The effect of longitudinal body weight and CD4 cell progression for the survival of HIV/AIDS patients

Figures & data

Table 1. Patient’s characteristics of HIV/AIDS data from Mekelle General Hospital

№	Covariates	Categories	Total No of patient’s (%)	Observed death (%)
1	Sex	Female	134 (62%)	10(4.6%)
		Male	82(38%)	21(9.7%)
2	Education level	Illiterate	57(26.4%)	16(7.4%)
		Elementary	45(20.8%)	8(3.7%)
		Secondary	74(34.3%)	6(2.8%)
		Tertiary	40(18.5%)	1(0.46%)
3	Marital status	Single	54(25%)	7(3.2%)
		Married	109(50.5%)	11(5%)
		Divorced	39(18%)	5(2.3%)
		Widowed	14(6.5%)	8(3.7%)
4	Functional status	Working	146(67.6%)	10(4.6%)
		Ambulatory	55(25.5%)	13(6%)
		Bedridden	15(6.9%)	8(3.7%)
5	WHO clinical stage	Stage-I	93(43%)	8 (3.7%)
		Stage-II	63(29.2%)	5(2.3%)
		Stage-III	45(20.8%)	12 (5.6%)
		Stage-IV	15(6.9%)	6(2.8%)
6	HIV/TB infection	No	193(89.4%)	21(10.9%)
		Yes	23(10.7%)	10(43.6%)
7	Adherence on treatment	Good	96 (44.5%)	5(2.3%)
		Fair	74 (34.2%)	10(4.6%)
		Poor	46 (21.29%)	13(6%)
8	Occupational status	Unemployed	163(75.5%)	23(10.7%)
		Employed	53(24.5%)	8(3.7%)
9	Place of residence	Urban	130(60.2%)	11(5%)
		Rural	86(39.8%)	20(9.3%)
10	Type of ART regiment	TDF+3TC+EFV	135(62.5%)	12(5.6%)
		D4t+3TC+NVP	20(9.25%)	13(6%)
		AZT+3TC+NVP	40(18.5%)	13(6%)
		AZT+3TC+EFV	21(9.7%)	3(1.4%)
	Continuous variables	mean	standard deviation
11	CD4 at base line	311	163.6
12	Body weight at base line	49.2	9.85
13	Hemoglobin at base line	13.6	1.98
14	Age at base line	34.8	11

Table 2. Shows the comparison of separate and joint model analysis √(CD4 cell) with survival time-to-death

No.	Parameter	Separate model analysis of survival analysis				Joint model sub model
	Fixed effect	$\stackrel{⌢}{\mathrm{B}}$	Se($\stackrel{⌢}{\mathrm{B}}$)	z-value	Pr(>|z|)	$\stackrel{⌢}{\mathrm{B}}$	Se($\stackrel{⌢}{\mathrm{B}}$)	z-value	p-value
1	Function status
	Bedridden(R)	——-	——-	——-	——-	——-	——-	——-	——-
	Ambulatory	−0.732	0.595	−1.231	0.218	−0.5247	1.0577	−0.496	0.125
	Working	−0.4316	0.7092	−0.609	0.5428	−0.42	1.0332	−0.4065	0.178
2	Baseline CD4	−0.00513	0.001433	−3.578	0.00037*	−0.0045	0.0015	−3.053	0.0023*
3	Adherence
	Poor(R)	——-	——-	——-	——-	——-	——-	——-	——-
	Fair	−1.493	0.513	−2.914	0.00357*	−1.5526	0.5323	−2.92	0.0035*
	Good	−1.837	0.64098	−2.866	0.004163*	−1.735	0.6405	−2.709	0.0068*
4	Baseline weight	0.0402	0.0229	1.755	0.04791*	0.0433	0.0227	1.9755	0.04793*
5	Sex; female(R)	——-	——-	——-	——-	——-	——-	——-	——-
	Male	1.443	0.494	2.921	0.00349*	1.227	0.486	2.522	0.0117*
6	HIV/TB status
	No(R)	——-	——-	——-	——-	——-	——-	——-	——-
	Yes	1.899	0.745	2.55	0.023*	2.101	0.676	3.1	0.0210*
	Separate model analysis of longitudinal				Joint model sub model
	Parameters	$\stackrel{⌢}{\mathrm{B}}$	Se($\stackrel{⌢}{\mathrm{B}}$)	z-value	Pr(>|z|)	$\stackrel{⌢}{\mathrm{B}}$	Se($\stackrel{⌢}{\mathrm{B}}$)	z-value	Pr(>|z|)
	Intercept	16.01	2.0398	7.86	0.0000*	16.053	1.98	8.1	<0.0001*
1	Time	−0.826	0.274	−3.01	0.0027*	−0.827	0.2702	−3.06	0.0022*
2	Baseline CD4	0.0213	0.0018	12.2	0.0000*	0.0234	0.00051	10.5	0.0000*
3	Baseline weight	0.061	0.0267	2.268	0.0244*	0.0605	0.0258	2.346	0.019*
4	Function status
	Bedridden(R)	——-	——-	——-	——-	——-	——-	——-	——-
	Ambulatory	−3.84	1.71	−2.246	0.0258*	−3.85	1.665	−2.31	0.0207*
	Working	−2.649	1.72	−1.536	0.1261	−2.665	1.679	−1.587	0.1124
5	HIV/TB status
	HIV/TB(R)	——-	——-	——-	——-	——-	——-	——-	——-
	HIV/TB(yes)	−3.2	1.276	−2.51	0.0130*	−2.169	1.245	−1.735	0.109
6	Marital status
	Single(R)	——-	——-	——-	——-	——-	——-	——-	——-
	Married	−1.181	0.5642	−2.094	0.0375*	−1.178	0.5442	2.164	0.00304*
	Divorced	−1.3357	0.731	−1.827	0.059	−1.338	0.7086	−1.988	0.049*
	Widowed	−0.647	1.037	−0.624	0.533	−0.6537	0.998	−0.655	0.5125
7	Time*Baseline CD4	0.0028	0.00037	7.512	0.0000*	0.00194	0.000191	5.322	<0.0001*
8	Time*HIV/TB
	Time*No(R)	——-	——-	——-	——-	——-	——-	——-	——-
	Time*Yes	0.531	0.236	2.25	0.025*	0.5209	0.233	2.239	0.025*
9	Time*function-status
	Time*Bedridden(R)	——-	——-	——-	——-	——-	——-	——-	——-
	Time*Ambulatory	0.923	0.297	3.102	0.002*	0.926	0.2925	3.165	0.0015*
	Time*working	0.905	0.296	3.06	0.0023*	0.91	0.291	3.126	0.0018*
	Random effect	variance	Std.Dev			variance	Std.Dev
	(Intercept)	19.98	4.47			18.49	4.3
	Time	0.5476	0.74			0.5184	0.72
	Residual	6.0025	2.45			5.9731	2.444
	Association	——	——	——	——	−0.6693	0.336	−1.992	0.0367*
	AIC	6823.45				6602.83
	*P -value< 0.05	R = reference group

Table 3. Shows comparison of separate and joint model analysis of Log₁₀ (Body-Weight) progression with survival Time-to-death

Parameter	Separate model analysis of survival				Joint model sub model
Fixed effect	$\mathit{B}$	Se($\mathit{B}$)	z-value	$\mathit{P}\mathit{r}\mathbf{(}\mathbf{>}\left|\mathit{z}\right|\mathbf{)}$	$\mathit{B}$	Se($B$)	z-value	p-value
Function status
Bedridden(R)	———-	———–	———	————	——–	——–	———	————
Ambulatory	0.732	0.595	1.231	0.218	1.060	0.0001	1.6*10^4	<0.0001*
Working	0.4316	0.7092	0.609	0.543	0.6241	0.0001	4.79*10^3	<0.0001*
Baseline CD4	0.00513	0.001433	3.578	0.00037*	0.0035	0.0014	2.46	0.0137*
adherence	——	———	——	———	——	———	———	———
Poor(R)	-1.493	0.513	-2.914	0.00357*	1.6216	0.0000	-2.17*10^5	<0.0001*
Fair Good	–1.837	0.64098	–2.866	0.004163*	–1.55	0.0000	-3.11*10^4	<0.0001*
Baseline weight	−0.0402	0.0229	−1.755	0.04791*	−0.084	0.0119	−7.0768	0 <0.0001*
Sex	——	———	——	———	——	———	———	———
female(R) male	— 1.443	0.494	2.921	0.00349*	– 0.7139	0.0001	4.9*10^3	<0.0001*
Education
Illiterate(R)	———	———	——	———	——	———	———	———
primary	0.5475	0.4964	1.103	0.2699	0.6073	0.0001	5.29*10^3	<0.0001*
secondary	–0.5086	0.547	–0.929	0.3527	–0.479	0.0001	-8.88*10^3	<0.0001*
Tertiary	-1.287	1.096	-1.175	0.2400	-1.13	0.0000	-5.28*10^4	<0.0001*
Parameter	Separate model analysis of longitudinal				Joint model-sub model
Fixed effect	$B$	Se($B$)	z-value	$Pr(>\left|z\right|)$	$B$	Se($B$)	z-value	$Pr(>\left|z\right|)$
Intercept	1.573	0.024	65.48	0.0000*	1.574	0.0081	194.98	<0.0001*
Time	0.00334	0.00279	1.197	0.2314	0.0033	0.0026	1.2658	0.2056
Age	0.0011	0.00038	2.944	0.0036*	0.0011	0.0004	3.001	0.0027*
Sex
female(R)	———-	———	———	—————0.0	——– 0.0394	——— 0.0086	——— 4.6119	———- <0.0001
male	0.0396	-0.0090	4.39	00*				*
Marital
single(R)	———-	———	———	———-	——–	———	——–	———-
married	0.01377	0.0104	1.323	0.187	0.0138	0.0078	1.7782	0.0754
Divorced	0.0155	0.0137	1.13	0.2599	0.0153	0.0102	1.5075	0.1317
Widowed	0.00449	0.019	0.236	0.8135	0.0036	0.0086	0.4217	0.6732
Baseline CD4	0.00012	0.00004	3.012	0.0029 *	0.0001	0.0000	3.3336	0.0009*
Baseline weight.	0.0066	0.00061	10.83	0.0000*	0.0068	0.0006	11.80	<0.0001*
Function status
Bedridden(R)	———-	———-	———-	———-	——–	———	———	———-
Ambulatory	0.036	0.0182	1.97	0.0498*	0.0357	0.0075	4.731	<0.0001*
Working	0.0718	0.0173	4.146	0.0000*	0.0714	0.0068	10.43	<0.0001*
time: BaselineCD4	0.00002	0.000008	1.907	0.0467*	0.0001	0.0000	2.0466	0.0407*
Random effect	variance	$C_{bend}$			Variance	$C_D$
(Intercept)	0.007	0.0838			0.007	0.0838
Time	0.00025	0.0157			0.00025	0.0157
Residual	0.0015	0.0392			0.0015	0.0392
Association	———-	———–	———-	————–	−1.975	1.0065	−1.9627	0.02798
AIC	3283.261				3327.523

*P-value < 0.05.

Table 4. Result of joint model of longitudinal $\sqrt{\mathbf{C}\mathbf{D}4\mathbf{c}\mathbf{e}\mathbf{l}\mathbf{l}}$& log (body weight) progression with survival Time-To-Death of HIV/AIDS patients

Event process sub survival model of $\mathit{F}$ on Time-To-Death					Event process sub survival model of $G_i$& log(weight) with Time-To-Death
Parameters	$\mathit{B}$	Se($B$)	z-value	$\mathit{P}\mathit{r}\mathbf{(}\mathbf{>}\left|\mathit{z}\right|\mathbf{)}$	$\mathit{B}$	Se($\mathit{B}$)	z-value	$\mathit{P}\mathit{r}\mathbf{(}\mathbf{>}\left|\mathit{z}\right|\mathbf{)}$
Sex
female(R), male	——-	——	——-	——–	———	——	—–	——
	1.3408	0.6136	2.1851	0.0289*	1.1632	0.5383	2.16	0.01154*
Baseline CD4	−0.0052	0.0016	−3.2072	0.0013*	−0.0048	0.0015	−3.20	0.00104*
Adherence
poor(R)	——-	——	——-	———-	———	——-	—–	——
fair	-1.6769	0.8610	-1.9476	0.0515	-1.5801	0.7092	-2.2281	0.0259*
good	–1.2532	0.6704	–1.8693	0.0616	–1.0152	0.54	–1.9574	0.04154*
HIV/TB
HIV/TB(R)	———-	——	——-	———-	———-	———-	———	———
HIV/TB(yes)	2.101	0.676	3.100	0.0210*	2.52	0.512	4.921	0.0025*
Associations
Gamma_1	−0.6693	0.336	−0.1.992	0.0367*	−0.3666	0.1600	−2.291	0.00487*
Gamma_2	–1.975	1.0065	–1.9627	0.02798*	–2.9448	1.2347	–2.385	0.004142*
AIC		6602.83				2833.126
Parameters	Longitudinal process sub model of${\mathit{M}}_i$ on Time-To Death				Longitudinal process sub model of$N_t$& log(weight) with Time-To Death_1
Parameters	$\mathit{B}$	Se($B$)	z-value	$\mathit{P}\mathit{r}\mathbf{(}\mathbf{>}\left|\mathit{z}\right|\mathbf{)}$	$\mathit{B}$	Se($\mathit{B}$)	z-value	$\mathit{P}\mathit{r}\mathbf{(}\mathbf{>}\left|\mathit{z}\right|\mathbf{)}$
(Intercept)_1	10.356	2.0583	5.0314	<0.0001*	10.46	2.0199	5.176	<0.0001*
time_1	0.0259	0.3835	0.0676	0.9461	0.0309	0.2480	0.1247	0.900
Baseline CD4_1	0.0208	0.0022	9.48	<0.0001*	0.0207	0.0019	10.977	<0.0001*
age_1	−0.0015	0.0251	−0.0586	0.950	−0.0040	0.0274	−0.1453	0.88
Functional status
Bedridden(R)_1	———	——	——-	———	——–	——–	——	——–
Ambulatory_1	1.8094	1.6722	1.082	0.02792*	2.49687	1.14876	2.183	0.01857*
Working_1	–0.4411	1.6919	–0.2607	0.07943	–0.5106	1.5874	–0.3217	0.0748
HIV/TB
No(R)_1	——–	——	——-	——–	——–	——–	——	———
Yes_1	-1.8287	1.4197	-1.288	0.01977	-2.0019	0.914	-2.191	0.00847*
Time* BaselinCD4	0.0025	0.0004	6.0157	<0.0001	0.0026	0.0003	8.152	0.0001*
Time*Functional
Time*Ambulator	0.7346	0.3631	2.0231	0.0431	0.7347	0.2223	3.3	0.0009*
Time* Working	0.7906	0.3453	2.289	0.0220	0.7927	0.2205	3.595	0.0003*
Parameters	Longitudinal process sub model of log(weight) on Time-To Death				Longitudinal process sub model of$v$& log(weight) on Time-To Death_2
Parameters	$\mathit{B}$	Se($B$)	z-value	$\mathit{P}\mathit{r}\mathbf{(}\mathbf{>}\left|\mathit{z}\right|\mathbf{)}$	$\mathit{B}$	Se($\mathit{B}$)	z-value	$\mathit{P}\mathit{r}\mathbf{(}\mathbf{>}\left|\mathit{z}\right|\mathbf{)}$
(Intercept)_2	1.261	0.0431	29.24	<0.0001	1.2610	0.0473	26.65	<0.0001*
time_2	0.0305	0.0094	3.2402	0.0012	0.0305	0.0106	2.885	0.0039*
age_2	0.0010	0.0005	2.00	0.0075	0.0011	0.0004	2.76	0.0058*
Sex
female(R)_2	——–	—–	——	——-	——	——–	——	——–
male_2	0.0061	0.0086	0.7099	0.04778	0.0067	0.00338	1.995	0.0417*
Baseline weight	0.00667	0.0009	7.2	<0.0001*	0.0067	0.0010	6.589	<0.0001*
Functional status
Bedridden(R)_2	——–	——	——	——–	——	——–	——	———
Ambulatory_2	0.0372	0.024	1.55	0.0135*	0.0395	0.0150	2.625	0.0087*
Working_2	0.0364	0.0575	0.633	0.0092*	0.0506	0.0176	2.866	0.0042*

Data availability statement

The authors have considered HIV/AIDS datasets from Mekelle General Hospital patient history card and are now attached as supplementary materials of the submission system.