.000133708	0.000246176	-0.000484356	-0.002225921	0.007332712	-3.10E-06	7.92E-05	-0.000148072	1.26E-05	-0.000148145	0.000288214	-2.17E-05	6.95E-05	-0.000160661
het_hisp_male	rcs(age, 4)age’	0.184444489	-0.005536102	0.020355975	-0.070648151	-5.89E-05	0.000726976	-0.001260045	0.001275819	0.00512579	-0.019220023	1.11E-05	-0.000265378	0.00049135	-1.81E-05	0.000225199	-0.000493365	2.62E-05	0.000321059	-0.00042876
het_hisp_male	rcs(age, 4)age’’	-0.582021792	0.017786914	-0.070648151	0.256409525	0.000219738	-0.002688694	0.004618256	-0.004644135	-0.010531615	0.048529588	-3.37E-05	0.000804796	-0.001492052	-3.88E-05	0.000453543	-0.00042552	0.000120956	-0.003641066	0.005845896
het_hisp_male	rcs(cd4n_ini, 4)cd4n_ini	-0.005869062	6.66E-06	-5.89E-05	0.000219738	0.000102123	-0.000849637	0.001387216	0.001309735	-0.005648788	0.010534493	-2.32E-05	0.000197024	-0.000323594	0.000101746	-0.000869904	0.001430284	-0.000189994	0.001624334	-0.002669947
het_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’	0.045722216	-0.000133708	0.000726976	-0.002688694	-0.000849637	0.007585185	-0.012528714	-0.009642363	0.042283687	-0.079120957	0.000195968	-0.001795077	0.002987728	-0.000864487	0.00796725	-0.013270683	0.001614844	-0.014867865	0.024752179
het_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’’	-0.074362994	0.000246176	-0.001260045	0.004618256	0.001387216	-0.012528714	0.020739436	0.015488389	-0.068104908	0.127496353	-0.000321339	0.002982848	-0.004977878	0.001419253	-0.013252249	0.022131736	-0.002650949	0.024724119	-0.041267448
het_hisp_male	rcs(time_from_h1yy, 4)time_from_h1yy	-0.084335019	-0.000484356	0.001275819	-0.004644135	0.001309735	-0.009642363	0.015488389	0.050385883	-0.247450526	0.46474967	-0.000636971	0.004702467	-0.007564195	0.003157422	-0.023326102	0.037496594	-0.00594719	0.043968588	-0.070672302
het_hisp_male	rcs(time_from_h1yy, 4)time_from_h1yy’	0.506400315	-0.002225921	0.00512579	-0.010531615	-0.005648788	0.042283687	-0.068104908	-0.247450526	1.596948931	-3.189713897	0.003154196	-0.023297083	0.037462762	-0.01999203	0.145475221	-0.233059946	0.039771725	-0.288526828	0.461882748
het_hisp_male	rcs(time_from_h1yy, 4)time_from_h1yy’’	-1.047521951	0.007332712	-0.019220023	0.048529588	0.010534493	-0.079120957	0.127496353	0.46474967	-3.189713897	6.481747118	-0.005939778	0.043920885	-0.07063348	0.039789876	-0.288805365	0.46241495	-0.080422489	0.581522742	-0.930246619
het_hisp_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy	0.001407894	-3.10E-06	1.11E-05	-3.37E-05	-2.32E-05	0.000195968	-0.000321339	-0.000636971	0.003154196	-0.005939778	1.14E-05	-9.75E-05	0.00016039	-5.81E-05	0.000498621	-0.000819523	0.000110331	-0.000948569	0.001558698
het_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy	-0.01235579	7.92E-05	-0.000265378	0.000804796	0.000197024	-0.001795077	0.002982848	0.004702467	-0.023297083	0.043920885	-9.75E-05	0.000910391	-0.001520052	0.000499073	-0.004668046	0.007780941	-0.000949803	0.008889389	-0.014810903
het_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy	0.020593568	-0.000148072	0.00049135	-0.001492052	-0.000323594	0.002987728	-0.004977878	-0.007564195	0.037462762	-0.07063348	0.00016039	-0.001520052	0.002545327	-0.000820617	0.007784876	-0.01301126	0.001561631	-0.014820916	0.024758915
het_hisp_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.006117877	1.26E-05	-1.81E-05	-3.88E-05	0.000101746	-0.000864487	0.001419253	0.003157422	-0.01999203	0.039789876	-5.81E-05	0.000499073	-0.000820617	0.000376774	-0.00322755	0.005291568	-0.000753367	0.006449205	-0.010567177
het_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’	0.048072329	-0.000148145	0.000225199	0.000453543	-0.000869904	0.00796725	-0.013252249	-0.023326102	0.145475222	-0.288805365	0.000498621	-0.004668046	0.007784876	-0.00322755	0.030086634	-0.049981329	0.006451639	-0.060103228	0.099769136
het_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.079303557	0.000288214	-0.000493365	-0.00042552	0.001430284	-0.013270683	0.022131736	0.037496594	-0.233059946	0.46241495	-0.000819523	0.007780941	-0.01301126	0.005291568	-0.049981329	0.083230377	-0.010572572	0.099783406	-0.166023099
het_hisp_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.011335895	-2.17E-05	2.62E-05	0.000120956	-0.000189994	0.001614844	-0.002650949	-0.00594719	0.039771725	-0.080422489	0.000110331	-0.000949803	0.001561631	-0.000753367	0.006451639	-0.010572572	0.001528755	-0.013078539	0.02141782
het_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.082826701	6.95E-05	0.000321059	-0.003641066	0.001624334	-0.014867865	0.024724119	0.043968588	-0.288526828	0.581522742	-0.000948569	0.008889389	-0.014820916	0.006449205	-0.060103228	0.099783406	-0.013078539	0.121808986	-0.202059759
het_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.13545393	-0.000160661	-0.00042876	0.005845896	-0.002669947	0.024752179	-0.041267448	-0.070672302	0.461882748	-0.930246619	0.001558698	-0.014810903	0.024758915	-0.010567177	0.099769136	-0.166023099	0.02141782	-0.202059759	0.335941348
het_white_female	(Intercept)	4.046631792	-0.086532959	0.202261954	-0.7215822	-0.005871308	0.018511295	-0.045217857	-0.222024839	1.028706842	-1.822535719	0.001324387	-0.004438967	0.010925183	-0.006295426	0.021862515	-0.054328067	0.011121303	-0.039020034	0.097413986
het_white_female	rcs(age, 4)age	-0.086532959	0.002411198	-0.005942306	0.021814125	7.65E-06	8.81E-06	-4.38E-05	0.000550208	-0.001872523	0.003187675	-2.99E-06	1.19E-05	-2.87E-05	1.06E-05	-5.21E-05	0.000127674	-1.52E-05	8.86E-05	-0.000231309
het_white_female	rcs(age, 4)age’	0.202261954	-0.005942306	0.018456331	-0.074614674	-3.31E-05	7.83E-05	-0.000179342	-0.002404773	0.003024522	-0.002235759	1.47E-05	-6.01E-05	0.000152572	-2.54E-05	0.00014957	-0.00040597	1.22E-05	-0.00020286	0.000659495
het_white_female	rcs(age, 4)age’’	-0.7215822	0.021814125	-0.074614674	0.323679603	9.85E-05	-0.000289937	0.000731297	0.00650127	0.010837676	-0.039507287	-4.32E-05	0.000189493	-0.00049254	-8.13E-05	5.73E-05	2.28E-05	0.000338742	-0.000502956	0.000450394
het_white_female	rcs(cd4n_ini, 4)cd4n_ini	-0.005871308	7.65E-06	-3.31E-05	9.85E-05	4.55E-05	-0.000182749	0.000477519	0.001257123	-0.005989364	0.01066416	-1.00E-05	4.01E-05	-0.000104527	4.82E-05	-0.000193396	0.000505503	-8.61E-05	0.000345966	-0.000904227
het_white_female	rcs(cd4n_ini, 4)cd4n_ini’	0.018511295	8.81E-06	7.83E-05	-0.000289937	-0.000182749	0.00082946	-0.002241607	-0.00417818	0.020271599	-0.036239622	4.02E-05	-0.000183975	0.000498723	-0.000193406	0.000881027	-0.002386266	0.000346081	-0.001575691	0.00426514
het_white_female	rcs(cd4n_ini, 4)cd4n_ini’’	-0.045217857	-4.38E-05	-0.000179342	0.000731297	0.000477519	-0.002241607	0.00611638	0.010343812	-0.050504868	0.090392375	-0.000104971	0.000499454	-0.001369066	0.000506073	-0.002389569	0.006543257	-0.000905784	0.004272704	-0.011690874
het_white_female	rcs(time_from_h1yy, 4)time_from_h1yy	-0.222024839	0.000550208	-0.002404773	0.00650127	0.001257123	-0.00417818	0.010343812	0.110445162	-0.523178783	0.918473109	-0.00069529	0.002397903	-0.006012602	0.003406036	-0.01203809	0.030459528	-0.006016665	0.02137262	-0.054185192
het_white_female	rcs(time_from_h1yy, 4)time_from_h1yy’	1.028706842	-0.001872523	0.003024522	0.010837676	-0.005989364	0.020271599	-0.050504868	-0.523178783	3.149746969	-5.809350892	0.003398666	-0.012013318	0.030389314	-0.0211301	0.076738148	-0.196257805	0.039132421	-0.142503679	0.364874693
het_white_female	rcs(time_from_h1yy, 4)time_from_h1yy’’	-1.822535719	0.003187675	-0.002235759	-0.039507286	0.01066416	-0.036239622	0.090392375	0.918473109	-5.809350892	10.84581947	-0.006012736	0.021373282	-0.054173058	0.039189629	-0.142842265	0.365844796	-0.07342099	0.268100529	-0.687242383
het_white_female	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy	0.001324387	-2.99E-06	1.47E-05	-4.32E-05	-1.00E-05	4.02E-05	-0.000104971	-0.00069529	0.003398666	-0.006012736	5.60E-06	-2.26E-05	5.94E-05	-2.80E-05	0.000114191	-0.000300897	4.98E-05	-0.000203865	0.00053795
het_white_female	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy	-0.004438967	1.19E-05	-6.01E-05	0.000189493	4.01E-05	-0.000183975	0.000499454	0.002397903	-0.012013318	0.021373282	-2.26E-05	0.000103801	-0.000282419	0.000114411	-0.000528877	0.001446265	-0.000204408	0.00094759	-0.002595767
het_white_female	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy	0.010925183	-2.87E-05	0.000152572	-0.00049254	-0.000104527	0.000498723	-0.001369066	-0.006012602	0.030389314	-0.054173058	5.94E-05	-0.000282419	0.000777464	-0.0003017	0.001447468	-0.004009674	0.000539851	-0.002598191	0.007212669
het_white_female	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.006295426	1.06E-05	-2.54E-05	-8.13E-05	4.82E-05	-0.000193406	0.000506073	0.003406036	-0.0211301	0.039189629	-2.80E-05	0.000114411	-0.0003017	0.000179358	-0.000751472	0.002002106	-0.000335209	0.001409807	-0.003762408
het_white_female	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’	0.021862515	-5.21E-05	0.00014957	5.73E-05	-0.000193396	0.000881027	-0.002389569	-0.01203809	0.076738148	-0.142842265	0.000114191	-0.000528877	0.001447468	-0.000751472	0.003583165	-0.009940201	0.001411195	-0.006765229	0.018817781
het_white_female	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.054328067	0.000127674	-0.00040597	2.28E-05	0.000505503	-0.002386266	0.006543257	0.030459528	-0.196257805	0.365844796	-0.000300897	0.001446265	-0.004009674	0.002002106	-0.009940201	0.02799254	-0.003767274	0.018822494	-0.05317954
het_white_female	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.011121303	-1.52E-05	1.22E-05	0.000338742	-8.61E-05	0.000346081	-0.000905784	-0.006016665	0.039132421	-0.07342099	4.98E-05	-0.000204408	0.000539851	-0.000335209	0.001411195	-0.003767274	0.000634342	-0.002680783	0.007168885
het_white_female	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.039020034	8.86E-05	-0.00020286	-0.000502956	0.000345966	-0.001575691	0.004272704	0.02137262	-0.142503679	0.268100529	-0.000203865	0.00094759	-0.002598191	0.001409807	-0.006765229	0.018822494	-0.002680783	0.012943527	-0.03612055
het_white_female	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.097413986	-0.000231309	0.000659495	0.000450394	-0.000904227	0.00426514	-0.011690874	-0.054185192	0.364874693	-0.687242383	0.00053795	-0.002595767	0.007212669	-0.003762408	0.018817781	-0.05317954	0.007168885	-0.03612055	0.102462109
het_white_male	(Intercept)	4.025413077	-0.088237818	0.212541598	-0.739516678	-0.003679168	0.011801445	-0.016702758	0.010625661	-0.340849688	0.744757867	-0.000170584	0.001174384	-0.00200669	0.002208221	-0.008687654	0.013399363	-0.004312007	0.014096354	-0.020847599
het_white_male	rcs(age, 4)age	-0.088237818	0.002165956	-0.005419992	0.019259669	-1.09E-05	0.000274743	-0.00051207	-0.00151789	0.012338588	-0.027680169	1.87E-05	-0.000113658	0.000188455	-9.64E-05	0.000457983	-0.0007301	0.000202257	-0.000898914	0.001417275
het_white_male	rcs(age, 4)age’	0.212541598	-0.005419992	0.016770153	-0.065276406	-1.35E-05	-0.000287916	0.00057861	0.002762872	-0.030878841	0.071689794	-4.54E-05	0.000283369	-0.000471387	0.000253949	-0.001254032	0.002016716	-0.000541561	0.002471602	-0.003925428
het_white_male	rcs(age, 4)age’’	-0.739516678	0.019259669	-0.065276406	0.272643307	5.41E-05	0.000753129	-0.001543321	-0.008523456	0.10671132	-0.251268346	0.000158201	-0.001030956	0.001724601	-0.000995189	0.005285086	-0.008613938	0.002153436	-0.010632842	0.017149829
het_white_male	rcs(cd4n_ini, 4)cd4n_ini	-0.003679168	-1.09E-05	-1.35E-05	5.41E-05	6.14E-05	-0.000399052	0.000667935	0.000601027	-0.001677109	0.003808943	-9.00E-06	5.92E-05	-9.89E-05	2.56E-05	-0.00017066	0.000285523	-5.68E-05	0.000378376	-0.000633166
het_white_male	rcs(cd4n_ini, 4)cd4n_ini’	0.011801445	0.000274743	-0.000287916	0.000753129	-0.000399052	0.002809395	-0.00476759	-0.003693714	0.01085735	-0.024445958	6.09E-05	-0.000431284	0.000729848	-0.000179517	0.001291218	-0.002188935	0.000396232	-0.002854182	0.004840435
het_white_male	rcs(cd4n_ini, 4)cd4n_ini’’	-0.016702758	-0.00051207	0.00057861	-0.001543321	0.000667935	-0.00476759	0.008112087	0.00612664	-0.0181639	0.040850363	-0.000102465	0.000734096	-0.001245305	0.000303286	-0.002208445	0.003753326	-0.000669005	0.004879923	-0.008296986
het_white_male	rcs(time_from_h1yy, 4)time_from_h1yy	0.010625661	-0.00151789	0.002762872	-0.008523456	0.000601027	-0.003693714	0.00612664	0.043436827	-0.203943252	0.468847059	-0.000442538	0.002546828	-0.004184675	0.0020261	-0.011506347	0.018865765	-0.004630401	0.026228795	-0.042986828
het_white_male	rcs(time_from_h1yy, 4)time_from_h1yy’	-0.340849688	0.012338588	-0.030878841	0.10671132	-0.001677109	0.01085735	-0.0181639	-0.203943252	1.302211818	-3.169785382	0.002047313	-0.011777143	0.019361687	-0.012958745	0.073758715	-0.121030747	0.031534333	-0.179162312	0.293881199
het_white_male	rcs(time_from_h1yy, 4)time_from_h1yy’’	0.744757867	-0.027680169	0.071689794	-0.251268346	0.003808943	-0.024445958	0.040850363	0.468847059	-3.169785382	7.84181734	-0.004689708	0.02696395	-0.044328487	0.031618119	-0.180149958	0.295654746	-0.078282252	0.445319147	-0.730591752
het_white_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy	-0.000170584	1.87E-05	-4.54E-05	0.000158201	-9.00E-06	6.09E-05	-0.000102465	-0.000442538	0.002047313	-0.004689708	6.13E-06	-3.99E-05	6.67E-05	-2.71E-05	0.000174368	-0.000291458	6.17E-05	-0.000396923	0.000663445
het_white_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy	0.001174384	-0.000113658	0.000283369	-0.001030956	5.92E-05	-0.000431284	0.000734096	0.002546828	-0.011777143	0.02696395	-3.99E-05	0.000278655	-0.000472049	0.000175843	-0.001217374	0.002058918	-0.000400719	0.002775275	-0.004694082
het_white_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy	-0.00200669	0.000188455	-0.000471387	0.001724601	-9.89E-05	0.000729848	-0.001245305	-0.004184675	0.019361687	-0.044328487	6.67E-05	-0.000472049	0.000801472	-0.000294384	0.0020619	-0.003494568	0.000670948	-0.004701494	0.007968734
het_white_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’	0.002208221	-9.64E-05	0.000253949	-0.000995189	2.56E-05	-0.000179517	0.000303286	0.0020261	-0.012958745	0.031618119	-2.71E-05	0.000175843	-0.000294384	0.000174453	-0.001128953	0.001889218	-0.000427574	0.002768182	-0.004632492
het_white_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.008687654	0.000457983	-0.001254032	0.005285086	-0.00017066	0.001291218	-0.002208445	-0.011506347	0.073758715	-0.180149958	0.000174368	-0.001217374	0.0020619	-0.001128953	0.007832124	-0.013251271	0.002772686	-0.019248121	0.032568094
het_white_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’	0.013399363	-0.0007301	0.002016716	-0.008613938	0.000285523	-0.002188935	0.003753326	0.018865765	-0.121030747	0.295654746	-0.000291458	0.002058918	-0.003494568	0.001889218	-0.013251271	0.022462935	-0.004641204	0.032575339	-0.055223389
het_white_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.004312007	0.000202257	-0.000541561	0.002153436	-5.68E-05	0.000396232	-0.000669005	-0.004630401	0.031534333	-0.078282252	6.17E-05	-0.000400719	0.000670948	-0.000427574	0.002772686	-0.004641204	0.001067554	-0.006926099	0.011593928
het_white_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.014096354	-0.000898914	0.002471602	-0.010632842	0.000378376	-0.002854182	0.004879923	0.026228795	-0.179162312	0.445319147	-0.000396923	0.002775275	-0.004701494	0.002768182	-0.019248121	0.032575339	-0.006926099	0.048201887	-0.081585827
het_white_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.020847599	0.001417275	-0.003925428	0.017149829	-0.000633166	0.004840435	-0.008296986	-0.042986828	0.293881199	-0.730591752	0.000663445	-0.004694082	0.007968734	-0.004632492	0.032568094	-0.055223389	0.011593928	-0.081585827	0.138357657
idu_black_female	(Intercept)	16.71085601	-0.291740162	0.617122165	-2.270508062	-0.032582192	0.11919231	-0.293324796	-0.520335456	1.028030828	-2.685921249	0.004482607	-0.017938672	0.045147935	-0.008583643	0.032115344	-0.077204046	0.021091848	-0.07207595	0.165428381
idu_black_female	rcs(age, 4)age	-0.291740162	0.006313528	-0.014353174	0.05520369	0.000169526	-0.00049928	0.001108004	-0.000172209	0.005321371	-0.01417988	-4.59E-06	2.70E-05	-6.35E-05	-2.87E-05	0.000138954	-0.000443603	0.000100813	-0.000615399	0.001953637
idu_black_female	rcs(age, 4)age’	0.617122165	-0.014353174	0.045453016	-0.199595864	-0.000343974	0.001152631	-0.002723334	0.001060905	-0.009299803	0.020473364	1.13E-05	-0.000103771	0.000303057	9.77E-06	-5.35E-05	0.00021738	-6.80E-05	0.000809382	-0.002737063
idu_black_female	rcs(age, 4)age’’	-2.270508062	0.05520369	-0.199595864	0.976949788	0.001137022	-0.004299838	0.010524626	-0.017460933	0.047152048	-0.116999576	1.96E-05	0.000186526	-0.00070685	-5.92E-05	0.000201964	-0.000332058	0.000293399	-0.00346693	0.010516022
idu_black_female	rcs(cd4n_ini, 4)cd4n_ini	-0.032582192	0.000169526	-0.000343974	0.001137022	0.00024647	-0.001068307	0.002772717	0.004276908	-0.010039276	0.026177171	-4.36E-05	0.000193298	-0.000506678	9.80E-05	-0.000430736	0.001131708	-0.000247987	0.001076758	-0.002826919
idu_black_female	rcs(cd4n_ini, 4)cd4n_ini’	0.11919231	-0.00049928	0.001152631	-0.004299838	-0.001068307	0.004999409	-0.013271798	-0.016855106	0.039336314	-0.102030251	0.00019317	-0.000928482	0.002495776	-0.000432723	0.002073961	-0.005610632	0.001084739	-0.00514405	0.013930382
idu_black_female	rcs(cd4n_ini, 4)cd4n_ini’’	-0.293324796	0.001108004	-0.002723334	0.010524626	0.002772717	-0.013271798	0.035504867	0.042693264	-0.099544737	0.257894283	-0.000505601	0.002492051	-0.006762699	0.001134473	-0.00559535	0.015307531	-0.00284069	0.013884105	-0.038057443
idu_black_female	rcs(time_from_h1yy, 4)time_from_h1yy	-0.520335456	-0.000172209	0.001060905	-0.017460933	0.004276908	-0.016855106	0.042693264	0.180244893	-0.573819712	1.590062756	-0.001450238	0.005782344	-0.014740058	0.004517343	-0.017816536	0.045315983	-0.012400616	0.04876164	-0.123971249
idu_black_female	rcs(time_from_h1yy, 4)time_from_h1yy’	1.028030828	0.005321371	-0.009299803	0.047152048	-0.010039276	0.039336314	-0.099544737	-0.573819712	2.435995454	-7.292477179	0.004524885	-0.017884881	0.045485425	-0.019165581	0.075580583	-0.191877642	0.057400964	-0.226454824	0.574795209
idu_black_female	rcs(time_from_h1yy, 4)time_from_h1yy’’	-2.685921248	-0.01417988	0.020473364	-0.116999576	0.026177171	-0.102030251	0.257894283	1.590062756	-7.292477179	22.48583328	-0.012451329	0.049067974	-0.124684043	0.057435941	-0.226557419	0.574917372	-0.177696752	0.702628302	-1.783989
idu_black_female	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy	0.004482607	-4.59E-06	1.13E-05	1.96E-05	-4.36E-05	0.00019317	-0.000505601	-0.001450238	0.004524885	-0.012451329	1.52E-05	-7.00E-05	0.000185876	-4.53E-05	0.000206293	-0.000547038	0.000122101	-0.000552439	0.001463218
idu_black_female	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy	-0.017938672	2.70E-05	-0.000103771	0.000186526	0.000193298	-0.000928482	0.002492051	0.005782344	-0.017884881	0.049067974	-7.00E-05	0.00035699	-0.000977223	0.000206646	-0.001045835	0.002864186	-0.000553726	0.002785981	-0.007624354
idu_black_female	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy	0.045147935	-6.35E-05	0.000303057	-0.00070685	-0.000506678	0.002495776	-0.006762699	-0.014740058	0.045485425	-0.124684043	0.000185876	-0.000977223	0.002705858	-0.000547924	0.002864032	-0.007939559	0.001466597	-0.00762466	0.021127045
idu_black_female	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.008583643	-2.87E-05	9.77E-06	-5.92E-05	9.80E-05	-0.000432723	0.001134473	0.004517343	-0.019165581	0.057435941	-4.53E-05	0.000206646	-0.000547924	0.000188842	-0.000855447	0.002259051	-0.00056317	0.002544219	-0.006709148
idu_black_female	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’	0.032115344	0.000138954	-5.35E-05	0.000201964	-0.000430736	0.002073961	-0.00559535	-0.017816536	0.075580583	-0.226557419	0.000206293	-0.001045835	0.002864032	-0.000855447	0.004308394	-0.011738431	0.002545462	-0.01278497	0.034776869
idu_black_female	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.077204046	-0.000443603	0.00021738	-0.000332058	0.001131708	-0.005610632	0.015307531	0.045315983	-0.191877642	0.574917372	-0.000547038	0.002864186	-0.007939559	0.002259051	-0.011738431	0.032356389	-0.00671407	0.034783553	-0.095707761
idu_black_female	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.021091848	0.000100813	-6.80E-05	0.000293399	-0.000247987	0.001084739	-0.00284069	-0.012400616	0.057400964	-0.177696752	0.000122101	-0.000553726	0.001466597	-0.00056317	0.002545462	-0.00671407	0.001746171	-0.007895644	0.02081784
idu_black_female	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.072075949	-0.000615399	0.000809382	-0.003466931	0.001076758	-0.00514405	0.013884105	0.04876164	-0.226454824	0.702628302	-0.000552439	0.002785981	-0.00762466	0.002544219	-0.01278497	0.034783553	-0.007895644	0.039728409	-0.108070789
idu_black_female	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.165428381	0.001953637	-0.002737063	0.010516022	-0.002826919	0.013930382	-0.038057443	-0.123971249	0.574795209	-1.783989	0.001463218	-0.007624354	0.021127045	-0.006709148	0.034776869	-0.095707761	0.02081784	-0.108070789	0.297387023
idu_black_male	(Intercept)	3.697719525	-0.061229914	0.114325654	-0.481038983	-0.007687539	0.042404484	-0.083189725	-0.155169778	0.350319704	-0.89782883	0.001342635	-0.00724745	0.01402442	-0.002798045	0.014397981	-0.027601681	0.006713392	-0.033639558	0.064045113
idu_black_male	rcs(age, 4)age	-0.061229914	0.001340757	-0.002634816	0.011479653	1.55E-05	-0.000143686	0.000319784	-0.000145293	-1.44E-05	0.001184258	-2.06E-06	2.16E-05	-4.70E-05	3.53E-06	-2.90E-05	6.36E-05	-7.60E-06	4.43E-05	-9.44E-05
idu_black_male	rcs(age, 4)age’	0.114325654	-0.002634816	0.008221882	-0.041553898	-4.81E-05	0.000358098	-0.000766993	-0.001085199	0.001329667	-0.003398084	6.15E-06	-3.46E-05	6.86E-05	-1.46E-05	7.49E-05	-0.000160459	2.71E-05	-0.000175307	0.000403264
idu_black_male	rcs(age, 4)age’’	-0.481038983	0.011479653	-0.041553898	0.243566434	0.000178935	-0.001401101	0.003024875	0.005755619	-0.008950885	0.010275221	-2.26E-05	5.98E-05	-9.48E-05	7.47E-05	-0.000408459	0.000880821	-0.000163899	0.001580171	-0.00363844
idu_black_male	rcs(cd4n_ini, 4)cd4n_ini	-0.007687539	1.55E-05	-4.81E-05	0.000178935	7.01E-05	-0.000413962	0.000817428	0.001255464	-0.002628722	0.006324343	-1.19E-05	6.76E-05	-0.000131853	2.47E-05	-0.000140542	0.000273324	-5.97E-05	0.000341578	-0.000665108
idu_black_male	rcs(cd4n_ini, 4)cd4n_ini’	0.042404484	-0.000143686	0.000358098	-0.001401101	-0.000413962	0.002710393	-0.00548366	-0.006243252	0.012953503	-0.031294766	6.77E-05	-0.000426345	0.000850328	-0.000140799	0.000893444	-0.001778628	0.000342263	-0.002199826	0.004388823
idu_black_male	rcs(cd4n_ini, 4)cd4n_ini’’	-0.083189725	0.000319784	-0.000766993	0.003024875	0.000817428	-0.00548366	0.01116545	0.011833335	-0.024488683	0.059237175	-0.000132134	0.000851779	-0.001708728	0.000274576	-0.001784599	0.003573974	-0.000668495	0.004405173	-0.008843196
idu_black_male	rcs(time_from_h1yy, 4)time_from_h1yy	-0.155169778	-0.000145293	-0.001085199	0.005755619	0.001255464	-0.006243252	0.011833335	0.060395445	-0.171574003	0.447982824	-0.000472646	0.002410506	-0.004592819	0.001369141	-0.0070601	0.013496322	-0.003597169	0.018653089	-0.035708711
idu_black_male	rcs(time_from_h1yy, 4)time_from_h1yy’	0.350319704	-1.44E-05	0.001329667	-0.008950885	-0.002628722	0.012953503	-0.024488683	-0.171574003	0.638698468	-1.81074608	0.001362853	-0.007027266	0.013433359	-0.005209951	0.027419142	-0.052718819	0.014895974	-0.078924616	0.151999601
idu_black_male	rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.89782883	0.001184258	-0.003398084	0.010275221	0.006324343	-0.031294766	0.059237175	0.447982824	-1.81074608	5.311267565	-0.003580141	0.018561621	-0.03553305	0.014878463	-0.078804514	0.151767883	-0.044027335	0.234978495	-0.45335746
idu_black_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy	0.001342635	-2.06E-06	6.15E-06	-2.26E-05	-1.19E-05	6.77E-05	-0.000132134	-0.000472646	0.001362853	-0.003580141	4.74E-06	-2.77E-05	5.43E-05	-1.39E-05	8.23E-05	-0.000161831	3.67E-05	-0.000218729	0.000430896
idu_black_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy	-0.00724745	2.16E-05	-3.46E-05	5.98E-05	6.76E-05	-0.000426345	0.000851779	0.002410506	-0.007027266	0.018561621	-2.77E-05	0.00017894	-0.000358605	8.22E-05	-0.000540543	0.001088495	-0.000218631	0.001448718	-0.002922385
idu_black_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy	0.01402442	-4.70E-05	6.86E-05	-9.48E-05	-0.000131853	0.000850328	-0.001708728	-0.004592819	0.013433359	-0.03553305	5.43E-05	-0.000358605	0.000722819	-0.0001618	0.001088879	-0.002206625	0.000430868	-0.002923887	0.005936436
idu_black_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.002798045	3.53E-06	-1.46E-05	7.47E-05	2.47E-05	-0.000140799	0.000274576	0.001369141	-0.005209951	0.014878463	-1.39E-05	8.22E-05	-0.0001618	5.54E-05	-0.00033722	0.000668602	-0.000160562	0.000986985	-0.001960905
idu_black_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’	0.014397981	-2.90E-05	7.49E-05	-0.000408459	-0.000140542	0.000893444	-0.001784599	-0.0070601	0.027419142	-0.078804514	8.23E-05	-0.000540543	0.001088879	-0.00033722	0.002290715	-0.00465615	0.000987181	-0.006792536	0.013841969
idu_black_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.027601681	6.36E-05	-0.000160459	0.000880821	0.000273324	-0.001778628	0.003573974	0.013496322	-0.052718819	0.151767883	-0.000161831	0.001088495	-0.002206625	0.000668602	-0.00465615	0.009530344	-0.001961567	0.013843799	-0.028409347
idu_black_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.006713392	-7.60E-06	2.71E-05	-0.000163899	-5.97E-05	0.000342263	-0.000668495	-0.003597169	0.014895974	-0.044027335	3.67E-05	-0.000218631	0.000430868	-0.000160562	0.000987181	-0.001961567	0.000484071	-0.003013276	0.006002318
idu_black_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.033639558	4.43E-05	-0.000175307	0.001580171	0.000341578	-0.002199826	0.004405173	0.018653089	-0.078924616	0.234978495	-0.000218729	0.001448718	-0.002923887	0.000986985	-0.006792536	0.013843799	-0.003013276	0.021078051	-0.043085268
idu_black_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.064045114	-9.44E-05	0.000403264	-0.00363844	-0.000665108	0.004388823	-0.008843196	-0.035708711	0.151999601	-0.45335746	0.000430896	-0.002922385	0.005936436	-0.001960905	0.013841969	-0.028409347	0.006002318	-0.043085268	0.088684631
idu_hisp_female	(Intercept)	70.67739095	-1.352107754	2.729117475	-10.71924503	-0.113774973	0.339862175	-0.856473465	-7.235453647	42.54203375	-68.49605353	0.055468518	-0.170678024	0.42592407	-0.303134572	0.878966501	-2.154757507	0.484822058	-1.384115661	3.378149917
idu_hisp_female	rcs(age, 4)age	-1.352107754	0.031221575	-0.062147251	0.242665678	0.000673101	-0.002056952	0.005411364	0.035860301	-0.196450126	0.303448241	-0.000350347	0.001131739	-0.002801831	0.001376299	-0.003199055	0.006868809	-0.002052958	0.004163317	-0.008292098
idu_hisp_female	rcs(age, 4)age’	2.729117475	-0.062147251	0.171687805	-0.748862117	-0.003196824	0.009305214	-0.022900852	-0.129782353	0.620315401	-0.932236708	0.00112038	-0.003065973	0.006957529	-0.005193379	0.010674651	-0.019561029	0.008116524	-0.015923902	0.02784287
idu_hisp_female	rcs(age, 4)age’’	-10.71924503	0.242665678	-0.748862117	3.432015865	0.015017607	-0.041884011	0.100181431	0.608243558	-2.887945418	4.224957022	-0.005282476	0.013406163	-0.028844602	0.026013835	-0.050514445	0.085350345	-0.040796471	0.077470265	-0.126463181
idu_hisp_female	rcs(cd4n_ini, 4)cd4n_ini	-0.113774973	0.000673101	-0.003196824	0.015017607	0.000776382	-0.002598322	0.006687216	0.043439156	-0.256961706	0.416930819	-0.000347683	0.001133987	-0.002896537	0.002070009	-0.006700107	0.017032501	-0.003359181	0.010859837	-0.027582659
idu_hisp_female	rcs(cd4n_ini, 4)cd4n_ini’	0.339862175	-0.002056952	0.009305214	-0.041884011	-0.002598322	0.010040104	-0.02717482	-0.131815913	0.785691944	-1.277679016	0.001144156	-0.004196393	0.011185034	-0.006811571	0.02461336	-0.065057481	0.011054355	-0.039838492	0.105136717
idu_hisp_female	rcs(cd4n_ini, 4)cd4n_ini’’	-0.856473465	0.005411364	-0.022900852	0.100181431	0.006687216	-0.02717482	0.075017354	0.3293954	-1.967747782	3.20262063	-0.002926857	0.011191258	-0.030346541	0.017380262	-0.065173664	0.174937396	-0.028197605	0.105361135	-0.282269501
idu_hisp_female	rcs(time_from_h1yy, 4)time_from_h1yy	-7.235453647	0.035860301	-0.129782353	0.608243558	0.043439156	-0.131815913	0.3293954	4.026054258	-25.65603544	42.0800195	-0.028169699	0.083228988	-0.20647084	0.179954112	-0.531732267	1.318326413	-0.29514177	0.872119047	-2.161584013
idu_hisp_female	rcs(time_from_h1yy, 4)time_from_h1yy’	42.54203375	-0.196450126	0.620315401	-2.887945417	-0.256961706	0.785691944	-1.967747782	-25.65603544	169.0208809	-277.9071009	0.179850916	-0.53509163	1.331997553	-1.190197765	3.554625875	-8.852300443	1.9578726	-5.851579805	14.57084413
idu_hisp_female	rcs(time_from_h1yy, 4)time_from_h1yy’’	-68.49605353	0.303448241	-0.932236708	4.22495702	0.416930819	-1.277679016	3.20262063	42.0800195	-277.9071009	457.8507434	-0.294870593	0.87884547	-2.189690611	1.957582997	-5.863037354	14.61842778	-3.225961208	9.669042918	-24.10453961
idu_hisp_female	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy	0.055468518	-0.000350347	0.00112038	-0.005282476	-0.000347683	0.001144156	-0.002926857	-0.028169699	0.179850916	-0.294870593	0.000217553	-0.000691988	0.001755792	-0.001384789	0.00439557	-0.011140432	0.002268383	-0.00719792	0.018235541
idu_hisp_female	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy	-0.170678024	0.001131739	-0.003065973	0.013406163	0.001133987	-0.004196393	0.011191258	0.083228988	-0.53509163	0.87884547	-0.000691988	0.002451691	-0.006475724	0.004419589	-0.015605971	0.041136633	-0.007243213	0.025555057	-0.067314562
idu_hisp_female	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy	0.42592407	-0.002801831	0.006957529	-0.028844602	-0.002896537	0.011185034	-0.030346541	-0.20647084	1.331997553	-2.189690611	0.001755792	-0.006475724	0.017398444	-0.011234335	0.041255475	-0.110550953	0.018416652	-0.067548687	0.180846426
idu_hisp_female	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.303134572	0.001376299	-0.005193379	0.026013835	0.002070009	-0.006811571	0.017380262	0.179954112	-1.190197765	1.957582997	-0.001384789	0.004419589	-0.011234335	0.00925987	-0.029785447	0.075801004	-0.015254967	0.049144856	-0.125070303
idu_hisp_female	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’	0.878966501	-0.003199055	0.010674651	-0.050514444	-0.006700107	0.02461336	-0.065173664	-0.531732267	3.554625874	-5.863037354	0.00439557	-0.015605971	0.041255475	-0.029785447	0.106894436	-0.282786366	0.049193018	-0.176877143	0.467827493
idu_hisp_female	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’	-2.154757506	0.006868809	-0.019561029	0.085350345	0.017032501	-0.065057481	0.174937396	1.318326413	-8.852300442	14.61842778	-0.011140432	0.041136633	-0.110550953	0.075801004	-0.282786366	0.759899096	-0.125279153	0.468110413	-1.25735166
idu_hisp_female	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.484822058	-0.002052958	0.008116524	-0.040796471	-0.003359181	0.011054355	-0.028197605	-0.29514177	1.9578726	-3.225961208	0.002268383	-0.007243213	0.018416652	-0.015254967	0.049193018	-0.125279153	0.025182485	-0.081359038	0.207207194
idu_hisp_female	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’’	-1.384115661	0.004163317	-0.015923902	0.077470265	0.010859837	-0.039838492	0.105361135	0.872119047	-5.851579804	9.669042918	-0.00719792	0.025555057	-0.067548687	0.049144856	-0.176877143	0.468110413	-0.081359038	0.293559986	-0.776810295
idu_hisp_female	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’’	3.378149916	-0.008292098	0.02784287	-0.126463181	-0.027582659	0.105136717	-0.282269501	-2.161584013	14.57084412	-24.10453961	0.018235541	-0.067314562	0.180846426	-0.125070303	0.467827493	-1.25735166	0.207207194	-0.776810295	2.086998362
idu_hisp_male	(Intercept)	13.57933102	-0.275806867	0.6697234	-2.396802181	-0.02028895	0.066780342	-0.14595265	-0.264968821	-0.801450002	2.902819103	0.002481751	-0.008353277	0.01806529	0.001685174	0.000265499	-0.006228065	-0.010544399	0.016795252	-0.017110231
idu_hisp_male	rcs(age, 4)age	-0.275806867	0.00668627	-0.016698294	0.060889843	8.63E-05	-0.000179085	0.000390932	-0.002421457	0.039346648	-0.111520686	1.52E-05	-7.93E-05	0.000186705	-0.000237219	0.000790538	-0.001657265	0.000686647	-0.002213139	0.004552825
idu_hisp_male	rcs(age, 4)age’	0.6697234	-0.016698294	0.053213149	-0.216753063	-0.000292495	0.000654776	-0.001314208	0.001196743	-0.081470048	0.245837729	-1.95E-05	0.000176754	-0.000456595	0.000483865	-0.001718052	0.003638832	-0.001485645	0.004980867	-0.010139123
idu_hisp_male	rcs(age, 4)age’’	-2.396802181	0.060889843	-0.216753063	0.949134057	0.000942009	-0.001764004	0.003303726	-0.003405298	0.279315188	-0.865203112	0.000121943	-0.000909008	0.002262223	-0.001645206	0.0054793	-0.010859122	0.00500573	-0.015322344	0.02811624
idu_hisp_male	rcs(cd4n_ini, 4)cd4n_ini	-0.02028895	8.63E-05	-0.000292495	0.000942009	0.000175374	-0.000711685	0.001604289	0.003129153	-0.007417278	0.015612849	-3.65E-05	0.000155159	-0.000353197	0.00010599	-0.000478355	0.001108592	-0.000237919	0.001097904	-0.00256638
idu_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’	0.066780342	-0.000179085	0.000654776	-0.001764004	-0.000711685	0.003156033	-0.007278398	-0.011536302	0.029785266	-0.064921581	0.000154951	-0.000705995	0.001636651	-0.000472586	0.002246069	-0.005282556	0.001077687	-0.005202138	0.012325263
idu_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’’	-0.14595265	0.000390932	-0.001314208	0.003303726	0.001604289	-0.007278398	0.016895056	0.025382061	-0.066750641	0.146448281	-0.00035231	0.001634766	-0.003810623	0.001085558	-0.005239992	0.012395083	-0.002482564	0.012156516	-0.028961488
idu_hisp_male	rcs(time_from_h1yy, 4)time_from_h1yy	-0.264968821	-0.002421457	0.001196743	-0.003405298	0.003129153	-0.011536302	0.025382061	0.216895391	-0.866014525	2.026631201	-0.001682326	0.006024946	-0.013198868	0.006580246	-0.023293425	0.050989155	-0.015335877	0.0542088	-0.11870046
idu_hisp_male	rcs(time_from_h1yy, 4)time_from_h1yy’	-0.801450002	0.039346648	-0.081470048	0.279315188	-0.007417278	0.029785266	-0.066750641	-0.866014525	4.493659329	-11.16147599	0.006514292	-0.023085301	0.050507799	-0.032754403	0.11392839	-0.249027557	0.081335035	-0.282872499	0.618969308
idu_hisp_male	rcs(time_from_h1yy, 4)time_from_h1yy’’	2.902819103	-0.111520686	0.245837729	-0.865203112	0.015612849	-0.064921581	0.146448281	2.026631201	-11.16147599	28.16963577	-0.015189253	0.053772172	-0.117652436	0.081272585	-0.282661473	0.618189389	-0.205987156	0.718518325	-1.575170176
idu_hisp_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy	0.002481751	1.52E-05	-1.95E-05	0.000121943	-3.65E-05	0.000154951	-0.00035231	-0.001682326	0.006514292	-0.015189253	1.75E-05	-7.25E-05	0.000164508	-6.67E-05	0.000276609	-0.000629583	0.00015535	-0.000645336	0.001471131
idu_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy	-0.008353277	-7.93E-05	0.000176754	-0.000909008	0.000155159	-0.000705995	0.001634766	0.006024946	-0.023085301	0.053772172	-7.25E-05	0.000326118	-0.00075518	0.000275543	-0.001250713	0.00291549	-0.000642093	0.002924618	-0.006830986
idu_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy	0.01806529	0.000186705	-0.000456595	0.002262223	-0.000353197	0.001636651	-0.003810623	-0.013198868	0.050507799	-0.117652436	0.000164508	-0.00075518	0.001759544	-0.000625523	0.002908022	-0.006829267	0.00145881	-0.006809529	0.01602887
idu_hisp_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’	0.001685174	-0.000237219	0.000483865	-0.001645206	0.00010599	-0.000472586	0.001085558	0.006580246	-0.032754403	0.081272585	-6.67E-05	0.000275543	-0.000625523	0.000320307	-0.001319377	0.003011545	-0.000796648	0.003290206	-0.007527875
idu_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’	0.000265499	0.000790538	-0.001718052	0.0054793	-0.000478355	0.002246069	-0.005239992	-0.023293425	0.11392839	-0.282661473	0.000276609	-0.001250713	0.002908022	-0.001319377	0.006080191	-0.014324031	0.003288701	-0.015232455	0.036016972
idu_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.006228065	-0.001657265	0.003638832	-0.010859122	0.001108592	-0.005282556	0.012395083	0.050989155	-0.249027557	0.618189389	-0.000629583	0.00291549	-0.006829267	0.003011545	-0.014324031	0.034123201	-0.007518502	0.035983345	-0.086101024
idu_hisp_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.010544399	0.000686647	-0.001485645	0.00500573	-0.000237919	0.001077687	-0.002482564	-0.015335877	0.081335035	-0.205987156	0.00015535	-0.000642093	0.00145881	-0.000796648	0.003288701	-0.007518502	0.002035409	-0.00844799	0.019385874
idu_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.016795252	-0.002213139	0.004980867	-0.015322344	0.001097904	-0.005202138	0.012156516	0.0542088	-0.282872499	0.718518325	-0.000645336	0.002924618	-0.006809529	0.003290206	-0.015232455	0.035983345	-0.00844799	0.039399364	-0.093568388
idu_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.017110231	0.004552825	-0.010139123	0.02811624	-0.00256638	0.012325263	-0.028961488	-0.11870046	0.618969308	-1.575170176	0.001471131	-0.006830986	0.01602887	-0.007527875	0.036016972	-0.086101024	0.019385874	-0.093568388	0.225135663
idu_white_female	(Intercept)	15.20983078	-0.291864803	0.858201167	-3.248279373	-0.033427911	0.111404639	-0.252548263	-1.550688193	6.08358855	-16.92230161	0.012057639	-0.041471349	0.094356075	-0.047033498	0.159897684	-0.36180937	0.129931811	-0.433469959	0.969297218
idu_white_female	rcs(age, 4)age	-0.291864803	0.007602589	-0.023521449	0.091801663	9.41E-05	-0.000119627	0.000114489	0.01118308	-0.04881653	0.135708813	-8.94E-05	0.00026887	-0.000566536	0.000398404	-0.001222972	0.002590064	-0.001100975	0.00319527	-0.006458369
idu_white_female	rcs(age, 4)age’	0.858201167	-0.023521449	0.096952773	-0.420259309	-8.72E-05	-0.000507062	0.001736201	-0.037387004	0.164021868	-0.456737062	0.00022028	-0.000493345	0.000861154	-0.001125713	0.002844192	-0.005439904	0.003102556	-0.006780235	0.011377725
idu_white_female	rcs(age, 4)age’’	-3.248279373	0.091801663	-0.420259309	1.942841587	-0.000609679	0.006367994	-0.017509406	0.141475466	-0.608026917	1.666706456	-0.000731818	0.001275843	-0.00169932	0.003747081	-0.007588105	0.01218492	-0.010091201	0.014830412	-0.014571252
idu_white_female	rcs(cd4n_ini, 4)cd4n_ini	-0.033427911	9.41E-05	-8.72E-05	-0.000609679	0.000264806	-0.001034509	0.002457172	0.008544432	-0.031518222	0.087094486	-7.43E-05	0.000284969	-0.00067323	0.000266465	-0.000993824	0.002332189	-0.000727383	0.002682746	-0.00627239
idu_white_female	rcs(cd4n_ini, 4)cd4n_ini’	0.111404639	-0.000119627	-0.000507062	0.006367994	-0.001034509	0.004400216	-0.010728268	-0.029956737	0.108012608	-0.296466248	0.000280278	-0.001151769	0.002782277	-0.000971019	0.003798606	-0.009066315	0.002622053	-0.010065951	0.0238845
idu_white_female	rcs(cd4n_ini, 4)cd4n_ini’’	-0.252548263	0.000114489	0.001736201	-0.017509406	0.002457172	-0.010728268	0.026394579	0.069113619	-0.247553517	0.678122643	-0.000658739	0.00276914	-0.006746467	0.002260986	-0.008996191	0.021637411	-0.006086157	0.023710326	-0.05666806
idu_white_female	rcs(time_from_h1yy, 4)time_from_h1yy	-1.550688193	0.01118308	-0.037387004	0.141475466	0.008544432	-0.029956737	0.069113619	0.588516118	-2.549299252	7.22089687	-0.004085471	0.013826777	-0.031653439	0.017049076	-0.056376735	0.12834698	-0.047699511	0.156331299	-0.354984154
idu_white_female	rcs(time_from_h1yy, 4)time_from_h1yy’	6.08358855	-0.04881653	0.164021868	-0.608026917	-0.031518222	0.108012608	-0.247553517	-2.549299252	12.36516015	-35.86725429	0.016905944	-0.055385028	0.125603175	-0.079768212	0.259374279	-0.588808002	0.229301784	-0.743053591	1.68616082
idu_white_female	rcs(time_from_h1yy, 4)time_from_h1yy’’	-16.92230161	0.135708813	-0.456737062	1.666706456	0.087094486	-0.296466248	0.678122643	7.22089687	-35.86725429	104.6911276	-0.047303587	0.153586008	-0.347356331	0.229495477	-0.743724377	1.687462551	-0.66476024	2.152171089	-4.885656692
idu_white_female	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy	0.012057639	-8.94E-05	0.00022028	-0.000731818	-7.43E-05	0.000280278	-0.000658739	-0.004085471	0.016905944	-0.047303587	3.45E-05	-0.000131644	0.000311548	-0.000137169	0.000515248	-0.001216846	0.00037912	-0.001416777	0.003342691
idu_white_female	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy	-0.041471349	0.00026887	-0.000493345	0.001275843	0.000284969	-0.001151769	0.00276914	0.013826777	-0.055385028	0.153586008	-0.000131644	0.000554142	-0.001352832	0.000511117	-0.002133422	0.005208251	-0.00140469	0.005847155	-0.014270451
idu_white_female	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy	0.094356075	-0.000566536	0.000861154	-0.00169932	-0.00067323	0.002782277	-0.006746467	-0.031653439	0.125603175	-0.347356331	0.000311548	-0.001352832	0.003340105	-0.00120354	0.005194387	-0.012836812	0.003303365	-0.014227738	0.035158798
idu_white_female	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.047033498	0.000398404	-0.001125713	0.003747081	0.000266465	-0.000971019	0.002260986	0.017049076	-0.079768212	0.229495477	-0.000137169	0.000511117	-0.00120354	0.000635564	-0.002415444	0.005746393	-0.001823769	0.006975521	-0.016640947
idu_white_female	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’	0.159897684	-0.001222972	0.002844192	-0.007588105	-0.000993824	0.003798606	-0.008996191	-0.056376735	0.259374279	-0.743724377	0.000515248	-0.002133422	0.005194387	-0.002415444	0.010478909	-0.025970261	0.006971767	-0.030703181	0.076455101
idu_white_female	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.36180937	0.002590064	-0.005439904	0.01218492	0.002332189	-0.009066315	0.021637411	0.12834698	-0.588808002	1.687462551	-0.001216846	0.005208251	-0.012836812	0.005746393	-0.025970261	0.065336838	-0.016627839	0.076439767	-0.193326283
idu_white_female	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.129931811	-0.001100975	0.003102556	-0.010091201	-0.000727383	0.002622053	-0.006086157	-0.047699511	0.229301784	-0.66476024	0.00037912	-0.00140469	0.003303365	-0.001823769	0.006971767	-0.016627839	0.005295397	-0.020479135	0.049055879
idu_white_female	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.433469959	0.00319527	-0.006780235	0.014830412	0.002682746	-0.010065951	0.023710326	0.156331299	-0.743053591	2.152171089	-0.001416777	0.005847155	-0.014227738	0.006975521	-0.030703181	0.076439767	-0.020479135	0.092266022	-0.231287212
idu_white_female	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.969297218	-0.006458369	0.011377725	-0.014571252	-0.00627239	0.0238845	-0.05666806	-0.354984154	1.68616082	-4.885656692	0.003342691	-0.014270451	0.035158798	-0.016640947	0.076455101	-0.193326283	0.049055879	-0.231287212	0.589169149
idu_white_male	(Intercept)	3.040176631	-0.061004318	0.129912211	-0.528310419	-0.005907498	0.021933409	-0.047231127	-0.192398561	0.662638393	-1.531753429	0.001524036	-0.00626908	0.013848844	-0.005422849	0.024463477	-0.055558611	0.012620143	-0.05875101	0.134674564
idu_white_male	rcs(age, 4)age	-0.061004318	0.001669951	-0.003799003	0.0157618	-6.44E-07	5.80E-05	-0.000158666	0.000489844	-0.003300955	0.009179889	-4.74E-06	1.93E-05	-4.11E-05	3.42E-05	-0.000197991	0.000473754	-9.17E-05	0.000557462	-0.001352286
idu_white_male	rcs(age, 4)age’	0.129912211	-0.003799003	0.010882882	-0.049445628	1.58E-05	-0.000160476	0.000404479	-0.001131313	0.005617235	-0.017049091	5.53E-06	-1.68E-05	3.17E-05	-5.86E-05	0.000368161	-0.000902094	0.000172797	-0.001143917	0.002841363
idu_white_male	rcs(age, 4)age’’	-0.528310419	0.0157618	-0.049445628	0.244939959	-8.75E-05	0.000803924	-0.002016422	0.005522768	-0.027861573	0.082219812	-2.27E-05	3.03E-05	-2.43E-05	0.000232175	-0.001386615	0.00338273	-0.000726219	0.004689845	-0.011651657
idu_white_male	rcs(cd4n_ini, 4)cd4n_ini	-0.005907498	-6.44E-07	1.58E-05	-8.75E-05	5.57E-05	-0.00025819	0.000589209	0.001320775	-0.004073785	0.009054465	-1.22E-05	5.66E-05	-0.000129756	3.73E-05	-0.000172052	0.00039431	-8.27E-05	0.000381444	-0.000874156
idu_white_male	rcs(cd4n_ini, 4)cd4n_ini’	0.021933409	5.80E-05	-0.000160476	0.000803924	-0.00025819	0.001322243	-0.003098312	-0.005393355	0.01659163	-0.036962694	5.61E-05	-0.000288049	0.000680075	-0.000169655	0.000863044	-0.002036671	0.000375547	-0.001903718	0.004492214
idu_white_male	rcs(cd4n_ini, 4)cd4n_ini’’	-0.047231127	-0.000158666	0.000404479	-0.002016422	0.000589209	-0.003098312	0.007316956	0.011935997	-0.036690906	0.081798155	-0.000128134	0.000677597	-0.001614591	0.000386931	-0.002025957	0.004827489	-0.000856145	0.004467009	-0.010646131
idu_white_male	rcs(time_from_h1yy, 4)time_from_h1yy	-0.192398561	0.000489844	-0.001131313	0.005522768	0.001320775	-0.005393355	0.011935997	0.073694467	-0.251988134	0.570698639	-0.000563967	0.002333445	-0.005188758	0.001935672	-0.008038577	0.01789289	-0.004389776	0.018257951	-0.040661079
idu_white_male	rcs(time_from_h1yy, 4)time_from_h1yy’	0.662638393	-0.003300955	0.005617235	-0.027861573	-0.004073785	0.01659163	-0.036690906	-0.251988134	1.050091358	-2.525082056	0.001942656	-0.008052701	0.017910543	-0.008180144	0.034274415	-0.076365807	0.019747471	-0.083048925	0.185206139
idu_white_male	rcs(time_from_h1yy, 4)time_from_h1yy’’	-1.531753429	0.009179889	-0.017049091	0.082219812	0.009054465	-0.036962694	0.081798155	0.570698639	-2.525082056	6.22962739	-0.004403678	0.018269027	-0.040640207	0.019745321	-0.083007709	0.185063499	-0.048938262	0.206744363	-0.461554366
idu_white_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy	0.001524036	-4.74E-06	5.53E-06	-2.27E-05	-1.22E-05	5.61E-05	-0.000128134	-0.000563967	0.001942656	-0.004403678	5.28E-06	-2.48E-05	5.71E-05	-1.84E-05	8.74E-05	-0.000201465	4.20E-05	-0.000199477	0.000460153
idu_white_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy	-0.00626908	1.93E-05	-1.68E-05	3.03E-05	5.66E-05	-0.000288049	0.000677597	0.002333445	-0.008052701	0.018269027	-2.48E-05	0.00012951	-0.000306977	8.72E-05	-0.000460039	0.001092588	-0.000198932	0.001052654	-0.002502034
idu_white_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy	0.013848844	-4.11E-05	3.17E-05	-2.43E-05	-0.000129756	0.000680075	-0.001614591	-0.005188758	0.017910543	-0.040640207	5.71E-05	-0.000306977	0.000734549	-0.000200939	0.001091446	-0.00261667	0.000458323	-0.002498369	0.005994325
idu_white_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.005422849	3.42E-05	-5.86E-05	0.000232175	3.73E-05	-0.000169655	0.000386931	0.001935672	-0.008180144	0.019745321	-1.84E-05	8.72E-05	-0.000200939	8.21E-05	-0.000397835	0.000919205	-0.000200327	0.000977602	-0.002261475
idu_white_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’	0.024463477	-0.000197991	0.000368161	-0.001386615	-0.000172052	0.000863044	-0.002025957	-0.008038577	0.034274415	-0.083007709	8.74E-05	-0.000460039	0.001091446	-0.000397835	0.00215053	-0.005112258	0.000976922	-0.005321357	0.012663518
idu_white_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.055558611	0.000473754	-0.000902094	0.00338273	0.00039431	-0.002036671	0.004827489	0.01789289	-0.076365807	0.185063499	-0.000201465	0.001092588	-0.00261667	0.000919205	-0.005112258	0.01225765	-0.002259089	0.01265858	-0.030378915
idu_white_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.012620143	-9.17E-05	0.000172797	-0.000726219	-8.27E-05	0.000375547	-0.000856145	-0.004389776	0.019747471	-0.048938262	4.20E-05	-0.000198932	0.000458323	-0.000200327	0.000976922	-0.002259089	0.000503236	-0.002475272	0.005734597
idu_white_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.05875101	0.000557462	-0.001143917	0.004689845	0.000381444	-0.001903718	0.004467009	0.018257951	-0.083048925	0.206744363	-0.000199477	0.001052654	-0.002498369	0.000977602	-0.005321357	0.01265858	-0.002475272	0.013612961	-0.032444869
idu_white_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.134674564	-0.001352286	0.002841363	-0.011651657	-0.000874156	0.004492214	-0.010646131	-0.040661079	0.185206139	-0.461554366	0.000460153	-0.002502034	0.005994325	-0.002261475	0.012663518	-0.030378915	0.005734597	-0.032444869	0.077975321
msm_black_male	(Intercept)	0.510439803	-0.012532841	0.04274991	-0.100486724	-0.001048869	0.003576952	-0.00793257	-0.037332491	0.181987496	-0.380550672	0.000278223	-0.000973911	0.002187023	-0.001370345	0.005175135	-0.011912284	0.002873419	-0.011080359	0.02566751
msm_black_male	rcs(age, 4)age	-0.012532841	0.000410204	-0.001476995	0.003521885	6.41E-06	-1.63E-05	3.15E-05	0.00018229	-0.000841528	0.001735081	-1.76E-06	4.87E-06	-1.01E-05	8.66E-06	-3.44E-05	8.04E-05	-1.80E-05	7.81E-05	-0.000186482
msm_black_male	rcs(age, 4)age’	0.04274991	-0.001476995	0.006366558	-0.01601669	-1.90E-05	5.45E-05	-0.000111884	-0.00093508	0.004129828	-0.008125798	6.86E-06	-1.74E-05	3.44E-05	-3.50E-05	0.00012511	-0.000279766	7.33E-05	-0.000289829	0.000666149
msm_black_male	rcs(age, 4)age’’	-0.100486724	0.003521885	-0.01601669	0.041406183	4.22E-05	-0.000123431	0.000255177	0.002323452	-0.011118113	0.021635687	-1.69E-05	4.34E-05	-8.66E-05	8.84E-05	-0.000306418	0.00067574	-0.000186919	0.000718311	-0.001629553
msm_black_male	rcs(cd4n_ini, 4)cd4n_ini	-0.001048869	6.41E-06	-1.90E-05	4.22E-05	7.56E-06	-3.14E-05	7.38E-05	0.00022654	-0.001119644	0.002353364	-1.98E-06	8.23E-06	-1.94E-05	1.00E-05	-4.27E-05	0.000101598	-2.12E-05	9.11E-05	-0.000217572
msm_black_male	rcs(cd4n_ini, 4)cd4n_ini’	0.003576952	-1.63E-05	5.45E-05	-0.000123431	-3.14E-05	0.000142562	-0.000344582	-0.000825501	0.004129699	-0.008718223	8.21E-06	-3.72E-05	8.99E-05	-4.23E-05	0.000197398	-0.000483285	9.03E-05	-0.000424654	0.001042762
msm_black_male	rcs(cd4n_ini, 4)cd4n_ini’’	-0.00793257	3.15E-05	-0.000111884	0.000255177	7.38E-05	-0.000344582	0.000840521	0.001875242	-0.009427932	0.01993576	-1.93E-05	8.98E-05	-0.000219336	0.000100499	-0.000481652	0.001191217	-0.000214871	0.001038648	-0.002576768
msm_black_male	rcs(time_from_h1yy, 4)time_from_h1yy	-0.037332491	0.00018229	-0.00093508	0.002323452	0.00022654	-0.000825501	0.001875242	0.018694686	-0.109934421	0.23807794	-0.00012959	0.000470858	-0.001067043	0.00076784	-0.002812917	0.006393958	-0.001665655	0.006117081	-0.013916802
msm_black_male	rcs(time_from_h1yy, 4)time_from_h1yy’	0.181987496	-0.000841528	0.004129828	-0.011118113	-0.001119644	0.004129699	-0.009427932	-0.109934421	0.83711361	-1.91059048	0.000767784	-0.002810247	0.006385426	-0.005883903	0.021752213	-0.049602746	0.013463907	-0.04991035	0.113913881
msm_black_male	rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.380550672	0.001735081	-0.008125798	0.021635687	0.002353364	-0.008718223	0.01993576	0.23807794	-1.91059048	4.41485102	-0.001665552	0.00610805	-0.013888183	0.013461776	-0.049893064	0.113868694	-0.031203489	0.116008172	-0.265021794
msm_black_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy	0.000278223	-1.76E-06	6.86E-06	-1.69E-05	-1.98E-06	8.21E-06	-1.93E-05	-0.00012959	0.000767784	-0.001665552	1.13E-06	-4.69E-06	1.10E-05	-6.81E-06	2.86E-05	-6.74E-05	1.48E-05	-6.26E-05	0.000147747
msm_black_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy	-0.000973911	4.87E-06	-1.74E-05	4.34E-05	8.23E-06	-3.72E-05	8.98E-05	0.000470858	-0.002810247	0.00610805	-4.69E-06	2.11E-05	-5.08E-05	2.85E-05	-0.000130597	0.000315884	-6.24E-05	0.000287152	-0.000695612
msm_black_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy	0.002187023	-1.01E-05	3.44E-05	-8.66E-05	-1.94E-05	8.99E-05	-0.000219336	-0.001067043	0.006385426	-0.013888183	1.10E-05	-5.08E-05	0.000123109	-6.72E-05	0.000315524	-0.000769755	0.000147099	-0.00069465	0.001697395
msm_black_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.001370345	8.66E-06	-3.50E-05	8.84E-05	1.00E-05	-4.23E-05	0.000100499	0.00076784	-0.005883903	0.013461776	-6.81E-06	2.85E-05	-6.72E-05	5.35E-05	-0.000228566	0.00054178	-0.000123273	0.000529434	-0.001256621
msm_black_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’	0.005175135	-3.44E-05	0.00012511	-0.000306418	-4.27E-05	0.000197398	-0.000481652	-0.002812917	0.021752213	-0.049893064	2.86E-05	-0.000130597	0.000315524	-0.000228566	0.001074459	-0.002616251	0.000529187	-0.002503178	0.006104594
msm_black_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.011912284	8.04E-05	-0.000279766	0.00067574	0.000101598	-0.000483285	0.001191217	0.006393958	-0.049602746	0.113868694	-6.74E-05	0.000315884	-0.000769755	0.00054178	-0.002616251	0.006429071	-0.001255834	0.006103626	-0.015023387
msm_black_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.002873419	-1.80E-05	7.33E-05	-0.000186919	-2.12E-05	9.03E-05	-0.000214871	-0.001665655	0.013463907	-0.031203489	1.48E-05	-6.24E-05	0.000147099	-0.000123273	0.000529187	-0.001255834	0.000288252	-0.001244407	0.002957483
msm_black_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.011080359	7.81E-05	-0.000289829	0.000718311	9.11E-05	-0.000424654	0.001038648	0.006117081	-0.04991035	0.116008172	-6.26E-05	0.000287152	-0.00069465	0.000529434	-0.002503178	0.006103626	-0.001244407	0.005924952	-0.014471761
msm_black_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.02566751	-0.000186482	0.000666149	-0.001629553	-0.000217572	0.001042762	-0.002576768	-0.013916802	0.113913881	-0.265021794	0.000147747	-0.000695612	0.001697395	-0.001256621	0.006104594	-0.015023387	0.002957483	-0.014471761	0.035679392
msm_hisp_male	(Intercept)	0.687612828	-0.015933909	0.047586528	-0.140471041	-0.001248833	0.004008877	-0.00893274	-0.04869	0.225514494	-0.489829779	0.00030486	-0.000946802	0.002086736	-0.001452299	0.004834618	-0.010894426	0.003149016	-0.010640429	0.02409442
msm_hisp_male	rcs(age, 4)age	-0.015933909	0.000496992	-0.001564111	0.004692003	2.72E-06	5.42E-06	-2.15E-05	0.000139651	-0.000490749	0.001156534	6.50E-08	-5.75E-06	1.67E-05	4.06E-07	1.60E-05	-4.81E-05	-1.45E-06	-2.81E-05	8.62E-05
msm_hisp_male	rcs(age, 4)age’	0.047586528	-0.001564111	0.006131942	-0.019804594	-4.26E-06	-3.15E-05	0.000100201	-0.000631123	0.002187673	-0.005098889	-1.80E-06	2.91E-05	-8.13E-05	4.09E-06	-0.000101773	0.000288406	-7.56E-06	0.000211105	-0.000596464
msm_hisp_male	rcs(age, 4)age’’	-0.140471041	0.004692003	-0.019804594	0.066889537	8.42E-06	0.000110657	-0.000339127	0.001793025	-0.00767877	0.018120483	8.47E-06	-0.000103495	0.000283843	-2.45E-05	0.000401229	-0.00112084	5.00E-05	-0.000873249	0.002433361
msm_hisp_male	rcs(cd4n_ini, 4)cd4n_ini	-0.001248833	2.72E-06	-4.26E-06	8.42E-06	9.68E-06	-3.94E-05	9.36E-05	0.000303485	-0.001427974	0.003078133	-2.61E-06	1.08E-05	-2.59E-05	1.21E-05	-5.04E-05	0.000120872	-2.59E-05	0.000108115	-0.000259553
msm_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’	0.004008877	5.42E-06	-3.15E-05	0.000110657	-3.94E-05	0.000175213	-0.000426653	-0.001099594	0.005199086	-0.011210716	1.08E-05	-4.92E-05	0.00012059	-5.01E-05	0.000229728	-0.000565802	0.000107566	-0.00049405	0.001218411
msm_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’’	-0.00893274	-2.15E-05	0.000100201	-0.000339127	9.36E-05	-0.000426653	0.001047172	0.00253822	-0.012028573	0.025947859	-2.59E-05	0.000120496	-0.000297972	0.000120119	-0.000565055	0.001404259	-0.000257871	0.001216923	-0.003029551
msm_hisp_male	rcs(time_from_h1yy, 4)time_from_h1yy	-0.04869	0.000139651	-0.000631123	0.001793025	0.000303485	-0.001099594	0.00253822	0.024334147	-0.130234061	0.287054857	-0.000164332	0.00059686	-0.001378889	0.000884432	-0.003229187	0.007478091	-0.001948259	0.007116546	-0.016485512
msm_hisp_male	rcs(time_from_h1yy, 4)time_from_h1yy’	0.225514494	-0.000490749	0.002187673	-0.00767877	-0.001427974	0.005199086	-0.012028573	-0.130234061	0.902491934	-2.10422075	0.000883443	-0.00322346	0.007461356	-0.0061723	0.02271304	-0.052771033	0.014388198	-0.052964327	0.123095955
msm_hisp_male	rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.489829779	0.001156534	-0.005098889	0.018120483	0.003078133	-0.011210716	0.025947859	0.287054857	-2.10422075	4.982076094	-0.001946386	0.007103288	-0.016446198	0.014389016	-0.052980575	0.123151974	-0.034051044	0.125415223	-0.291639452
msm_hisp_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy	0.00030486	6.50E-08	-1.80E-06	8.47E-06	-2.61E-06	1.08E-05	-2.59E-05	-0.000164332	0.000883443	-0.001946386	1.44E-06	-6.05E-06	1.45E-05	-7.75E-06	3.27E-05	-7.87E-05	1.71E-05	-7.21E-05	0.000173452
msm_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy	-0.000946802	-5.75E-06	2.91E-05	-0.000103495	1.08E-05	-4.92E-05	0.000120496	0.00059686	-0.00322346	0.007103288	-6.05E-06	2.79E-05	-6.87E-05	3.27E-05	-0.000151985	0.000375508	-7.20E-05	0.000335778	-0.000830567
msm_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy	0.002086736	1.67E-05	-8.13E-05	0.000283843	-2.59E-05	0.00012059	-0.000297972	-0.001378889	0.007461356	-0.016446198	1.45E-05	-6.87E-05	0.000170563	-7.86E-05	0.000375387	-0.000936099	0.000173221	-0.000830377	0.002073774
msm_hisp_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.001452299	4.06E-07	4.09E-06	-2.45E-05	1.21E-05	-5.01E-05	0.000120119	0.000884432	-0.0061723	0.014389016	-7.75E-06	3.27E-05	-7.86E-05	5.47E-05	-0.000232844	0.000562309	-0.000127568	0.000544409	-0.001315939
msm_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’	0.004834618	1.60E-05	-0.000101773	0.000401229	-5.04E-05	0.000229728	-0.000565055	-0.003229187	0.02271304	-0.052980575	3.27E-05	-0.000151985	0.000375387	-0.000232844	0.001100941	-0.002740473	0.000544546	-0.002587034	0.006452362
msm_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.010894426	-4.81E-05	0.000288406	-0.00112084	0.000120872	-0.000565802	0.001404259	0.007478091	-0.052771033	0.123151974	-7.87E-05	0.000375508	-0.000936099	0.000562309	-0.002740473	0.006897387	-0.001316475	0.006453271	-0.016281878
msm_hisp_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.003149016	-1.45E-06	-7.56E-06	5.00E-05	-2.59E-05	0.000107566	-0.000257871	-0.001948259	0.014388198	-0.034051044	1.71E-05	-7.20E-05	0.000173221	-0.000127568	0.000544546	-0.001316475	0.000302405	-0.001294283	0.003132971
msm_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.010640429	-2.81E-05	0.000211105	-0.000873249	0.000108115	-0.00049405	0.001216923	0.007116546	-0.052964327	0.125415223	-7.21E-05	0.000335778	-0.000830377	0.000544409	-0.002587034	0.006453271	-0.001294283	0.006188544	-0.015476514
msm_hisp_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.02409442	8.62E-05	-0.000596464	0.002433361	-0.000259553	0.001218411	-0.003029551	-0.016485512	0.123095955	-0.291639452	0.000173452	-0.000830567	0.002073774	-0.001315939	0.006452362	-0.016281878	0.003132971	-0.015476514	0.039176532
msm_white_male	(Intercept)	0.287636835	-0.005317935	0.012211237	-0.051060312	-0.000567709	0.001734393	-0.004395659	-0.019844503	0.052463656	-0.112586387	0.000119556	-0.000378823	0.000969299	-0.0003281	0.001084809	-0.002810652	0.000702439	-0.002340457	0.006071378
msm_white_male	rcs(age, 4)age	-0.005317935	0.000145467	-0.000354098	0.001517667	8.77E-07	-6.81E-08	-2.04E-06	3.46E-05	7.57E-06	-4.26E-05	-2.37E-07	4.37E-07	-7.67E-07	4.08E-07	-1.38E-06	3.14E-06	-6.77E-07	2.66E-06	-6.00E-06
msm_white_male	rcs(age, 4)age’	0.012211237	-0.000354098	0.00110507	-0.005224643	-1.55E-06	-1.43E-06	8.46E-06	-0.000156315	6.71E-06	7.35E-05	5.69E-07	-4.80E-07	-2.33E-07	-9.62E-07	1.43E-06	-9.54E-07	1.86E-06	-3.31E-06	3.03E-06
msm_white_male	rcs(age, 4)age’’	-0.051060312	0.001517667	-0.005224643	0.026868037	5.78E-06	3.85E-06	-2.56E-05	0.000725763	-0.000705265	0.001273835	-2.75E-06	2.82E-06	-7.19E-07	8.06E-06	-1.68E-05	2.98E-05	-1.98E-05	4.89E-05	-1.00E-04
msm_white_male	rcs(cd4n_ini, 4)cd4n_ini	-0.000567709	8.77E-07	-1.55E-06	5.78E-06	3.82E-06	-1.41E-05	3.78E-05	0.000110725	-0.000312241	0.000676165	-7.84E-07	2.90E-06	-7.79E-06	2.24E-06	-8.42E-06	2.28E-05	-4.89E-06	1.85E-05	-5.02E-05
msm_white_male	rcs(cd4n_ini, 4)cd4n_ini’	0.001734393	-6.81E-08	-1.43E-06	3.85E-06	-1.41E-05	5.77E-05	-0.00016051	-0.000359075	0.00102585	-0.002228254	2.89E-06	-1.19E-05	3.30E-05	-8.41E-06	3.53E-05	-9.90E-05	1.85E-05	-7.81E-05	0.000220232
msm_white_male	rcs(cd4n_ini, 4)cd4n_ini’’	-0.004395659	-2.04E-06	8.46E-06	-2.56E-05	3.78E-05	-0.00016051	0.000451915	0.00092842	-0.00266662	0.005800393	-7.77E-06	3.30E-05	-9.30E-05	2.28E-05	-9.89E-05	0.00028164	-5.01E-05	0.000219923	-0.000628475
msm_white_male	rcs(time_from_h1yy, 4)time_from_h1yy	-0.019844503	3.46E-05	-0.000156315	0.000725763	0.000110725	-0.000359075	0.00092842	0.008021179	-0.027250418	0.061702875	-4.73E-05	0.000154257	-0.000399704	0.000161513	-0.000530285	0.001378863	-0.000365915	0.001203749	-0.003133714
msm_white_male	rcs(time_from_h1yy, 4)time_from_h1yy’	0.052463656	7.57E-06	6.71E-06	-0.000705265	-0.000312241	0.00102585	-0.00266662	-0.027250418	0.125271064	-0.308022873	0.000161755	-0.000531944	0.001383905	-0.000743938	0.002466727	-0.006448472	0.001831071	-0.006086618	0.015933479
msm_white_male	rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.112586387	-4.26E-05	7.35E-05	0.001273835	0.000676165	-0.002228254	0.005800393	0.061702875	-0.308022873	0.779123144	-0.000366572	0.001207912	-0.003146051	0.001830496	-0.006085125	0.015929285	-0.00463708	0.015461922	-0.040538458
msm_white_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy	0.000119556	-2.37E-07	5.69E-07	-2.75E-06	-7.84E-07	2.89E-06	-7.77E-06	-4.73E-05	0.000161755	-0.000366572	3.42E-07	-1.28E-06	3.46E-06	-1.19E-06	4.51E-06	-1.23E-05	2.70E-06	-1.03E-05	2.81E-05
msm_white_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy	-0.000378823	4.37E-07	-4.80E-07	2.82E-06	2.90E-06	-1.19E-05	3.30E-05	0.000154257	-0.000531944	0.001207912	-1.28E-06	5.38E-06	-1.51E-05	4.51E-06	-1.93E-05	5.46E-05	-1.03E-05	4.46E-05	-0.000126322
msm_white_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy	0.000969299	-7.67E-07	-2.33E-07	-7.19E-07	-7.79E-06	3.30E-05	-9.30E-05	-0.000399704	0.001383905	-0.003146051	3.46E-06	-1.51E-05	4.28E-05	-1.23E-05	5.46E-05	-0.000156635	2.81E-05	-0.000126262	0.000363285
msm_white_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.0003281	4.08E-07	-9.62E-07	8.06E-06	2.24E-06	-8.41E-06	2.28E-05	0.000161513	-0.000743938	0.001830496	-1.19E-06	4.51E-06	-1.23E-05	5.57E-06	-2.17E-05	5.94E-05	-1.38E-05	5.40E-05	-0.000148449
msm_white_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’	0.001084809	-1.38E-06	1.43E-06	-1.68E-05	-8.42E-06	3.53E-05	-9.89E-05	-0.000530285	0.002466727	-0.006085125	4.51E-06	-1.93E-05	5.46E-05	-2.17E-05	9.61E-05	-0.000275016	5.40E-05	-0.000241701	0.000694024
msm_white_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’	-0.002810652	3.14E-06	-9.54E-07	2.98E-05	2.28E-05	-9.90E-05	0.00028164	0.001378863	-0.006448472	0.015929285	-1.23E-05	5.46E-05	-0.000156635	5.94E-05	-0.000275016	0.000799927	-0.000148408	0.000693922	-0.002025736
msm_white_male	rcs(cd4n_ini, 4)cd4n_ini:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.000702439	-6.77E-07	1.86E-06	-1.98E-05	-4.89E-06	1.85E-05	-5.01E-05	-0.000365915	0.001831071	-0.00463708	2.70E-06	-1.03E-05	2.81E-05	-1.38E-05	5.40E-05	-0.000148408	3.52E-05	-0.00013871	0.000382588
msm_white_male	rcs(cd4n_ini, 4)cd4n_ini’:rcs(time_from_h1yy, 4)time_from_h1yy’’	-0.002340457	2.66E-06	-3.31E-06	4.89E-05	1.85E-05	-7.81E-05	0.000219923	0.001203749	-0.006086618	0.015461922	-1.03E-05	4.46E-05	-0.000126262	5.40E-05	-0.000241701	0.000693922	-0.00013871	0.00062772	-0.001808538
msm_white_male	rcs(cd4n_ini, 4)cd4n_ini’‘:rcs(time_from_h1yy, 4)time_from_h1yy’’	0.006071378	-6.00E-06	3.03E-06	-1.00E-04	-5.02E-05	0.000220232	-0.000628475	-0.003133714	0.015933479	-0.040538458	2.81E-05	-0.000126322	0.000363285	-0.000148449	0.000694024	-0.002025736	0.000382588	-0.001808538	0.005298995

CD4 Dynamics Out of Care </>

The decrease in CD4 count off ART was modeled using a linear regression scheme. NA-ACCORD participants that left care from 2010 – 2021 and returned 2011 – 2022 and had a valid CD4 measurement at entry and exit were used in the analysis. Patients whose CD4 count had increased or stayed the same as well as those who had a suppressed viral load on return were dropped as well. All sub-populations had to be collapsed in order to provide enough data. We assumed that the difference (\(\mathrm{diff\_log}\)) of the log of the entry CD4 count (\(\mathrm{sqrt\_cd4}^2\)) from the log of CD4 count at exit from care (\(\mathrm{sqrt\_cd4\_exit}^2\)) varies linearly with number of years spent out of care (\(\mathrm{years\_out}\)), and square root of CD4 count at exit from care (\(\mathrm{sqrt\_cd4\_exit}\)):

\[\mathrm{diff\_log} = \beta_0 + \beta_\mathrm{years\_out} \cdot \mathrm{years\_out} + \beta_\mathrm{sqrt\_cd4\_exit} \cdot \mathrm{sqrt\_cd4\_exit}\]

where

\[\mathrm{diff\_log} = \log(\mathrm{sqrt\_cd4}^2) - \log(\mathrm{sqrt\_cd4\_exit}^2)\]

The variable of interest is the time varying CD4 count (\(\mathrm{cd4\_entry}\)). Solving for \(\mathrm{sqrt\_cd4}\) leaves us with

\[\mathrm{sqrt\_cd4} = (c_s \cdot e^{\mathrm{diff\_log}}\cdot \mathrm{sqrt\_cd4\_exit}^2)^\frac{1}{2}\]

where \(c_s = 1.42\) is the smearing retransformation term resulting from fitting a linear regression to a log-transformed variable. The fit was performed using the glm function of the stats package in base R. The estimated coefficients are shown in Table 17 and the covariance matrix is shown in Table 18.

Table 17: CD4 Out of Care Coefficient Estimates

intercept	time_out_of_naaccord	sqrtcd4n_exit
-1.554	-0.039	0.025

Table 18: CD4 Out of Care Covariance Matrix

(Intercept)	time_out_of_naaccord	sqrtcd4_exit
0.011646	-6.84E-04	-4.34E-04
-6.84E-04	3.45E-04	-7.17E-06
-4.34E-04	-7.17E-06	2.18E-05

Multimorbidity and BMI

The simulation may be run with or without the presence of comorbid conditions and BMI. The possible comorbid conditions are partitioned into multiple “stages” depending on how they are modeled in the simulation. Smoking and hepatitis C virus are risk factors, anxiety and depression are stage 1, chronic kidney disease, hyperlipidemia, diabetes mellitus, and hypertension are stage 2, and cancer, end-stage liver disease and myocardial infarction are stage 3. Incidence of conditions of a certain stage are influenced by presence of conditions from previous stages as well as other factors as detailed in the following. Mortality functions are modified to account for the comorbid conditions as well.

BMI </>

In order to capture the important clinical effect of change in BMI resulting from ART treatment, we model both pre-ART BMI and post-ART BMI for all agents. Both BMI measurements then have an effect on comorbid conditions and mortality.

Pre-ART BMI </>

Pre-ART BMI (\(\mathrm{pre\_art\_bmi}\)) is calculated from one of four different models depending on the subpopulation.

Model 1

Model 1 is used by Heterosexual Hispanic Male, Heterosexual White Male, and IDU Hispanic Male populations. We model \(\log_{10}(\mathrm{pre\_art\_bmi})\) as a function of age (\(\mathrm{age}\)) and \(\mathrm{art\_init\_year}\).

A restricted cubic spline is used to model \(\mathrm{art\_init\_year}\) with the following knots:

Table 19: Pre-ART BMI Model 1 Knots

group	1	2	3	4
Heterosexual Hispanic Male	2002	2010	2013	2018.9
Heterosexual White Male	2001	2008	2013	2019
IDU Hispanic Male	2001	2009	2012	2018

The full function is given by:

\[\begin{split} \log_{10}(\mathrm{pre\_art\_bmi}) = \beta_0 &+ \beta_\mathrm{age\_cat\_1} \cdot \mathrm{age\_cat\_1} + \beta_\mathrm{age\_cat\_2} \cdot \mathrm{age\_cat\_2} + \beta_\mathrm{age\_cat\_3} \cdot \mathrm{age\_cat\_3} + \beta_\mathrm{age\_cat\_4} \cdot \mathrm{age\_cat\_4}\\[2ex] &+ \beta_\mathrm{art\_init\_year} \cdot \mathrm{art\_init\_year}+ \beta_\mathrm{art\_init\_year\_1} \cdot \mathrm{art\_init\_year\_1} + \beta_\mathrm{art\_init\_year\_2} \cdot \mathrm{art\_init\_year\_2} \end{split}\]

Table 20: Pre-ART BMI Model 1 Estimates

group	age	h1yy	h1yy’	h1yy’’	intercept
Heterosexual Hispanic Male	0.000	0.003	-0.007	0.067	-5.384
Heterosexual White Male	0.000	0.003	-0.010	0.052	-4.686
IDU Hispanic Male	0.001	-0.011	0.027	-0.160	23.631

Model 2

Model 2 is used by the Heterosexual White Female, IDU Black Female, and IDU White Male populations. We model \(\log_{10}(\mathrm{pre\_art\_bmi})\) as a linear function of \(\mathrm{age}\) and \(\mathrm{art\_init\_year}\)

\[\log_{10}(\mathrm{pre\_art\_bmi}) = \beta_0 + \beta_\mathrm{age} \cdot \mathrm{age} + \beta_\mathrm{art\_init\_year} \cdot \mathrm{art\_init\_year}\]

Table 21: Pre-ART BMI Model 2 Estimates

group	age	h1yy	intercept
Heterosexual White Female	-0.001	0.002	-1.662
IDU Black Female	-0.001	0.001	-0.745
IDU White Male	0.001	0.001	-0.455

Model 3

Model 3 is used by the Heterosexual Black Female, Heterosexual Hispanic Female, IDU Black Male, IDU Hispanic Female, IDU White Female, MSM Black Male, and MSM Hispanic Male populations. We model \(\log_{10}(\mathrm{pre\_art\_bmi})\) as a restricted cubic spline function of \(\mathrm{age}\) and a linear function of \(\mathrm{art\_init\_year}\).

Table 22: Pre-ART BMI Model 3 Knots

group	k_1	k_2	k_3	k_4
Heterosexual Black Female	23	36	46	60
Heterosexual Hispanic Female	24.85	35.95	46	63.15
IDU Black Male	31	47	53	63
IDU Hispanic Female	26	38	45.75	59.25
IDU White Female	26	38	45.75	59.25
MSM Black Male	21	27	37	55
MSM Hispanic Male	22	31	39	53

The function and its estimates follow.

\[\log_{10}(\mathrm{pre\_art\_bmi}) = \beta_0 + \beta_\mathrm{age} \cdot \mathrm{age} + \beta_\mathrm{age\_1} \cdot \mathrm{age\_1} + \beta_\mathrm{age\_2} \cdot \mathrm{age\_2} + \beta_\mathrm{art\_init\_year} \cdot \mathrm{art\_init\_year}\]

Table 23: Pre-ART BMI Model 3 Estimates

group	age	age’	age’’	h1yy	intercept
Heterosexual Black Male	0.003	-0.003	0.005	0.002	-2.409
Heterosexual Hispanic Female	0.002	-0.007	0.014	0.001	-0.318
IDU Black Male	0.004	-0.006	0.025	0.002	-3.330
IDU Hispanic Female	0.003	-0.015	0.058	0.002	-2.240
IDU White Female	0.003	-0.015	0.058	0.002	-2.240
MSM Black Male	0.004	-0.006	0.006	0.002	-3.216
MSM Hispanic Male	0.003	-0.003	0.005	0.002	-2.270

Model 4

Model 2 is used by the Heterosexual Black Female and MSM White Male populations. We model \(\log_{10}(\mathrm{pre\_art\_bmi})\) as a restricted cubic spline function of age \(\mathrm{age}\) and \(\mathrm{art\_init\_year}\).

Table 24: Pre-ART BMI Model 4 Age Knots

group	1	2	3	4
Het Black Female	23	36	46	60
MSM White Male	24	37	46	61

Table 25: Pre-ART BMI Model 4 ART Initiation Year Knots

group	1	2	3	4
Het Black Female	2003	2010	2013	2019
MSM White Male	2003	2009	2012	2018

The function and its estimates are:

\[\begin{split} \log_{10}(\mathrm{pre\_art\_bmi}) = \beta_0 &+ \beta_\mathrm{age} \cdot \mathrm{age} + \beta_\mathrm{age\_1} \cdot \mathrm{age\_1} + \beta_\mathrm{age\_2} \cdot \mathrm{age\_2}+ \beta_\mathrm{art\_init\_year} \cdot \mathrm{art\_init\_year}\\[2ex] &+ \beta_\mathrm{art\_init\_year\_1} \cdot \mathrm{art\_init\_year\_1} + \beta_\mathrm{art\_init\_year\_2} \cdot \mathrm{art\_init\_year\_2} \end{split}\]

Table 26: Pre-ART BMI Model 4 Estimates

group	age	age’	age’’	h1yy	h1yy’	h1yy’’	intercept
Het Black Female	0.001	-0.001	0.001	0.003	0.003	-0.027	-5.553
MSM White Male	0.003	-0.004	0.006	0.002	-0.002	0.015	-3.306

Post-ART BMI </>

Post-ART BMI (\(\mathrm{post\_art\_bmi}\)) is calculated using only a single model for all 15 subpopulations. We model \(\mathrm{sqrt\_post\_art\_bmi}\) as a function of \(\mathrm{age}\), square root of pre-ART BMI (\(\mathrm{sqrt\_pre\_art\_bmi}\)), square root of CD4 count at ART initiation (\(\mathrm{sqrt\_init\_cd4}\)), and square root of CD4 count 2 years after ART initiation (\(\mathrm{sqrt\_cd4\_post\_art}\)) modeled by restricted cubic splines as well as a linear function of \(\mathrm{art\_init\_year}\). The full equation is:

\[\begin{split} \mathrm{sqrt\_post\_art\_bmi} = \beta_0 &+ \beta_\mathrm{age} \cdot \mathrm{age} + \beta_\mathrm{age\_1} \cdot \mathrm{age\_1} + \beta_\mathrm{age\_2} \cdot \mathrm{age\_2} + \beta_\mathrm{sqrt\_pre\_art\_bmi} \cdot \mathrm{sqrt\_pre\_art\_bmi}\\[2ex] &+ \beta_\mathrm{sqrt\_pre\_art\_bmi\_1} \cdot \mathrm{sqrt\_pre\_art\_bmi\_1}+ \beta_\mathrm{sqrt\_pre\_art\_bmi\_2} \cdot \mathrm{sqrt\_pre\_art\_bmi\_2}\\[2ex] &+ \beta_\mathrm{sqrt\_init\_cd4} \cdot \mathrm{sqrt\_init\_cd4} + \beta_\mathrm{sqrt\_init\_cd4\_1} \cdot \mathrm{sqrt\_init\_cd4\_1} + \beta_\mathrm{sqrt\_init\_cd4\_2} \cdot \mathrm{sqrt\_init\_cd4\_2}\\[2ex] &+ \beta_\mathrm{sqrt\_cd4\_post\_art} \cdot \mathrm{sqrt\_cd4\_post\_art} + \beta_\mathrm{sqrt\_cd4\_post\_art\_1} \cdot \mathrm{sqrt\_cd4\_post\_art\_1}\\[2ex] &+ \beta_\mathrm{sqrt\_cd4\_post\_art\_2} \cdot \mathrm{sqrt\_cd4\_post\_art\_2} + \beta_\mathrm{art\_init\_year} \cdot \mathrm{art\_init\_year} \end{split}\]

The various knot locations are in the following tables.

Table 27: Post-ART BMI Age Knots

group	1	2	3	4
Het Black Female	23	36	46	60
Het Black Male	26	41	49	63
Het Hispanic Female	24.35	35	45	61
Het Hispanic Male	25	37	47	61
Het White Female	23	36	47	61
Het White Male	27	40	49	64
IDU Black Female	30.65	44	51	62.35
IDU Black Male	32	47	53	63
IDU Hispanic Female	26.65	39	46	60.35
IDU Hispanic Male	27	38	47	59.6
IDU White Female	26.65	39	46	60.35
IDU White Male	25	37	45	59
MSM Black Male	21	27	37	54
MSM Hispanic Male	22	31	39	53
MSM White Male	24	37	46	60

Table 28: Post-ART BMI Pre-ART CD4 Knots

group	1	2	3	4
Het Black Female	3.31662479	14.38749457	19.46535231	28.98275349
Het Black Male	3,11.66190379	18.22223818	26.92582404
Het Hispanic Female	4.164942897	14.52235611	19.73701703	29.23263133
Het Hispanic Male	3.16227766	9.110433579	16.27267184	24.75470072
Het White Female	4.582575695	14.54302941	19.49358869	28.21327158
Het White Male	3.397737044	11.35781669	18.19752466	27.09700895
IDU Black Female	3.592895978	13.70524821	19.32485018	28.84086736
IDU Black Male	3.605551275	13.41640786	18.70828693	27.99986351
IDU Hispanic Female	3.504427006	14.3404076	19.17804239	26.90433515
IDU Hispanic Male	4.624931818	13.94258875	19.77624693	26.98294383
IDU White Female	3.504427006	14.3404076	19.17804239	26.90433515
IDU White Male	4.472135955	15.03329638	19.92485885	29.49063308
MSM Black Male	3.741657387	15.26433752	20.24845673	28.72281323
MSM Hispanic Male	5.099019514	15.77973384	20.61552813	28.67228102
MSM White Male	5.196152423	16	20.83266666	29.15475947

Table 28: Post-ART BMI Post-ART CD4 Knots

group	1	2	3	4
Het Black Female	11.23830881	19.59591794	24.52549694	33.49327172
Het Black Male	9.811944301	17.72004515	22.69361144	30.48073148
Het Hispanic Female	10.96051222	19.77813551	24.89275198	32.36502066
Het Hispanic Male	9.407443861	16.64331698	21.04518894	28.70191124
Het White Female	11.72586496	20.48780034	26.02878587	34.13561519
Het White Male	10.65595865	18.47971861	23.97915762	31.77617008
IDU Black Female	9.415378768	18.65609343	23.0618506	32.65260068
IDU Black Male	8.752097787	17.09969163	22.08619293	30.34458972
IDU Hispanic Female	11.50325573	18.46009086	22.95648057	30.41841781
IDU Hispanic Male	8.991653767	18.16314763	23.63366222	30.01080204
IDU White Female	11.50325573	18.46009086	22.95648057	30.41841781
IDU White Male	10.9735453	19.27238902	24.07436367	32.00194717
MSM Black Male	11.27606979	20.03808855	24.8997992	32.9066858
MSM Hispanic Male	12.36931688	20.4450483	25.15949125	31.97184748
MSM White Male	12.88409873	20.98451503	25.3179778	32.70321085

The estimates are as follows:

Table 29: Post-ART BMI Coefficient Estimates

group	age	age’	age’’	h1yy	intercept	pre_sqrt	pre_sqrt’	pre_sqrt’’	sqrtcd4	sqrtcd4’	sqrtcd4’’	sqrtcd4_post	sqrtcd4_post’	sqrtcd4_post’’
Het Black Female	0.002	-0.006	0.014	0.006	-10.698	0.815	0.422	-1.264	-0.032	0.012	0.027	0.027	-0.030	0.070
Het Black Male	0.003	-0.010	0.042	0.005	-8.518	0.838	0.182	-0.331	-0.022	-0.005	0.043	0.023	-0.020	0.047
Het Hispanic Female	0.004	-0.028	0.084	0.007	-12.628	0.844	0.327	-1.038	-0.030	0.006	0.057	0.026	-0.026	0.043
Het Hispanic Male	-0.003	0.015	-0.047	0.006	-11.995	0.925	0.130	-0.617	-0.017	-0.033	0.092	0.021	-0.021	0.054
Het White Female	0.001	0.004	-0.017	0.005	-7.868	0.736	0.775	-1.751	-0.043	0.032	-0.055	0.021	-0.012	0.011
Het White Male	0.002	-0.002	0.002	0.006	-10.905	0.694	0.515	-0.916	-0.024	0.007	0.023	0.019	-0.022	0.052
IDU Black Female	-0.014	0.027	-0.108	0.009	-15.259	0.523	2.069	-5.122	-0.007	-0.036	0.160	0.031	-0.048	0.182
IDU Black Male	0.003	-0.009	0.057	0.002	-2.667	0.885	-0.041	0.449	-0.011	-0.010	0.093	0.011	-0.003	-0.020
IDU Hispanic Female, IDU White Female	0.010	-0.031	0.115	0.010	-17.294	0.502	1.630	-3.920	-0.033	0.010	-0.009	0.017	0.032	-0.202
IDU Hispanic Male	-0.009	0.043	-0.139	0.008	-13.203	0.535	1.641	-5.465	-0.027	0.018	-0.021	0.028	-0.036	0.134
IDU White Male	0.000	-0.009	0.033	0.002	-3.242	0.822	0.297	-0.613	-0.030	0.034	-0.081	0.021	-0.036	0.120
MSM Black Male	0.003	-0.006	0.005	0.005	-9.916	0.951	0.169	-0.502	-0.026	0.011	0.005	0.024	-0.030	0.088
MSM Hispanic Male	0.000	0.005	-0.018	0.005	-10.241	0.905	0.001	0.184	-0.027	0.020	-0.052	0.020	-0.030	0.111
MSM White Male	0.003	-0.006	0.016	0.004	-6.320	0.797	0.366	-0.911	-0.026	0.016	-0.020	0.016	-0.014	0.038

Risk Factors </>

The stage 0 conditions are smoking and hepatitis C (HCV). These conditions are assumed to be ever/never for each person in the population, meaning that no incidence is modeled. From NA-ACCORD data, we generate an average prevalence in ART users from 2009 - 2022 for our initial 2009 population and an average prevalence in ART initiators from 2009 - 2022 for our initiator population.

Smoking </>

At population creation, each agent has a probability of being a smoker given by the following table:

Table 30: Smoking Prevalences

group	prevalence in ART User	prevalence in ART Initiator
het_black_female	60.1	58.5
het_black_male	76.9	70.6
het_hisp_female	45.4	47.9
het_hisp_male	69.6	59.0
het_white_female	72.1	67.7
het_white_male	77.3	71.3
idu_black_female	94.5	89.1
idu_black_male	95.9	93.2
idu_hisp_male	92.1	82.3
idu_white_female and idu_hisp_female	94.9	90.4
idu_white_male	90.5	88.0
msm_black_male	70.6	65.0
msm_hisp_male	59.8	50.2
msm_white_male	67.1	62.3

Hepatitis C Virus </>

At population creation, each agent has a probability of ever having hepatitis C virus given by the following table:

Table 31: Hepatitis C Prevalence

Group	Prevalence in ART users (%)	Prevalence in ART initiators (%)
het_black_male	19.4	11.5
het_hisp_male	13.2	8.5
het_white_male	14.1	9.8
idu_black_male	79.2	61.4
idu_hisp_male	60.5	43.6
idu_white_male	54.0	42.4
msm_black_male	14.1	7.7
msm_hisp_male	9.7	6.0
msm_white_male	9.9	7.1
het_black_female	10.8	8.4
het_hisp_female	9.0	7.9
het_white_female	13.7	14.2
idu_black_female	73.5	58.3
idu_hisp_female	47.1	53.9
idu_white_female	81.9	76.6

Stage 1 </>

The stage 1 conditions are anxiety and depression. Prevalence in the ART user and initiator populations is computed in a similar way to the stage 0 conditions. However, only the 2009 NA-ACCORD population was used to model ART users in 2009. Prevalence in ART initiators was taken 2009 - 2022. In addition, we allow for incidence of both conditions in addition to prevalence. Incidence is modeled using logistic regression.

Anxiety </>

The prevalence of anxiety in ART users and initiators is shown in the following table:

Table 32: Anxiety Prevalence

Subgroup	Prevalence in ART Users	Prevalence in ART Initiators
het_black_male	11.3	7.4
het_hisp_male	19.4	9.2
het_white_male	19.2	18
idu_black_male	17.8	13.7
idu_hisp_male	31	27.8
idu_white_male	34.8	28.8
msm_black_male	15.5	11.8
msm_hisp_male	30.7	17.8
msm_white_male	27.6	23.6
het_black_female	17.7	17.4
het_hisp_female	29.8	24.3
het_white_female	30.6	30.2
idu_black_female	19.5	26.7
idu_hisp_female	–	–
idu_white_female	31.5	34

We use logistic regression to model the probability of incidence of anxiety as a function of calendar year (\(\mathrm{year}\)), age (\(\mathrm{age}\)), square root of CD4 count at ART initiation (\(\mathrm{sqrt\_init\_cd4}\)), number of years since ART initiation (\(\mathrm{time\_since\_art}\)), smoking status (\(\mathrm{smoking}\)), HCV status (\(\mathrm{hcv}\)) and depression status (\(\mathrm{depression}\)). The status variables are encoded as Boolean variables. This choice of regressors leads to the following regression equation:

\[\begin{split} \mathrm{logit}(p) = \beta_0 &+ \beta_\mathrm{year} \cdot\mathrm{year} + \beta_\mathrm{age} \cdot \mathrm{age} + \beta_\mathrm{sqrt\_init\_cd4}\cdot\mathrm{sqrt\_init\_cd4} + \beta_\mathrm{time\_since\_art} \cdot \mathrm{time\_since\_art} \\[2ex] &+ \beta_\mathrm{smoking} \cdot \mathrm{smoking} + \beta_\mathrm{hcv} \cdot \mathrm{hcv} + \beta_\mathrm{depression} \cdot \mathrm{depression} \end{split}\]

where

\[\mathrm{logit}(p) = \log \frac{p}{1 - p}\]

is the logit function and \(p\) is the probability of incidence of anxiety.

The fitted coefficients are:

Table 33: Anxiety Incidence

group_combined	age	cd4n_entry	dpr	h1yy_time	hcv	intercept	smoking	year
het_black_female	-0.001	0.000	0.899	-0.078	0.190	-142.690	0.174	0.069
het_black_male	-0.010	0.000	0.900	-0.047	0.265	-70.209	0.011	0.033
het_hisp_female	-0.004	0.000	1.244	-0.115	0.182	-223.807	0.238	0.110
het_hisp_male	-0.021	-0.001	1.525	-0.129	0.327	-324.570	0.520	0.160
het_white_female	-0.004	0.000	0.941	-0.062	0.852	-62.451	0.120	0.030
het_white_male	-0.019	0.000	0.796	-0.063	0.637	-161.510	-0.077	0.079
idu_black_female, idu_hisp_female, idu_white_female	-0.032	-0.001	0.140	-0.056	0.122	-56.408	-0.118	0.028
idu_black_male	-0.025	0.000	0.555	-0.047	0.076	-174.287	0.462	0.085
idu_hisp_male	-0.031	0.000	0.768	-0.052	-0.015	-56.662	0.585	0.027
idu_white_male	-0.012	0.000	0.571	-0.086	-0.009	-46.832	-0.063	0.022
msm_black_male	-0.008	0.000	0.876	-0.045	0.098	-121.170	0.144	0.058
msm_hisp_male	-0.007	0.000	1.165	-0.086	-0.042	-48.087	0.004	0.023
msm_white_male	-0.014	0.000	0.880	-0.070	-0.012	-51.632	0.143	0.024

Depression </>

The prevalence of depression in ART users and initiators is shown in the following table:

Table 34: Depression Prevalence

Subgroup	Prevalence in ART Users	Prevalence in ART Initiators
het_black_male	29.6	14.6
het_hisp_male	32.3	13.4
het_white_male	31.9	17.8
idu_black_male	42.4	32.2
idu_hisp_male	43.9	23
idu_white_male	47.6	31.8
msm_black_male	34.8	17.9
msm_hisp_male	39.4	17.1
msm_white_male	39.6	25.9
het_black_female	38.9	28.6
het_hisp_female	43.9	29.5
het_white_female	40.9	30.7
idu_black_female	49.8	38.3
idu_hisp_female	–	–
idu_white_female	53.8	34

We use logistic regression to model the probability of incidence of depression as a function of calendar year (\(\mathrm{year}\)), age (\(\mathrm{age}\)), square root of CD4 count at ART initiation (\(\mathrm{sqrt\_init\_cd4}\)), number of years since ART initiation (\(\mathrm{time\_since\_art}\)), smoking status (\(\mathrm{smoking}\)), HCV status (\(\mathrm{hcv}\)) and anxiety status (\(\mathrm{anxiety}\)). The status variables are encoded as Boolean variables. This choice of regressors leads to the following regression equation:

\[\begin{split} \mathrm{logit}(p) = \beta_0 &+ \beta_\mathrm{year} \cdot\mathrm{year} + \beta_\mathrm{age} \cdot \mathrm{age} + \beta_\mathrm{sqrt\_init\_cd4}\cdot\mathrm{sqrt\_init\_cd4} + \beta_\mathrm{time\_since\_art} \cdot \mathrm{time\_since\_art} \\[2ex] &+ \beta_\mathrm{smoking} \cdot \mathrm{smoking} + \beta_\mathrm{hcv} \cdot \mathrm{hcv} + \beta_\mathrm{anxiety} \cdot \mathrm{anxiety} \end{split}\]

where

\[\mathrm{logit}(p) = \log \frac{p}{1 - p}\]

is the logit function and \(p\) is the probability of incidence of depression.

The fitted coefficients are:

Table 35: Depression Incidence

group_combined	age	anx	cd4n_entry	h1yy_time	hcv	intercept	smoking	year
het_black_female	-0.012	0.677	-0.001	-0.083	-0.132	47.664	0.281	-0.025
het_black_male	-0.024	0.879	0.000	-0.046	0.217	77.617	0.563	-0.040
het_hisp_female	0.000	0.467	-0.001	-0.124	-1.151	145.644	-0.266	-0.073
het_hisp_male	-0.021	1.878	-0.001	-0.106	0.807	178.706	0.104	-0.090
het_white_female	0.008	0.866	-0.001	-0.046	-0.348	37.281	0.176	-0.020
het_white_male	0.005	1.020	0.000	-0.072	-0.004	79.341	0.059	-0.041
idu_black_female, idu_hisp_female, idu_white_female	0.006	0.185	0.000	-0.085	-0.581	135.387	0.334	-0.069
idu_black_male	-0.005	0.343	0.000	-0.080	0.006	6.868	1.324	-0.005
idu_hisp_male, idu_white_male	-0.006	0.070	0.000	-0.107	-0.248	21.090	0.271	-0.012
msm_black_male	-0.007	0.889	0.000	-0.067	0.118	36.074	0.444	-0.019
msm_hisp_male	-0.014	0.977	0.000	-0.053	0.100	85.357	0.190	-0.044
msm_white_male	-0.007	0.776	0.000	-0.085	-0.054	47.605	0.225	-0.025

Stage 2 </>

The stage 2 conditions are chronic kidney disease (CKD), hyperlipidemia, diabetes mellitus, and hypertension. Prevalence in the 2009 ART user population is taken from the 2009 NA-ACCORD population, while prevalence in ART initiators was taken from the 2009 - 2022 NA-ACCORD ART initiator population. Incidence is modeled using logistic regression and is based on NA-ACCORD data. The logistic regression models the logit of probability for incidence of a stage 2 condition as a linear function of calendar year (\(\mathrm{year}\)), age (\(\mathrm{age}\)), square root of CD4 count at ART initiation (\(\mathrm{sqrt\_init\_cd4}\)), number of years since ART initiation (\(\mathrm{time\_since\_art}\)), change in BMI after ART initiation (\(\mathrm{delta\_bmi}\)) and BMI after ART initiation (\(\mathrm{post\_art\_bmi}\)) modeled as restricted cubic splines, stage 0 condition status (\(\mathrm{smoking}\), \(\mathrm{hcv}\)), stage 1 condition status (\(\mathrm{anxiety}\), \(\mathrm{depression}\)), and other stage 2 condition status (\(\mathrm{ckd}\), \(\mathrm{lipid}\), \(\mathrm{diabetes}\), \(\mathrm{hypertension}\)).

Chronic Kidney Disease </>

At the beginning of the simulation each member of the initial population begins with \(\mathrm{ckd} = 1\) with probability given by the first column in the table. At the start of each year new ART initiators are added where \(\mathrm{ckd} = 1\) with probability given by the second column in the table.

Table 36: CKD Prevalence

Group	Prevalence in ART users (%)	Prevalence in ART initiators (%)
het_black_female	14.2	7.6
het_black_male	19.1	9.7
het_hisp_female	3.6	2.8
idu_hisp_female	3.6	2.8
het_hisp_male	8.9	1.2
idu_hisp_male	8.9	1.2
het_white_female	8.9	2.8
idu_white_female	8.9	2.8
het_white_male	10.6	2.6
idu_black_female	27.4	7.6
idu_black_male	23.6	9.7
idu_white_male	6.4	2.6
msm_black_male	14.6	4.2
msm_hisp_male	5.6	1.2
msm_white_male	7.9	2.6

At the beginning of each year the in care and out of care populations with \(\mathrm{ckd} = 0\) have probability for incidence of CKD given by

\[\begin{aligned} \mathrm{logit}(p) = \beta_0 &+ \beta_{\mathrm{year}} \cdot \mathrm{year} + \beta_{\mathrm{age}} \cdot \mathrm{age} + \beta_{\mathrm{sqrt\_init\_cd4}} \cdot \mathrm{sqrt\_init\_cd4} + \beta_{\mathrm{time\_since\_art}} \cdot \mathrm{time\_since\_art} \\[2ex] & + \beta_{\mathrm{delta\_bmi}} \cdot \mathrm{delta\_bmi} + \beta_{\mathrm{delta\_bmi\_1}} \cdot \mathrm{delta\_bmi\_1} + \beta_{\mathrm{delta\_bmi\_2}} \cdot \mathrm{delta\_bmi\_2} \\[2ex] & + \beta_{\mathrm{post\_art\_bmi}} \cdot \mathrm{post\_art\_bmi} + \beta_{\mathrm{post\_art\_bmi\_1}} \cdot \mathrm{post\_art\_bmi\_1} + \beta_{\mathrm{post\_art\_bmi\_2}} \cdot \mathrm{post\_art\_bmi\_2} \\[2ex] & + \beta_{\mathrm{smoking}} \cdot \mathrm{smoking} + \beta_{\mathrm{hcv}} \cdot \mathrm{hcv} + \beta_{\mathrm{anxiety}} \cdot \mathrm{anxiety} + \beta_{\mathrm{depression}} \cdot \mathrm{depression} \\[2ex] & + \beta_{\mathrm{lipid}} \cdot \mathrm{lipid} + \beta_{\mathrm{diabetes}} \cdot \mathrm{diabetes} + \beta_{\mathrm{hypertension}} \cdot \mathrm{hypertension} \end{aligned}\]

where

\[\mathrm{logit}(p) = \log \frac{p}{1 - p}\]

is the logit function and \(p\) is the probability of incidence of CKD.

The fitted coefficients and knot locations are given in the following tables.

Table 37: CKD Incidence

group	age	anx	bmi_dif1	bmi_dif2	bmi_diff	bmi_raw_post	bmi_raw_post1	bmi_raw_post2	cd4n_entry	dm	dpr	h1yy_time	hcv	ht	intercept	lipid	smoking	year
het_black_female, idu_black_female	0.063	-0.194	0.355	-0.857	-0.122	-0.073	0.221	-0.485	0.000	0.427	0.208	-0.026	0.118	0.732	45.898	0.250	0.246	-0.026
het_black_male	0.042	0.003	0.151	-0.241	-0.107	0.056	-0.317	0.837	-0.001	0.472	-0.069	-0.050	0.322	0.882	-48.070	0.380	-0.211	0.020
het_hisp_female, het_white_female, idu_hisp_female, idu_white_female	0.073	0.570	0.659	-2.607	-0.214	0.075	-0.245	0.437	-0.001	0.497	-0.045	-0.009	0.503	0.364	84.830	0.302	0.307	-0.047
het_hisp_male, het_white_male	0.077	0.572	0.807	-2.089	-0.247	0.178	-0.651	1.729	-0.001	0.126	0.034	-0.089	-0.036	0.805	-10.718	-0.212	-0.223	-0.001
idu_black_male	0.038	-0.208	1.046	-4.331	-0.246	-0.175	0.620	-1.549	0.000	-0.095	0.088	-0.016	-0.031	0.792	-3.618	0.371	0.347	0.000
idu_hisp_male, idu_white_male	0.064	-0.300	0.882	-2.212	-0.233	-0.057	-0.264	0.700	0.000	0.111	-0.074	0.009	0.083	0.652	89.970	0.153	0.465	-0.048
msm_black_male	0.063	-0.060	0.123	-0.368	-0.022	0.114	-0.364	0.702	0.000	0.104	0.150	-0.038	-0.022	0.776	-16.229	0.141	-0.217	0.003
msm_hisp_male	0.076	-0.249	-1.047	3.601	0.272	0.058	-0.509	1.643	-0.001	0.377	0.270	-0.032	0.207	0.684	-69.551	0.344	-0.137	0.030
msm_white_male	0.069	0.101	0.455	-1.297	-0.087	0.028	-0.398	1.276	0.000	0.268	-0.052	-0.022	0.093	0.567	1.464	0.177	-0.183	-0.005

Table 38: CKD Delta BMI Knots

group	knot_1	knot_2	knot_3	knot_4
het_black_female, idu_black_female	-3.067	0.350	2.300	8.050
het_black_male	-2.350	0.300	1.900	6.200
het_hisp_female, het_white_female, idu_hisp_female, idu_white_female	-3.735	0.100	2.100	7.200
het_hisp_male, het_white_male	-1.890	0.350	2.000	6.380
idu_black_male	-3.015	-0.303	1.052	5.550
idu_hisp_male, idu_white_male	-2.300	0.000	1.350	5.188
msm_black_male	-2.050	0.100	1.500	5.700
msm_hisp_male, msm_white_male	-1.900	0.150	1.350	4.900
msm_hisp_male, msm_white_male	-1.900	0.050	1.250	4.600

Table 39: CKD Post-ART BMI Knots

group	knot_1	knot_2	knot_3	knot_4
het_black_female, idu_black_female	19.733	26.300	32.35	46.468
het_black_male	19.850	24.700	28.50	38.170
het_hisp_female, het_white_female, idu_hisp_female, idu_white_female	19.530	24.900	30.20	43.570
het_hisp_male, het_white_male, msm_hisp_male	20.500	25.000	28.68	36.190
het_hisp_male, het_white_male, msm_hisp_male	20.500	24.700	27.65	35.700
idu_black_male	19.442	23.698	26.80	34.700
idu_hisp_male, idu_white_male	20.400	23.800	27.10	33.837
msm_black_male	19.400	23.750	27.72	37.500
msm_white_male	20.000	24.100	27.00	34.700

Hyperlipidemia </>

At the beginning of the simulation each member of the initial population begins with \(\mathrm{lipid} = 1\) with probability given by the first column in the table. At the start of each year new ART initiators are added where \(\mathrm{lipid} = 1\) with probability given by the second column in the table.

Table 40: Hyperlipidemia Prevalence

Group	Prevalence in ART users (%)	Prevalence in ART initiators (%)
het_black_female	35.1	13.4
het_black_male	42.2	16.6
het_hisp_female	36.3	10.8
idu_hisp_female	36.3	10.8
het_hisp_male	42.5	14.8
het_white_female	45.6	14.7
het_white_male	45.5	14.8
idu_black_female	30.9	13.4
idu_black_male	31.8	16.6
idu_hisp_male	28.7	9.6
idu_white_female	20.3	14.7
idu_white_male	33.6	9.6
msm_black_male	35.2	6.3
msm_hisp_male	37.5	7.2
msm_white_male	46.4	13.7

At the beginning of each year the in care and out of care populations with \(\mathrm{lipid} = 0\) have probability for incidence of hyperlipidemia given by

\[\begin{aligned} \mathrm{logit}(p) = \beta_0 &+ \beta_{\mathrm{year}} \cdot \mathrm{year} + \beta_{\mathrm{age}} \cdot \mathrm{age} + \beta_{\mathrm{sqrt\_init\_cd4}} \cdot \mathrm{sqrt\_init\_cd4} + \beta_{\mathrm{time\_since\_art}} \cdot \mathrm{time\_since\_art} \\[2ex] & + \beta_{\mathrm{delta\_bmi}} \cdot \mathrm{delta\_bmi} + \beta_{\mathrm{delta\_bmi\_1}} \cdot \mathrm{delta\_bmi\_1} + \beta_{\mathrm{delta\_bmi\_2}} \cdot \mathrm{delta\_bmi\_2} \\[2ex] & + \beta_{\mathrm{post\_art\_bmi}} \cdot \mathrm{post\_art\_bmi} + \beta_{\mathrm{post\_art\_bmi\_1}} \cdot \mathrm{post\_art\_bmi\_1} + \beta_{\mathrm{post\_art\_bmi\_2}} \cdot \mathrm{post\_art\_bmi\_2} \\[2ex] & + \beta_{\mathrm{smoking}} \cdot \mathrm{smoking} + \beta_{\mathrm{hcv}} \cdot \mathrm{hcv} + \beta_{\mathrm{anxiety}} \cdot \mathrm{anxiety} + \beta_{\mathrm{depression}} \cdot \mathrm{depression} \\[2ex] & + \beta_{\mathrm{ckd}} \cdot \mathrm{ckd} + \beta_{\mathrm{diabetes}} \cdot \mathrm{diabetes} + \beta_{\mathrm{hypertension}} \cdot \mathrm{hypertension} \end{aligned}\]

where

\[\mathrm{logit}(p) = \log \frac{p}{1 - p}\]

is the logit function and \(p\) is the probability of incidence of hyperlipidemia.

The fitted coefficients and knot locations are given in the following tables.

Table 41: Hyperlipidemia Incidence

group2	age	anx	bmi_dif1	bmi_dif2	bmi_diff	bmi_raw_post	bmi_raw_post1	bmi_raw_post2	cd4n_entry	ckd	dm	dpr	h1yy_time	hcv	ht	intercept	smoking	year
het_black_female, idu_black_female	0.049	0.165	-0.151	0.320	0.092	-0.041	0.220	-0.564	0	0.404	1.002	0.315	-0.047	-0.204	0.176	-103.534	-0.115	0.049
het_black_male	0.028	0.025	0.162	-0.952	0.072	0.043	0.007	-0.088	0	0.116	0.561	-0.009	-0.030	-0.292	0.650	-139.448	0.039	0.066
het_hisp_female, het_white_female, idu_hisp_female, idu_white_female	0.035	-0.301	-0.237	0.626	0.137	0.030	-0.152	0.326	0	0.719	0.530	0.440	-0.052	-0.458	0.467	26.906	-0.058	-0.016
het_hisp_male	0.040	0.537	0.657	-2.290	0.166	0.326	-1.359	4.042	0	-0.041	1.182	-0.276	-0.038	-0.347	0.837	-82.765	-0.406	0.035
het_white_male	0.028	-0.017	-0.194	0.438	0.122	-0.211	0.922	-2.214	0	-0.053	1.078	-0.297	-0.061	-0.368	0.616	-126.074	0.132	0.063
idu_black_male	0.026	0.358	1.086	-4.927	-0.237	0.214	-0.821	2.226	0	0.327	0.600	-0.299	-0.009	-0.304	0.698	-319.781	-0.522	0.154
idu_hisp_male, idu_white_male	0.053	-0.130	0.359	-1.116	-0.157	-0.103	0.406	-0.820	0	0.383	1.292	0.003	-0.005	-0.485	0.290	-96.094	0.117	0.046
msm_black_male	0.048	0.002	-0.306	0.947	0.045	0.115	-0.270	0.532	0	0.103	1.266	0.169	-0.045	-0.254	0.581	-87.233	0.144	0.039
msm_hisp_male	0.032	-0.107	-0.126	0.530	0.049	0.229	-0.731	1.874	0	0.077	1.315	0.010	-0.039	-0.492	0.609	-147.265	-0.034	0.068
msm_white_male	0.035	-0.021	0.472	-1.627	-0.021	0.037	-0.013	-0.097	0	0.245	1.053	-0.045	-0.027	-0.197	0.336	-77.160	0.130	0.035

Table 42: Hyperlipidemia Delta BMI Knots

group	knot_1	knot_2	knot_3	knot_4
het_black_female, idu_black_female	-3.168	0.350	2.322	8.150
het_black_male	-2.303	0.300	1.900	6.400
het_hisp_female, het_white_female, idu_hisp_female, idu_white_female	-3.735	0.150	2.100	7.200
het_hisp_male	-1.067	0.650	2.772	6.435
het_white_male	-2.000	0.200	1.820	6.260
idu_black_male	-3.100	-0.268	1.100	5.015
idu_hisp_male, idu_white_male	-2.300	0.000	1.300	5.195
msm_black_male	-2.050	0.100	1.500	5.650
msm_hisp_male	-1.905	0.150	1.335	4.900
msm_white_male	-1.800	0.100	1.300	4.540

Table 43: Hyperlipidemia Post-ART BMI Knots

group	knot_1	knot_2	knot_3	knot_4
het_black_female, idu_black_female	19.582	26.300	32.300	46.600
het_black_male	19.600	24.332	28.368	37.005
het_hisp_female, het_white_female, idu_hisp_female, idu_white_female	19.260	24.600	29.800	43.670
het_hisp_male	21.032	25.600	29.000	35.970
het_white_male, msm_hisp_male	20.300	24.300	27.800	36.020
het_white_male, msm_hisp_male	20.300	24.515	27.500	35.310
idu_black_male	19.300	23.500	26.600	34.405
idu_hisp_male, idu_white_male	20.355	23.770	26.900	32.990
msm_black_male	19.350	23.600	27.600	37.300
msm_white_male	19.900	23.850	26.800	34.400

Diabetes Mellitus </>

At the beginning of the simulation each member of the initial population begins with \(\mathrm{diabetes} = 1\) with probability given by the first column in the table. At the start of each year new ART initiators are added where \(\mathrm{diabetes} = 1\) with probability given by the second column in the table.

Table 44: Diabetes Prevalence

Group	Prevalence in ART users (%)	Prevalence in ART initiators (%)
het_black_female	14.0	10.2
idu_black_female	14.0	10.2
het_black_male	17.3	10.3
het_hisp_female	9.9	12.4
idu_hisp_female	9.9	12.4
het_hisp_male	16.2	10.3
het_white_female	7.8	6.3
idu_white_female	7.8	6.3
het_white_male	10.4	7.1
idu_black_male	19.6	10.3
idu_hisp_male	19.6	10.3
idu_white_male	9.2	4.0
msm_black_male	10.8	4.0
msm_hisp_male	10.1	3.8
msm_white_male	7.4	4.0

At the beginning of each year the in care and out of care populations with \(\mathrm{diabetes} = 0\) have probability for incidence of diabetes mellitus given by

\[\begin{aligned} \mathrm{logit}(p) = \beta_0 &+ \beta_{\mathrm{year}} \cdot \mathrm{year} + \beta_{\mathrm{age}} \cdot \mathrm{age} + \beta_{\mathrm{sqrt\_init\_cd4}} \cdot \mathrm{sqrt\_init\_cd4} + \beta_{\mathrm{time\_since\_art}} \cdot \mathrm{time\_since\_art} \\[2ex] & + \beta_{\mathrm{delta\_bmi}} \cdot \mathrm{delta\_bmi} + \beta_{\mathrm{delta\_bmi\_1}} \cdot \mathrm{delta\_bmi\_1} + \beta_{\mathrm{delta\_bmi\_2}} \cdot \mathrm{delta\_bmi\_2} \\[2ex] & + \beta_{\mathrm{post\_art\_bmi}} \cdot \mathrm{post\_art\_bmi} + \beta_{\mathrm{post\_art\_bmi\_1}} \cdot \mathrm{post\_art\_bmi\_1} + \beta_{\mathrm{post\_art\_bmi\_2}} \cdot \mathrm{post\_art\_bmi\_2} \\[2ex] & + \beta_{\mathrm{smoking}} \cdot \mathrm{smoking} + \beta_{\mathrm{hcv}} \cdot \mathrm{hcv} + \beta_{\mathrm{anxiety}} \cdot \mathrm{anxiety} + \beta_{\mathrm{depression}} \cdot \mathrm{depression} \\[2ex] & + \beta_{\mathrm{lipid}} \cdot \mathrm{lipid} + \beta_{\mathrm{CKD}} \cdot \mathrm{CKD} + \beta_{\mathrm{hypertension}} \cdot \mathrm{hypertension} \end{aligned}\]

where

\[\mathrm{logit}(p) = \log \frac{p}{1 - p}\]

is the logit function and \(p\) is the probability of incidence of diabetes mellitus.

The fitted coefficients and knot locations are given in the following tables.

Table 45: Diabetes Incidence

group	age	anx	bmi_dif1	bmi_dif2	bmi_diff	bmi_raw_post	bmi_raw_post1	bmi_raw_post2	cd4n_entry	ckd	dpr	h1yy_time	hcv	ht	intercept	lipid	smoking	year
het_black_female, idu_black_female	0.003	0.121	0.026	-0.242	0.029	0.042	0.033	-0.088	-0.001	0.326	0.094	-0.027	0.173	0.624	-157.122	0.323	-0.032	0.075
het_black_male	0.015	-0.111	0.383	-1.218	-0.067	0.059	0.154	-0.522	0.000	-0.079	-0.029	-0.025	-0.088	0.213	-186.994	0.896	0.182	0.089
het_hisp_female, het_white_female, idu_hisp_female, idu_white_female	0.006	-0.078	0.581	-2.469	-0.140	-0.002	0.394	-0.892	0.000	0.299	0.616	-0.018	-0.340	0.692	-215.674	0.736	0.203	0.104
het_hisp_male	0.024	0.283	-0.170	0.818	-0.168	-0.115	0.804	-2.154	-0.001	-0.304	-0.060	-0.013	0.476	0.848	-33.525	0.459	0.010	0.015
het_white_male	0.012	-0.107	-1.704	4.030	0.683	0.264	-0.567	1.420	0.000	0.289	0.138	0.032	0.251	0.421	-125.654	0.543	-0.105	0.056
idu_black_male	0.012	0.379	0.194	-1.352	0.081	-0.061	0.617	-1.865	0.000	0.285	-0.031	0.005	0.340	0.616	-24.294	0.757	-0.328	0.010
idu_hisp_male, idu_white_male	0.015	0.060	-0.398	1.275	0.173	-0.137	0.921	-2.194	0.000	-0.291	-0.451	-0.019	0.486	1.098	-43.801	0.981	-0.269	0.020
msm_black_male	0.020	0.230	0.692	-1.940	-0.161	0.054	0.311	-0.857	0.000	0.090	0.091	-0.016	0.402	0.548	-129.903	0.750	-0.170	0.061
msm_hisp_male	0.035	0.089	0.946	-3.211	-0.139	0.103	0.113	-0.366	0.000	0.174	-0.051	-0.042	0.562	0.644	-186.737	0.867	0.292	0.088
msm_white_male	0.021	0.209	0.320	-1.059	-0.032	-0.092	0.590	-1.485	0.000	-0.060	0.010	-0.003	0.118	0.760	-98.474	0.709	0.337	0.046

Table 46: Diabetes Delta BMI Knots

group	knot_1	knot_2	knot_3	knot_4
het_black_female, idu_black_female	-3.072	0.350	2.400	8.222
het_black_male	-2.290	0.250	1.900	6.350
het_hisp_female, het_white_female, idu_hisp_female, idu_white_female	-3.700	0.190	2.110	7.200
het_hisp_male	-1.300	0.550	2.513	6.500
het_white_male	-2.020	0.200	1.900	6.090
idu_black_male	-2.822	-0.200	1.150	4.772
idu_hisp_male, idu_white_male	-2.300	0.000	1.300	5.150
msm_black_male	-2.000	0.115	1.500	5.705
msm_hisp_male	-1.900	0.150	1.300	4.850
msm_white_male	-1.850	0.050	1.250	4.600

Table 47: Diabetes Post-ART BMI Knots

group	knot_1	knot_2	knot_3	knot_4
het_black_female, idu_black_female	19.500	25.90	31.900	45.900
het_black_male	19.700	24.35	28.200	36.590
het_hisp_female, het_white_female, idu_hisp_female, idu_white_female	19.420	24.60	29.610	41.820
het_hisp_male	20.600	25.00	28.925	35.675
het_white_male	20.340	24.50	28.050	36.630
idu_black_male	19.355	23.40	26.308	33.767
idu_hisp_male, idu_white_male	20.400	23.80	26.800	32.752
msm_black_male	19.400	23.70	27.600	36.910
msm_hisp_male	20.500	24.60	27.500	35.000
msm_white_male	20.000	24.00	26.900	34.200

Hypertension </>

At the beginning of the simulation each member of the initial population begins with \(\mathrm{hypertension} = 1\) with probability given by the first column in the table. At the start of each year new ART initiators are added where \(\mathrm{hypertension} = 1\) with probability given by the second column in the table.

Table 48: Hypertension Prevalence

Group	Prevalence in ART users (%)	Prevalence in ART initiators (%)
het_black_female	35.0	30.8
het_black_male	46.2	31.3
het_hisp_female	20.8	11.9
het_white_female	20.8	19.0
idu_hisp_female	20.8	11.9
idu_white_female	20.8	19.0
het_hisp_male	26.7	13.4
het_white_male	29.7	16.4
idu_black_female	48.9	30.8
idu_black_male	54.8	39.6
idu_hisp_male	39.5	13.4
idu_white_male	27.1	13.3
msm_black_male	33.4	14.4
msm_hisp_male	21.3	6.9
msm_white_male	26.5	13.7

At the beginning of each year the in care and out of care populations with \(\mathrm{hypertension} = 0\) have probability for incidence of hypertension given by

\[\begin{aligned} \mathrm{logit}(p) = \beta_0 &+ \beta_{\mathrm{year}} \cdot \mathrm{year} + \beta_{\mathrm{age}} \cdot \mathrm{age} + \beta_{\mathrm{sqrt\_init\_cd4}} \cdot \mathrm{sqrt\_init\_cd4} + \beta_{\mathrm{time\_since\_art}} \cdot \mathrm{time\_since\_art} \\[2ex] & + \beta_{\mathrm{delta\_bmi}} \cdot \mathrm{delta\_bmi} + \beta_{\mathrm{delta\_bmi\_1}} \cdot \mathrm{delta\_bmi\_1} + \beta_{\mathrm{delta\_bmi\_2}} \cdot \mathrm{delta\_bmi\_2} \\[2ex] & + \beta_{\mathrm{post\_art\_bmi}} \cdot \mathrm{post\_art\_bmi} + \beta_{\mathrm{post\_art\_bmi\_1}} \cdot \mathrm{post\_art\_bmi\_1} + \beta_{\mathrm{post\_art\_bmi\_2}} \cdot \mathrm{post\_art\_bmi\_2} \\[2ex] & + \beta_{\mathrm{smoking}} \cdot \mathrm{smoking} + \beta_{\mathrm{hcv}} \cdot \mathrm{hcv} + \beta_{\mathrm{anxiety}} \cdot \mathrm{anxiety} + \beta_{\mathrm{depression}} \cdot \mathrm{depression} \\[2ex] & + \beta_{\mathrm{lipid}} \cdot \mathrm{lipid} + \beta_{\mathrm{diabetes}} \cdot \mathrm{diabetes} + \beta_{\mathrm{CKD}} \cdot \mathrm{CKD} \end{aligned}\]

where

\[\mathrm{logit}(p) = \log \frac{p}{1 - p}\]

is the logit function and \(p\) is the probability of incidence of hypertension.

The fitted coefficients and knot locations are given in the following tables.

Table 49: Hypertension Incidence

group2	age	anx	bmi_dif1	bmi_dif2	bmi_diff	bmi_raw_post	bmi_raw_post1	bmi_raw_post2	cd4n_entry	ckd	dm	dpr	h1yy_time	hcv	intercept	lipid	smoking	year
het_black_female	0.032	0.188	0.072	-0.092	-0.028	0.009	0.207	-0.528	0.000	0.286	0.798	0.200	-0.026	0.185	69.100	0.191	0.269	-0.037
het_black_male	0.027	-0.163	0.632	-1.798	-0.138	0.007	0.253	-0.804	0.000	0.845	0.249	-0.043	-0.057	0.099	-28.548	0.415	0.221	0.012
het_hisp_female, het_white_female	0.029	0.210	0.418	-1.892	-0.045	-0.024	0.419	-0.945	0.000	0.716	0.534	0.305	-0.048	-0.095	50.409	0.154	0.163	-0.028
het_hisp_male	0.028	0.366	-0.268	1.459	-0.137	-0.157	0.486	-1.389	0.000	1.189	1.209	-0.012	-0.054	0.889	-129.672	0.639	0.519	0.064
het_white_male	0.026	0.714	0.414	-1.382	-0.101	0.136	-0.679	1.997	-0.001	0.611	0.655	-0.114	-0.074	0.135	-90.692	0.670	0.459	0.041
idu_black_female, idu_hisp_female, idu_white_female	0.052	0.009	-0.426	1.839	0.114	-0.018	0.071	-0.134	0.000	0.700	0.205	-0.177	-0.036	-0.090	3.393	0.571	0.272	-0.004
idu_black_male	0.022	0.062	-0.601	2.683	0.245	-0.007	0.291	-0.852	0.000	0.678	1.042	-0.303	-0.028	0.634	47.656	0.204	0.710	-0.026
idu_hisp_male, idu_white_male	0.042	0.199	0.895	-3.219	-0.259	0.155	-0.322	0.814	0.000	0.763	1.486	-0.051	-0.071	0.268	-117.663	0.135	0.237	0.054
msm_black_male	0.029	0.179	0.671	-2.358	-0.080	0.099	-0.096	0.230	0.000	0.630	0.322	0.109	-0.025	0.156	24.934	0.506	0.239	-0.016
msm_hisp_male	0.022	0.096	1.045	-3.672	-0.170	0.169	-0.615	1.938	0.001	0.831	0.488	0.134	0.031	0.369	-51.746	0.797	0.433	0.021
msm_white_male	0.022	0.266	0.329	-1.021	-0.041	0.086	0.032	-0.168	0.000	0.328	0.434	0.161	-0.020	0.146	-25.474	0.469	0.277	0.009

Table 50: Hypertension Delta BMI Knots

group	knot_1	knot_2	knot_3	knot_4
het_black_female	-3.230	0.340	2.350	8.030
het_black_male	-1.850	0.450	2.000	6.350
het_hisp_female, het_white_female	-3.630	0.100	2.100	7.140
het_hisp_male	-1.350	0.697	2.800	6.515
het_white_male, msm_black_male	-2.000	0.150	1.852	5.837
het_white_male, msm_black_male	-2.000	0.100	1.500	5.418
idu_black_female, idu_hisp_female, idu_white_female	-3.368	0.000	1.900	7.640
idu_black_male	-3.300	-0.230	1.130	4.600
idu_hisp_male, idu_white_male	-2.388	0.000	1.250	4.975
msm_hisp_male, msm_white_male	-1.800	0.200	1.350	4.902
msm_hisp_male, msm_white_male	-1.800	0.100	1.250	4.600

Table 51: Hypertension Post-ART BMI Knots

group	knot_1	knot_2	knot_3	knot_4
het_black_male, het_black_female	19.500	24.100	27.900	35.888
het_black_male, het_black_female	19.500	25.600	31.460	44.850
het_hisp_female, het_white_female	19.520	24.640	29.980	43.200
het_hisp_male	20.600	25.295	28.700	34.858
het_white_male	20.292	24.300	27.602	35.235
idu_black_female, idu_hisp_female, idu_white_female	18.900	24.255	28.023	37.712
idu_black_male	19.050	22.850	25.830	33.280
idu_hisp_male, idu_white_male	20.363	23.688	26.600	31.887
msm_black_male	19.282	23.400	27.000	35.667
msm_hisp_male	20.400	24.500	27.450	34.650
msm_white_male	19.900	23.800	26.622	33.500

Stage 3 </>

The stage 3 conditions are cancer, end-stage liver disease (ELSD), and myocardial infarction (MI). Prevalence in the 2009 ART user population is taken from the 2009 NA-ACCORD population, while prevalence in ART initiators was taken from the 2009 - 2022 NA-ACCORD ART initiator population. Incidence is modeled using logistic regression and is based on NA-ACCORD data. The logistic regression models the logit of probability for incidence of a stage 3 condition as a linear function of calendar year (\(\mathrm{year}\)), age (\(\mathrm{age}\)), square root of CD4 count at ART initiation (\(\mathrm{sqrt\_init\_cd4}\)), number of years since ART initiation (\(\mathrm{time\_since\_art}\)), change in BMI after ART initiation (\(\mathrm{delta\_bmi}\)) and BMI after ART initiation (\(\mathrm{post\_art\_bmi}\)) modeled as restricted cubic splines, stage 0 condition status (\(\mathrm{smoking}\), \(\mathrm{hcv}\)), stage 1 condition status (\(\mathrm{anxiety}\), \(\mathrm{depression}\)), and stage 2 condition status (\(\mathrm{ckd}\), \(\mathrm{lipid}\), \(\mathrm{diabetes}\), \(\mathrm{hypertension}\)).

At the beginning of the simulation each member of the initial population begins with \(\mathrm{stage\_3} = 1\) with probability given by the first column in the table. At the start of each year new ART initiators are added where \(\mathrm{stage\_3} = 1\) with probability given by the second column in the table. Here \(\mathrm{stage\_3}\) are \(\mathrm{cancer}\), \(\mathrm{esld}\), and \(\mathrm{mi}\). These prevalences are:

Table 52: Cancer Prevalence

Table 53: ESLD Prevalence

Table 54: MI Prevalence

All three stage 3 comorbidities use the same incidence probability function given by

\[\begin{split} \mathrm{logit}(p) = \beta_0 &+ \beta_\mathrm{year}\cdot\mathrm{year} + \beta_\mathrm{age}\cdot\mathrm{age} + \beta_\mathrm{sqrt\_init\_cd4}\cdot\mathrm{sqrt\_init\_cd4} + \beta_\mathrm{time\_since\_art} \cdot \mathrm{time\_since\_art} \\[2ex] &+ \beta_\mathrm{delta\_bmi} \cdot \mathrm{delta\_bmi} + \beta_\mathrm{delta\_bmi\_1} \cdot \mathrm{delta\_bmi\_1} + \beta_\mathrm{delta\_bmi\_2} \cdot \mathrm{delta\_bmi\_2} \\[2ex] &+ \beta_\mathrm{post\_art\_bmi} \cdot \mathrm{post\_art\_bmi} + \beta_\mathrm{post\_art\_bmi\_1} \cdot \mathrm{post\_art\_bmi\_1} + \beta_\mathrm{post\_art\_bmi\_2} \cdot \mathrm{post\_art\_bmi\_2} \\[2ex] &+ \beta_\mathrm{smoking} \cdot \mathrm{smoking} + \beta_\mathrm{hcv} \cdot \mathrm{hcv} + \beta_\mathrm{anxiety} \cdot \mathrm{anxiety} + \beta_\mathrm{depression} \cdot \mathrm{depression} \\[2ex] &+ \beta_\mathrm{ckd} \cdot \mathrm{ckd} + \beta_\mathrm{lipid} \cdot \mathrm{lipid} + \beta_\mathrm{diabetes} \cdot \mathrm{diabetes} +\beta_\mathrm{hypertension} \cdot \mathrm{hypertension}. \end{split}\]

The fitted coefficients and knot locations are given in the following tables.

Table 55: Cancer Incidence

Table 55

Table 56: Cancer Delta BMI Knots

Table 57: Cancer Post-ART BMI Knots

Table 58: ESLD Incidence

Table 58

Table 59: ESLD Delta BMI Knots

Table 60: ESLD Post-ART BMI Knots

Table 61: MI Incidence

Table 61

Table 62: MI Delta BMI Knots

Table 63: MI Post-ART BMI Knots

Modified Mortality Functions with Comorbidities

The mortality functions are modified to include all stages of comorbidity.

Mortality In Care </>

We use logistic regression to model the probability of dying in care as a function of calendar year (\(\mathrm{year}\)), 10 year age category (\(\mathrm{age\_cat}\)), CD4 count at ART initiation (\(\mathrm{sqrt\_init\_cd4}\)), year of ART initiation (\(\mathrm{art\_init\_year}\)), BMI after ART initiation (\(\mathrm{post\_art\_bmi}\)) modeled as a restricted cubic spline, stage 0 comorbiditities (\(\mathrm{smoking}\), \(\mathrm{hcv}\)), stage 1 comorbidities (\(\mathrm{anxiety}\), \(\mathrm{depression}\)), stage 2 comorbiditities (\(\mathrm{ckd}\), \(\mathrm{lipid}\), \(\mathrm{diabetes}\), \(\mathrm{hypertension}\)), and stage 3 comorbidities (\(\mathrm{cancer}\), \(\mathrm{esld}\), \(\mathrm{mi}\)).

\[\begin{aligned} \mathrm{logit}(p) = \beta_0 &+ \beta_{\mathrm{year}} \cdot \mathrm{year} + \beta_{\mathrm{age\_cat}} \cdot \mathrm{age\_cat} + \beta_{\mathrm{sqrt\_init\_cd4}} \cdot \mathrm{sqrt\_init\_cd4} + \beta_{\mathrm{art\_init\_year}} \cdot \mathrm{art\_init\_year} \\[2ex] & + \beta_{\mathrm{post\_art\_bmi}} \cdot \mathrm{post\_art\_bmi} + \beta_{\mathrm{post\_art\_bmi\_1}} \cdot \mathrm{post\_art\_bmi\_1} + \beta_{\mathrm{post\_art\_bmi\_2}} \cdot \mathrm{post\_art\_bmi\_2} \\[2ex] & + \beta_{\mathrm{smoking}} \cdot \mathrm{smoking} + \beta_{\mathrm{hcv}} \cdot \mathrm{hcv} + \beta_{\mathrm{anxiety}} \cdot \mathrm{anxiety} + \beta_{\mathrm{depression}} \cdot \mathrm{depression} + \beta_{\mathrm{ckd}} \cdot \mathrm{ckd} \\[2ex] & + \beta_{\mathrm{lipid}} \cdot \mathrm{lipid} + \beta_{\mathrm{diabetes}} \cdot \mathrm{diabetes} + \beta_{\mathrm{hypertension}} \cdot \mathrm{hypertension} + \beta_{\mathrm{cancer}} \cdot \mathrm{cancer} + \beta_{\mathrm{esld}} \cdot \mathrm{esld} + \beta_{\mathrm{mi}} \cdot \mathrm{mi} \end{aligned}\]

where

\[\mathrm{logit}(p) = \log \frac{p}{1 - p}\]

is the logit function and \(p\) is probability of dying in care. The coefficients were estimated using a Generalized Estimating Equation (GEE) with a logit link and an unstructured correlation structure using the geepack software package for R. The NA-ACCORD dataset was restricted to the years 2009-2020 and each patient is represented by a data point for each year they were alive and under observation in NA-ACCORD. The regression resulted in the following coefficient estimates and knots:

Table 64: Mortality In Care Coefficient Estimates

group2	agecat	anx	bmi_raw_post	bmi_raw_post1	bmi_raw_post2	ckd	dm	dpr	esld	h1yy	hcv	ht	intercept	lipid	malig	mi	smoking	sqrtcd4n	year
het_black_female	0.013	-0.247	-0.153	0.557	-1.163	0.701	0.557	0.110	2.054	0.000	0.177	0.353	181.495	-0.364	1.364	1.172	0.111	-0.026	-0.090
het_black_male	0.223	0.348	-0.124	0.188	-0.369	0.471	1.094	0.001	2.248	-0.004	0.215	0.111	140.208	0.069	1.750	0.771	0.311	-0.017	-0.067
het_hisp_female, het_white_female	0.168	0.715	-0.184	0.952	-2.046	0.237	0.789	-0.124	2.782	0.039	0.718	-0.181	49.849	-0.463	1.797	1.653	0.781	-0.044	-0.064
het_hisp_male, het_white_male	0.360	0.770	-0.154	0.477	-1.315	-0.021	1.012	0.238	1.825	-0.009	0.362	-0.113	52.388	-0.173	1.128	0.801	0.105	-0.030	-0.018
idu_black_female, idu_hisp_female, idu_white_female	0.094	-0.275	-0.180	0.538	-1.198	-0.097	-0.175	0.435	2.254	-0.007	0.987	0.176	-20.121	-0.359	1.918	-0.842	0.582	0.001	0.017
idu_black_male	0.103	0.420	-0.189	0.420	-0.903	0.494	0.507	-0.266	1.783	0.037	0.371	0.683	102.242	-0.122	0.784	0.270	-0.009	-0.025	-0.088
idu_hisp_male, idu_white_male	0.497	0.203	-0.083	-0.100	0.526	0.332	0.521	0.259	1.379	0.025	0.655	0.372	25.419	-0.573	0.774	0.699	0.043	-0.032	-0.040
msm_black_male	0.160	0.065	-0.189	0.583	-1.354	0.147	1.507	0.524	2.125	-0.008	-0.163	0.249	235.135	-0.512	1.615	0.981	0.072	-0.033	-0.110
msm_hisp_male, msm_white_male	0.394	0.072	-0.250	0.527	-1.093	0.117	0.918	0.230	2.110	0.042	0.186	0.103	173.318	-0.268	1.310	0.904	0.314	-0.025	-0.128

Table 65: Mortality In Care Post-ART BMI Knots

group	knot_1	knot_2	knot_3	knot_4
het_black_female	19.9	26.4	32.9	47.5
het_black_male	19.6	24.2	28.5	38.3
het_hisp_female, het_white_female	20.0	25.2	30.8	43.2
het_hisp_male, het_white_male	20.5	24.7	28.4	35.0
idu_black_female, idu_hisp_female, idu_white_female	19.2	24.8	28.9	40.7
idu_black_male	19.7	23.4	26.6	33.9
idu_hisp_male, idu_white_male	20.0	23.6	26.6	32.5
msm_black_male	19.3	23.5	27.4	37.0
msm_hisp_male, msm_white_male	19.9	23.9	26.9	34.9

Mortality Out of Care </>

We use logistic regression to model the probability of dying in care as a function of calendar year (\(\mathrm{year}\)), 10 year age category (\(\mathrm{age\_cat}\)), CD4 count(\(\mathrm{sqrt\_cd4}\)), BMI after ART initiation (\(\mathrm{post\_art\_bmi}\)) modeled as a restricted cubic spline, stage 0 comorbidities (\(\mathrm{smoking}\), \(\mathrm{hcv}\)), stage 1 comorbidities (\(\mathrm{anxiety}\), \(\mathrm{depression}\)), stage 2 comorbiditities (\(\mathrm{ckd}\), \(\mathrm{lipid}\), \(\mathrm{diabetes}\), \(\mathrm{hypertension}\)), and stage 3 comorbidities (\(\mathrm{cancer}\), \(\mathrm{esld}\), \(\mathrm{mi}\)).

\[\begin{aligned} \text{logit}(p) = \beta_0 &+ \beta_{\text{year}} \cdot \text{year} + \beta_{\text{age\_cat}} \cdot \text{age\_cat} + \beta_{\text{sqrt\_cd4}} \cdot \text{sqrt\_cd4} + \beta_{\text{post\_art\_bmi}} \cdot \text{post\_art\_bmi} \\[2ex] & + \beta_{\text{post\_art\_bmi\_1}} \cdot \text{post\_art\_bmi\_1} + \beta_{\text{post\_art\_bmi\_2}} \cdot \text{post\_art\_bmi\_2} + \beta_{\text{smoking}} \cdot \text{smoking} \\[2ex] & + \beta_{\text{hcv}} \cdot \text{hcv} + \beta_{\text{anxiety}} \cdot \text{anxiety} + \beta_{\text{depression}} \cdot \text{depression} + \beta_{\text{ckd}} \cdot \text{ckd} + \beta_{\text{lipid}} \cdot \text{lipid} \\[2ex] & + \beta_{\text{diabetes}} \cdot \text{diabetes} + \beta_{\text{hypertension}} \cdot \text{hypertension} + \beta_{\text{cancer}} \cdot \text{cancer} + \beta_{\text{esld}} \cdot \text{esld} + \beta_{\text{mi}} \cdot \text{mi} \end{aligned}\]

where

\[\mathrm{logit}(p) = \log \frac{p}{1 - p}\]

is the logit function and \(p\) is the probability of dying out of care. The coefficients were estimated using a Generalized Estimating Equation (GEE) with a logit link and an unstructured correlation structure using the geepack software package for R. The NA-ACCORD dataset was restricted to the years 2009-2020 and each patient was represented by a data point for each year they were alive and under observation in NA-ACCORD. The regression resulted in the following coefficient estimates and knots:

Table 66: Mortality Out Of Care Coefficient Estimates

group2	agecat	anx	bmi_raw_post	bmi_raw_post1	bmi_raw_post2	ckd	dm	dpr	esld	hcv	ht	intercept	lipid	malig	mi	smoking	tv_sqrtcd4n	year
het_black_female	0.128	-0.266	-0.121	0.491	-1.027	0.629	0.405	0.180	1.460	0.359	0.474	115.450	-0.066	1.410	0.957	0.146	-0.127	-0.058
het_black_male	0.311	0.474	-0.115	0.310	-0.729	0.355	1.032	0.014	1.767	0.257	0.197	101.491	0.315	1.627	0.684	0.371	-0.104	-0.051
het_hisp_female, het_white_female	0.178	0.835	-0.118	0.591	-1.233	0.370	0.465	-0.185	1.990	0.681	-0.130	-30.198	-0.386	1.612	1.571	0.673	-0.141	0.015
het_hisp_male, het_white_male	0.336	0.946	-0.129	0.467	-1.331	0.131	0.601	0.312	1.735	0.295	0.045	-0.185	0.095	1.033	0.947	0.243	-0.107	-0.001
idu_black_female, idu_hisp_female, idu_white_female	0.274	-0.274	-0.144	0.499	-1.137	-0.232	-0.143	0.494	2.158	0.796	0.107	-76.538	-0.327	1.624	-0.451	1.216	-0.116	0.037
idu_black_male	0.155	0.483	-0.143	0.422	-1.009	0.453	0.300	-0.328	1.971	0.163	0.728	101.010	0.240	0.772	0.254	0.076	-0.115	-0.050
idu_hisp_male, idu_white_male	0.491	0.375	-0.077	0.059	-0.038	0.485	0.403	0.215	1.385	0.607	0.348	12.438	-0.292	0.545	0.774	0.001	-0.109	-0.008
msm_black_male	0.200	0.255	-0.139	0.556	-1.353	0.017	1.386	0.408	1.646	-0.208	0.378	139.339	-0.138	1.413	0.950	-0.105	-0.144	-0.069
msm_hisp_male, msm_white_male	0.379	0.053	-0.208	0.470	-0.965	0.116	0.708	0.151	1.545	0.184	0.107	129.514	-0.128	1.121	0.875	0.311	-0.124	-0.064

Table 67: Mortality Out Of Care Post-ART BMI Knots

group	knot_1	knot_2	knot_3	knot_4
het_black_female	19.920	26.400	32.860	47.450
het_black_male	19.600	24.200	28.500	38.275
het_hisp_female, het_white_female	19.960	25.170	30.800	43.200
het_hisp_male, het_white_male	20.500	24.700	28.400	35.013
idu_black_female, idu_hisp_female, idu_white_female	19.215	24.785	28.865	40.735
idu_black_male	19.655	23.442	26.600	33.945
idu_hisp_male, idu_white_male	20.030	23.600	26.600	32.540
msm_black_male	19.300	23.500	27.350	37.050
msm_hisp_male, msm_white_male	19.900	23.900	26.900	34.900

End Stage Liver Disease (ESLD) </>

Table 68: ESLD Prevalence

Group	Prevalence in ART users (%)	Prevalence in ART initiators (%)
msm_black_male, msm_hisp_male, msm_white_male	1.07	0.38
het_black_male, het_hisp_male, het_white_male, idu_black_male, idu_hisp_male, idu_white_male, het_black_female, het_hisp_female, het_white_female, idu_black_female, idu_hisp_female, idu_white_female	1.15	0.38

We use generalized estimating equations with a logit link and exchangable correlation structure to model the probability of incident ESLD as a function of:

\[\begin{aligned} \mathrm{logit}(p) = \beta_0 &+ \beta_{\mathrm{year}} \cdot \mathrm{year} + \beta_{\mathrm{age}} \cdot \mathrm{age} + \beta_{\mathrm{sqrt\_init\_cd4}} \cdot \mathrm{sqrt\_init\_cd4} + \beta_{\mathrm{time\_since\_art}} \cdot \mathrm{time\_since\_art} \\[2ex] & + \beta_{\mathrm{delta\_bmi}} \cdot \mathrm{delta\_bmi} + \beta_{\mathrm{delta\_bmi\_1}} \cdot \mathrm{delta\_bmi\_1} + \beta_{\mathrm{delta\_bmi\_2}} \cdot \mathrm{delta\_bmi\_2} \\[2ex] & + \beta_{\mathrm{post\_art\_bmi}} \cdot \mathrm{post\_art\_bmi} + \beta_{\mathrm{post\_art\_bmi\_1}} \cdot \mathrm{post\_art\_bmi\_1} + \beta_{\mathrm{post\_art\_bmi\_2}} \cdot \mathrm{post\_art\_bmi\_2} \\[2ex] & + \beta_{\mathrm{smoking}} \cdot \mathrm{smoking} + \beta_{\mathrm{hcv}} \cdot \mathrm{hcv} + \beta_{\mathrm{anxiety}} \cdot \mathrm{anxiety} + \beta_{\mathrm{depression}} \cdot \mathrm{depression} \\[2ex] & + \beta_{\mathrm{ckd}} \cdot \mathrm{ckd} + \beta_{\mathrm{lipid}} \cdot \mathrm{lipid} + \beta_{\mathrm{diabetes}} \cdot \mathrm{diabetes} + \beta_{\mathrm{hypertension}} \cdot \mathrm{hypertension} \end{aligned}\]

where

\[\mathrm{logit}(p) = \log \frac{p}{1 - p}\]

is the logit function and \(p\) is the probability of incidence of ESLD

Table 69: ESLD Coefficient Estimates

group	age	anx	bmi_dif1	bmi_dif2	bmi_diff	bmi_raw_post	bmi_raw_post1	bmi_raw_post2	cd4n_entry	ckd	dm	dpr	h1yy_time	hcv	ht	intercept	lipid	smoking	year
All 15 subgroups	0.015	0.033	1.069	-3.958	-0.089	-0.001	-0.195	0.362	0	0.395	1.581	0.443	-0.018	1.552	0.477	109.514	-0.857	0.817	-0.059

Table 70: ESLD Post-ART BMI Knots

group	knot_1	knot_2	knot_3	knot_4
het_black_male, het_hisp_male, het_white_male, idu_black_male, idu_hisp_male, idu_white_male, msm_black_male, msm_hisp_male, msm_white_male, het_black_female, het_hisp_female, het_white_female, idu_black_female, idu_hisp_female, idu_white_female	19.8	24.15	27.95	38.5

Table 71: ESLD Delta BMI Knots

group	knot_1	knot_2	knot_3	knot_4
het_black_male, het_hisp_male, het_white_male, idu_black_male, idu_hisp_male, idu_white_male, msm_black_male, msm_hisp_male, msm_white_male, het_black_female, het_hisp_female, het_white_female, idu_black_female, idu_hisp_female, idu_white_female	-2.35	0.2	1.75	6.293

Malignancy </>

Table 72: Malig Prevalence

Group	Prevalence in ART users (%)	Prevalence in ART initiators (%)
het_black_female	5.35	3.52
het_hisp_female	5.35	3.52
het_white_female	5.35	3.52
idu_black_female	5.35	3.52
idu_hisp_female	5.35	3.52
idu_white_female	5.35	3.52
het_hisp_male	6.00	5.15
idu_hisp_male	6.00	3.31
msm_black_male	7.20	2.40
het_black_male	7.25	5.15
idu_black_male	9.19	3.31
idu_white_male	9.33	3.31
msm_hisp_male	9.82		2.40
het_white_male	10.67	5.15
msm_white_male	11.92	4.38

We use generalized estimating equations with a logit link and exchangable correlation structure to model the probability of incident malignancy diagnosis as a function of:

\[\begin{aligned} \mathrm{logit}(p) = \beta_0 &+ \beta_{\mathrm{year}} \cdot \mathrm{year} + \beta_{\mathrm{age}} \cdot \mathrm{age} + \beta_{\mathrm{sqrt\_init\_cd4}} \cdot \mathrm{sqrt\_init\_cd4} + \beta_{\mathrm{time\_since\_art}} \cdot \mathrm{time\_since\_art} \\[2ex] & + \beta_{\mathrm{delta\_bmi}} \cdot \mathrm{delta\_bmi} + \beta_{\mathrm{delta\_bmi\_1}} \cdot \mathrm{delta\_bmi\_1} + \beta_{\mathrm{delta\_bmi\_2}} \cdot \mathrm{delta\_bmi\_2} \\[2ex] & + \beta_{\mathrm{post\_art\_bmi}} \cdot \mathrm{post\_art\_bmi} + \beta_{\mathrm{post\_art\_bmi\_1}} \cdot \mathrm{post\_art\_bmi\_1} + \beta_{\mathrm{post\_art\_bmi\_2}} \cdot \mathrm{post\_art\_bmi\_2} \\[2ex] & + \beta_{\mathrm{smoking}} \cdot \mathrm{smoking} + \beta_{\mathrm{hcv}} \cdot \mathrm{hcv} + \beta_{\mathrm{anxiety}} \cdot \mathrm{anxiety} + \beta_{\mathrm{depression}} \cdot \mathrm{depression} \\[2ex] & + \beta_{\mathrm{ckd}} \cdot \mathrm{ckd} + \beta_{\mathrm{lipid}} \cdot \mathrm{lipid} + \beta_{\mathrm{diabetes}} \cdot \mathrm{diabetes} + \beta_{\mathrm{hypertension}} \cdot \mathrm{hypertension} \end{aligned}\]

where

\[\mathrm{logit}(p) = \log \frac{p}{1 - p}\]

is the logit function and \(p\) is the probability of incidence of malignancy

Table 73: Malig Coefficient Estimates

group	age	anx	bmi_dif1	bmi_dif2	bmi_diff	bmi_raw_post	bmi_raw_post1	bmi_raw_post2	cd4n_entry	ckd	dm	dpr	h1yy_time	hcv	ht	intercept	lipid	smoking	year
het_black_female, het_hisp_female, het_white_female, idu_black_female, idu_hisp_female, idu_white_female	0.025	0.079	-0.013	-0.229	0.060	-0.084	0.227	-0.432	-0.001	0.380	0.308	0.167	-0.045	0.455	0.292	-84.368	-0.641	0.483	0.040
het_black_male	0.051	0.037	-1.824	5.955	0.528	-0.122	0.253	-0.606	0.000	0.141	0.129	0.168	-0.009	-0.233	-0.018	70.900	-0.145	0.716	-0.037
het_hisp_male, idu_hisp_male, msm_hisp_male	0.036	-0.053	0.272	-0.341	-0.181	-0.158	0.432	-1.316	-0.003	0.161	0.332	0.198	-0.028	0.205	0.582	-10.738	-0.434	0.672	0.004
het_white_male, idu_white_male	0.067	0.458	-1.606	5.110	0.442	-0.133	0.410	-0.956	0.000	-0.415	0.550	-0.227	-0.021	0.317	-0.397	-71.380	0.281	0.174	0.033
idu_black_male	0.054	-0.252	-1.094	4.492	0.338	0.067	-0.167	0.374	-0.001	0.373	0.301	0.457	-0.024	-0.075	0.590	-93.110	-0.485	0.896	0.042
msm_black_male	0.038	-0.161	0.629	-1.971	-0.156	-0.150	0.526	-1.280	0.000	0.076	0.455	0.045	0.038	0.104	0.433	135.901	-0.221	0.091	-0.069
msm_white_male	0.059	0.479	0.606	-2.305	-0.099	0.177	-0.915	2.589	-0.001	-0.045	0.688	-0.163	-0.055	0.270	-0.213	-51.811	0.299	0.322	0.020

Table 74: Malig Post-ART BMI Knots

group	knot_1	knot_2	knot_3	knot_4
het_black_female, het_hisp_female, het_white_female, idu_black_female, idu_hisp_female, idu_white_female	19.700	25.900	31.700	45.380
het_black_male	19.900	24.795	28.450	37.160
het_hisp_male, idu_hisp_male, msm_hisp_male	20.517	24.672	27.650	34.932
het_white_male, idu_white_male	20.300	24.100	27.450	34.845
idu_black_male	19.400	23.550	26.565	33.895
msm_black_male	19.433	23.800	27.600	36.667
msm_white_male	20.000	24.000	27.000	34.900

Table 75: Malig Delta BMI Knots

group	knot_1	knot_2	knot_3	knot_4
het_black_female, het_hisp_female, het_white_female, idu_black_female, idu_hisp_female, idu_white_female	-3.40	0.30	2.3	8.150
het_black_male	-2.35	0.25	1.8	6.365
het_hisp_male, idu_hisp_male, msm_hisp_male	-2.00	0.15	1.4	5.000
het_white_male, idu_white_male	-2.25	0.10	1.6	5.400
idu_black_male	-3.00	-0.30	1.1	4.795
msm_black_male	-2.20	0.10	1.5	5.600
msm_white_male	-1.80	0.10	1.3	4.550

Myocardial Infarction (MI) </>

Table 76: MI Prevalence

Group	Prevalence in ART users (%)	Prevalence in ART initiators (%)
het_black_male, het_hisp_male, het_white_male, idu_black_male, idu_hisp_male, idu_white_male, msm_black_male, msm_hisp_male, het_black_female, het_hisp_female, het_white_female, idu_black_female, idu_hisp_female, idu_white_female	1.85	0.56
msm_white_male	2.79	0.56

We use generalized estimating equations with a logit link and exchangeable correlation structure to model the probability of incident MI as a function of:

\[\begin{aligned} \mathrm{logit}(p) = \beta_{0} &+ \beta_{\mathrm{year}} \cdot \mathrm{year} + \beta_{\mathrm{age}} \cdot \mathrm{age} + \beta_{\mathrm{sqrt\_init\_cd4}} \cdot \mathrm{sqrt\_init\_cd4} + \beta_{\mathrm{time\_since\_art}} \cdot \mathrm{time\_since\_art} \\[2ex] & + \beta_{\mathrm{delta\_bmi}} \cdot \mathrm{delta\_bmi} + \beta_{\mathrm{delta\_bmi\_1}} \cdot \mathrm{delta\_bmi\_1} + \beta_{\mathrm{delta\_bmi\_2}} \cdot \mathrm{delta\_bmi\_2} \\[2ex] & + \beta_{\mathrm{post\_art\_bmi}} \cdot \mathrm{post\_art\_bmi} + \beta_{\mathrm{post\_art\_bmi\_1}} \cdot \mathrm{post\_art\_bmi\_1} + \beta_{\mathrm{post\_art\_bmi\_2}} \cdot \mathrm{post\_art\_bmi\_2} \\[2ex] & + \beta_{\mathrm{smoking}} \cdot \mathrm{smoking} + \beta_{\mathrm{hcv}} \cdot \mathrm{hcv} + \beta_{\mathrm{anxiety}} \cdot \mathrm{anxiety} + \beta_{\mathrm{depression}} \cdot \mathrm{depression} \\[2ex] & + \beta_{\mathrm{ckd}} \cdot \mathrm{ckd} + \beta_{\mathrm{lipid}} \cdot \mathrm{lipid} + \beta_{\mathrm{diabetes}} \cdot \mathrm{diabetes} + \beta_{\mathrm{hypertension}} \cdot \mathrm{hypertension} \end{aligned}\]

where

\[\mathrm{logit}(p) = \log \frac{p}{1 - p}\]

is the logit function and \(p\) is the probability of incidence of MI

Table 77: MI Coefficient Estimates

group	age	anx	bmi_dif1	bmi_dif2	bmi_diff	bmi_raw_post	bmi_raw_post1	bmi_raw_post2	cd4n_entry	ckd	dm	dpr	h1yy_time	hcv	ht	intercept	lipid	smoking	year
All 15 subgroups	0.032	0.088	0.471	-2.024	-0.064	0.013	-0.233	0.631	0	-0.114	0.243	0.304	0	0.294	1.014	219.784	2.3	0.558	-0.114

Table 78: MI Post-ART BMI Knots

subgroup	knot_1	knot_2	knot_3	knot_4
All 15 subgroups	19.9	24.4	28.15	38.35

Table 79: MI Delta BMI Knots

subgroup	knot_1	knot_2	knot_3	knot_4
All 15 subgroups	-2.25	0.2	1.6	6.05

Restricted Cubic Spline </>

Many functions in PEARL model variables using a restricted cubic spline. These spline variables are defined as

\[x\_1 = \max{\left( 0, \frac{x - k_1}{k_\mathrm{norm}}\right) }^3 - \left( \frac{k_4 - k_1}{k_4 - k_3}\right) \cdot \max{\left( 0, \frac{x - k_3}{k_\mathrm{norm}}\right) } ^3 + \left( \frac{k_3 - k_1}{k_4 - k_3}\right) \cdot \max{\left( 0, \frac{x - k_4}{k_\mathrm{norm}}\right) } ^3\]

and

\[x\_2 = \max{\left( 0, \frac{x - k_2}{k_\mathrm{norm}}\right) }^3 - \left( \frac{k_4 - k_2}{k_4 - k_3}\right) \cdot \max{\left( 0, \frac{x - k_3}{k_\mathrm{norm}}\right) } ^3 + \left( \frac{k_3 - k_2}{k_4 - k_3}\right) \cdot \max{\left( 0, \frac{x - k_4}{k_\mathrm{norm}}\right) } ^3\]

where \(k\) are the knot locations and

\[k_\mathrm{norm} = \left( k_4 - k_1 \right)^\frac{2}{3}\]

is a normalization factor.