The summary statistics of the baseline socio-demographic and clinical variables of patients included in the study are indicated in Table1. Table1 shows that out of the sample of 792 patients: 40.9% were rural residents; 50.6% were females; 56.3% were living with their partner; 33.6 % disclosed their disease to family members, 49.2% were owners of cell phones, 25.5% were medication adherent, only 11.5% had high income and 20.6% had no education. The average(median) weight was 58kg (IQR: (52,64)), average years of all patients was 36 years (IQR: (28,48)). Among the participants, 80.1% of the patients were abnormal BMI( either under-weight or over-weight baseline BMI). The average (median) baseline CD4 cell count for all patients was 134 cells/mm3(IQR: (113,180)(Refer to Table1).
In the analysis, patients who disclosed the disease reported that they got better social support from communities around them. To investigate this, HIV/AIDS stigma scale was used by the health staff at each visiting time. Among those patients disclosed the disease (266 patients), more than half of them (165 or 62%) got social support. Similarly, mental depression of participants was also invented using Beck’s depression inventory scale at each visit and 180 (22.7%) were mentally depressed.
The exploratory data analysis of each visit in current investigation indicates that the expected CD4 cell count for all follow up times/visits varies 150 cells/mm3 with standard deviations 18 cells/mm3 at the first visit and 494 cells/mm3 with standard deviations 27 cells/mm3 at the 23rd visit in the study period. Hence, the distribution was ove-disperssed (variance > mean) and the expected CD4 cell count was linearly increased with corresponding follow-up times/visits(Refer to Figure1). This was supported by the Cochran–Armitage test (z =16.34, p-value < 0.0001) [24].
Figure1:
Check for Missing Completely at Random (MCAR) for current study
Missing completely at random (MCAR) refers to missingness in such a way that the missing values at the jth visit are independent of both the observed and unobserved values in the(j-1)th visit. There have been different approaches to check the MCAR assumptions when the missingness pattern is monotone(dropout). The nature of missingness pattern in current investigation was monotone(dropouts). This pattern in Figure2 indicates that there was no missing observation.in the first two visits and the number of dropouts increased linearly with follow-up times/visits. Hence, at the last visit(23rd visit), about 174 (21.5%) of the HAART attendents were dropouts among 792 sampled data under current investigation.
Figure2:
[Please see the supplementary files to view this section.]
Table1: Baseline Socio-demographic, clinical and individual characteristics of HIV positive adults
Variables
|
Median (IQR)
|
Categories
|
No (%)
|
Weight (kg)
|
58 (52, 64)
|
-
|
-
|
Age (years)
|
36 (28, 48)
|
-
|
-
|
Height (meter)
|
1.45(1.28, 1.68)
|
-
|
-
|
Gender
|
-
|
Male
|
392 (49.4)
|
-
|
Female
|
400 (50.6)
|
Baseline BMI
|
-
|
Normal
|
158(19.9)
|
-
|
Abnormal (over/under weight)
|
634(80.1)
|
Baseline CD4 cell count/ mm3
|
134 (113, 180)
|
-
|
-
|
WHO HIV stage
|
-
|
Stage I
|
101 (12.8)
|
-
|
Stage II
|
259 (32.7)
|
-
|
Stage III
|
199 (25.1)
|
-
|
Stage IV
|
233 (29.4)
|
Follow-up times/visits
|
-
|
-
|
23
|
Medcation adherence
|
-
|
Adherent
|
202 (25.5)
|
-
|
Non-adherent
|
590 (74.5)
|
Dietary instruction adherence
|
-
|
Adherent
|
245(30.9)
|
-
|
Non-adherent
|
547(69.1)
|
Educational status
|
-
|
no education
|
163 (20.6)
|
-
|
Primary
|
209 (26.4)
|
-
|
Secondary
|
274 (34.6)
|
-
|
Tertiary
|
146 (18.4)
|
Residence area
|
-
|
Urban
|
468 (59.1)
|
-
|
Rural
|
324 (40.9)
|
Marital status
|
-
|
living with partner
|
446 (56.3)
|
-
|
living without Partner
|
346 (43.7)
|
Disclosure of the disease
|
-
|
Yes
|
266 (33.6)
|
-
|
No
|
526 (66.4)
|
Level of income
|
-
|
low income (< 500 ETB per month)
|
41 (5.2)
|
-
|
middle income (5001-999 ETB per month)
|
660 (83.3)
|
-
|
high income ( 1000ETB per month)
|
91 (11.5)
|
Ownership of Cell phone
|
-
|
Yes
|
390 (49.2)
|
-
|
No
|
402 (50.8)
|
Table2 shows that after controlling for some basic covariates, the existence of missingness in the previous (j-1)th visit has insignificant effect for the existence of missingness at the jth visit which implies that there is no evidence against the null hypothesis (MCAR) (p-values > 0.05). Hence, the result in (j-1) th visiting time had no any effect for the missing observation obtained at the jth visiting time. Hence, the missingness occurred at the jth follow up visit was independent on observed and unobserved values of the variable of interest which implies that the missingness pattern in current unvestigation was MCAR.
Table2: The results from fitting the logistic regression model (6) for checking MCAR assumptions
Effect
|
Estimate
|
Standard Error
|
t Value
|
Pr > |t|
|
Intercept
|
-11.4015
|
3.8059
|
-3
|
< 0.001
|
Follow-up time/visit
|
0.05463
|
0.02451
|
1.453
|
0.3245
|
CD4 cell count
|
0.0534
|
0.03957
|
1.35
|
0.1772
|
Baseline CD4 cell count
|
0.001768
|
0.005317
|
0.33
|
0.7394
|
Age
|
0.0229
|
0.03054
|
0.75
|
0.4532
|
Residential area (Ref.=urban)
|
rural
|
-1.1643
|
1.3618
|
-0.85
|
0.3926
|
Gender (Ref. = female)
|
male
|
-0.3117
|
0.2353
|
-1.32
|
0.1854
|
Adherence (Ref= adherent)
|
non-adherent
|
5.7708
|
4.3239
|
1.33
|
0.182
|
To fit the joint models of CD4 cell count and BMI data collected from the hospital, first quasi-Poisson for CD4 cell count data and binary logistic model for BMI data were considered separately [29]. The reason for doing this was to visualize the advantage of joint models over the separate models.
Table3 shows the separate or joint mariginal models of CD4 cell count and BMI with link function of log and logit functions respectively. As it is indicated in Table3, age, weight, baseline CD4 cell count, follow up times/visits, baseline CD4 cell count, residence area, gender, level of disclosure of the disease to people living together, medication and dietary instruction adherence, marital status and ownership of cell phone significantely affected both response variables. The separate model shown in Table3 was univariate distribution. The combination of separate models of the two response variables are indicated in Table4.
Table4 was created by imposing joint multivatiate distribution of random effects. The conditional independence random intercept model in Table4 indicates that age, weight, follow up times/visits, baseline CD4 cell count, gender, medication adherence, dietary instruction adherence, marital status and level of income significantely affected both response variables. The two response variables, CD4 cell count and BMI in Table4 had the same sign in parametric estimation which indicates that the two outcomes are positively correlated to each other.
The conditional independence assumptions in Table4 was too restrictive in introducing estimation errors and the parameter estimation is not reliable. During this time, relaxation of conditional independence by re-fitting the joint random inrcepts model with possible correlated errors is important[19]. However, the relaxation of conditional independence approach for the current investigation lacked to be converged. In this condition, it is important to introduce conditional dependence of one response in terms of the other using linear predictor[19] which validates the observed correlation between the two responses arising from the association of random intercepts. This was done using generalized linear mixed effect model for BMI as a response and CD4 cell count as a linear predictor. The generalized linear mixed effect model of BMI considering CD4 cell count as linear predictor is indicated in Table5.
In Table5, the main effect predictors like age of patients, weight of patients, baseline CD4 cell count, the number of followed-up visits, marital status, sex, residence area, cell phone ownership, level of disease disclosure, level of education, residence area, medication and food adherence and level of income had significant effect on the variables of interests. Hence, as age of patients increased by one year, the odds of being normal BMI of HIV patiens decreased by by 2.7% (AOR= 0.9732,95% CI:( 0.42315, 0.9999), P-value = 0.0153)) given the other variables constant. As baseline CD4 cell count increased by one cell per mm3, the odds of being normal BMI for HIV patients was increased by 5.4% (AOR= 1.0538, 95% CI:( 1.0032, 1.2489), P-value = 0.0231)) given the other variables constant.
Gender had significant effect for the variables of interests. Thus, comparing female patients with males, the odds of being normal BMI for females was smaller by 24.1% than males (AOR= 0.7590, 95% CI:( 0.5231,0.8999), P-value = 0.0231) given the other variables constant.
The odds of being normal BNI for patients who did not disclosed their disease to people around them was decreased by 12% as comapared to those patients disclosed their disease (AOR=0.8795, 95%CI:( 0.6232, 0.9892), p-value=0.0153) keeping the other variables constant. Similarly, the odds of being normal BMI for medication non-adherent patients was decreased by 76.9% as compared to those of medication adherent patients (AOR=0.2312, 95% CI:( 0.1231, 0.4982), p-value = 0.0231) given the other conditions constant. The odds of being normal BMI for patients who did not adhere dietary instruction given by the health staff was decreased by 29.2% as compared to those HIV positive adults who adhere their prscribed dietary instruction (AOR=0.7081, 95% CI:( 0.5231, 0.8972), p-value =0.0142) keeping the other conditions constant. Among the socio-demographic covariates, mariatal status has significant effect on BMI of HIV patients. Thus, the odds of being normal BMI of HIV patients living with their partner was increased by 43.8% as compared to those patients living without their partner (AOR= 1.4378, 95% CI:( 1.3489, 1.5245), p-value = 0.0164) keeping the other conditions constant.
The odds of being normal BMI for patients without cell phone was deacreased by 38.3% as compared those patients with cellphone (AOR=0.6175, 95% CI:( 0.4232, 0.8982), p-value = 0.0324) keeping the other conditions constant. Similarly, level of education, residence area and level of income had significant effect on the variables of interest.
Some of the interaction effects of covariates also had significatnt effect on the response variable. In Table5, only significant interaction effects are present for the table to be manageable in one page. Hence, follow-up times/visits * cell phone ownership, follow up times/visits * gender and age * gender significantly affected both response variables through a linear link function (Refer to Table5).
Table5 indicate that, as patients’ follow-up times/visits increased by one unit, the incearing rate of odds of being normal BMI for patients without cell phone was decreased by 3% (AOR=0.9704, 95% CI:( 0.7342, 0.9989), p-value = 0.0324) (P-value < 0.01) keeping the other conditions constant. Whenever, the number of follow-ups of patients increased by one unit, the rate of increasing the odds of being normal BMI for female patients was increased by 4.1% as comapared to males, keeping the other variables constant (AOR= 1.0408, 95% CI:( 1.0184, 1.1893), p-value = 0.0324). In Table5, it is also indicated that as patients’ age increased by one year, the decreasing rate of the odds of being normal BMI for female patients was decreased by 1% as compared to males(AOR= 0.9900, 95% CI:( 0.6543, 0.9998), p-value = 0.0321) keeping the other conditions constant.
Table3: Parameter estimates and corresponding standard errors of joint mariginal /separate analysis for CD4 cell count and BMI data with AR (1) working covariance
Effect
|
BMI
|
CD4 cell count
|
Estimate
|
Standard Error
|
Pr > |t|
|
Estimate
|
Standard Error
|
Pr > |t|
|
Intercept
|
-6.1123
|
0.9131
|
0.0152
|
3.0243
|
0.0392
|
0.0156
|
age
|
-0.0272
|
0.0134
|
0.0153*
|
-0.0182
|
0.0821
|
0.0226*
|
weight
|
0.2034
|
0.0431
|
0.0125*
|
0.0194
|
0.0278
|
0.0353*
|
Follow up visits
|
0.0524
|
0.0154
|
0.0231*
|
0.0346
|
0.0124
|
0.0145*
|
Baseline CD4 cell count
|
0.0163
|
0.0182
|
0.0141*
|
0.0192
|
0.0351
|
0.0245*
|
Residence(Ref.=Urban)
|
Rural
|
-0.1162
|
0.0825
|
0.1921
|
-0.0265
|
0.8637
|
0.0435*
|
Gender(Ref.=Male)
|
Female
|
-0.2757
|
0.08289
|
0.0231*
|
0.0352
|
0.8343
|
0.0182*
|
Disclosed(Ref.=Yes)
|
No
|
-5.1284
|
0.1435
|
< 0.0153*
|
-0.9251
|
0.6432
|
0.0421*
|
Who(Stage4)
|
Stage1
|
0.8642
|
0.3252
|
0.8452
|
0.0723
|
0.9152
|
0.0432*
|
Stage2
|
0.9433
|
0.2145
|
0.0546
|
0.0562
|
0.8251
|
0.0241*
|
Stage3
|
1.1452
|
0.1262
|
0.0752
|
-0.0254
|
0.9245
|
0.0354*
|
Medication adherence(Ref.=Adherence)
|
Non-adherent
|
-1.4643
|
1.0228
|
0.0231*
|
-1.4365
|
0.8729
|
0.0143*
|
Food adherence(Ref.=adherent)
|
Non-adherent
|
-0.9452
|
0.9435
|
0.0142*
|
-0.8263
|
0.2384
|
0.0139*
|
Marital status(Ref.= without partner)
|
With partner
|
0.7631
|
0.7857
|
0.0164*
|
0.2482
|
0.8281
|
0.0165*
|
Phone(Ref.=Yes)
|
No
|
-1.4821
|
0.6404
|
0.0324*
|
-0.8354
|
0.0653
|
0.0153*
|
Education (Ref.=Tertiary)
|
No education
|
-0.7837
|
0.7245
|
0.04532
|
-0.0431
|
0.7862
|
0.0432*
|
Primary
|
-0.0263
|
0.1465
|
0.8854
|
0.0652
|
0.8549
|
0.1732
|
Secondary
|
-0.6321
|
0.8432
|
0.3821
|
0.0224
|
0.6543
|
0.1432
|
Income(Ref.=Low)
|
High
|
0.3554
|
0.9228
|
0.2182
|
0.7336
|
0.8432
|
0.0345*
|
Middle
|
1.7951
|
0.2523
|
0.0134*
|
-0.2845
|
0.7869
|
0.0421*
|
*stands for statistically significant variables.
Table4: Parameter estimates and corresponding standard errors for conditional independenc random intercept models of CD4 cell count and BMI data(Laplace approximation)
parameter
|
BNI
|
CD4 cell count
|
Estimate
|
Standard Error
|
Pr > |t|
|
Estimate
|
Standard Error
|
Pr > |t|
|
Intercept
|
6.1123
|
0.6131
|
0.0152
|
3.0243
|
0.0192
|
0.0156
|
age
|
-0.0272
|
0.0034
|
0.0153*
|
-0.0182
|
0.0321
|
0.0226*
|
weight
|
0.2034
|
0.0331
|
0.0125*
|
0.0194
|
0.0178
|
0.0353*
|
Follow up visits
|
0.0524
|
0.0054
|
0.0231*
|
0.0346
|
0.0114
|
0.0145*
|
Baseline CD4 cell count
|
0.0163
|
0.0082
|
0.0231*
|
0.0192
|
0.0151
|
0.0245*
|
Residence(Ref.=Urban)
|
Rural
|
-0.1162
|
0.0425
|
0.1921
|
-0.0265
|
0.6637
|
0.0435*
|
Gender(Ref.=Male)
|
Female
|
-0.2757
|
0.05289
|
0.0231*
|
0.0352
|
0.4343
|
0.0182*
|
Disclosed(Ref.=Yes)
|
No
|
-5.1284
|
0.0435
|
< 0.0153*
|
-0.9251
|
0.3432
|
0.0421*
|
Who(Stage4)
|
Stage1
|
0.8642
|
0.1252
|
0.8452
|
0.0723
|
0.2152
|
0.0432*
|
Stage2
|
0.9433
|
0.1145
|
0.0546
|
0.0562
|
0.3251
|
0.0241*
|
Stage3
|
1.1452
|
0.1162
|
0.0752
|
-0.0254
|
0.2245
|
0.0354*
|
Medication adherence(Ref.=Adherence)
|
Non-adherent
|
-1.4643
|
1.0128
|
0.0231*
|
-1.4365
|
0.1729
|
0.0143*
|
Food adherence(Ref.=adherent)
|
Non-adherent
|
-0.9452
|
0.5435
|
0.0142*
|
-0.8263
|
0.3384
|
0.0139*
|
Marital status(Ref.= without partner)
|
With partner
|
0.7631
|
0.5857
|
0.0164*
|
0.2482
|
0.2281
|
0.0165*
|
Phone(Ref.=Yes)
|
No
|
-1.4821
|
0.2404
|
0.0324*
|
-0.8354
|
0.0153
|
0.0153*
|
Education (Ref.=Tertiary)
|
No education
|
-0.7837
|
0.4245
|
0.04532*
|
-0.0431
|
0.1862
|
0.0432*
|
Primary
|
-0.0263
|
0.0465
|
0.0254*
|
0.0652
|
0.3549
|
0.1732
|
Secondary
|
-0.6321
|
0.3432
|
0.3821*
|
0.0224
|
0.2543
|
0.1432
|
Income(Ref.=Low)
|
High
|
0.3554
|
0.0228
|
0.0182*
|
0.7336
|
0.3432
|
0.0345*
|
Middle
|
1.7951
|
0.1523
|
0.0134*
|
-0.2845
|
0.2869
|
0.0421*
|
*stands for statistically significant variables.
Table5: Parameter estimates for joint model of BMI data considering CD4 cell count as linear predictor
Parameter
|
Estimate
|
Standard Error
|
Adjusted odds Ratio(AOR)
|
Wald 95% CI for AOR
|
Pr > |t|
|
Intercept
|
1.1123
|
0.2131
|
3.0413
|
1.2345
|
6.3245
|
0.0152
|
age*dist
|
-0.0272
|
0.0024
|
0.9732
|
0.42315
|
0.9999
|
0.0153*
|
weight*dist
|
0.2034
|
0.0231
|
1.2256
|
1.0874
|
2.3425
|
0.0125*
|
Baseline CD4 cell count*dist
|
0.0524
|
0.0024
|
1.0538
|
1.0032
|
1.2489
|
0.0231*
|
CD4 cell count *dist
|
0.5242
|
0.0024
|
1.6891
|
1.0032
|
1.2489
|
0.0231*
|
dist*residence(Ref.=Urban)
|
Rural
|
-0.1162
|
0.0225
|
0.8903
|
0.42315
|
0.9982
|
0.0121*
|
dist*gender (Ref.=Male)
|
Female
|
-0.2757
|
0.02289
|
0.7590
|
0.52315
|
0.8999
|
0.0231*
|
dist*disclosed(Ref.= yes)
|
No
|
-0.1284
|
0.0335
|
0.8795
|
0.0565
|
0.9993
|
0.0153*
|
dist*who (Ref.=stage4)
|
Stage 1
|
0.8642
|
0.1152
|
2.3731
|
0.42315
|
1.2999
|
0.8452
|
Stage 2
|
0.9433
|
0.1045
|
2.5684
|
0.44315
|
1.2999
|
0.0546
|
Stage 3
|
1.1452
|
0.0162
|
3.1431
|
0.8255
|
1.2999
|
0.0752
|
Medication adherent*dist(Ref.=adherent)
|
Non-adhe.
|
-0.4643
|
1.0118
|
0.8592
|
0.62315
|
0.9892
|
0.0231*
|
Food adh.*dist(Ref.=adherent)
|
Non-adherent.
|
-0.3452
|
0.2435
|
0.7081
|
0.5231
|
0.8972
|
0.0142*
|
dist*marital status stat(Ref.=Without partner)
|
With partner
|
0.3631
|
0.2857
|
1.4378
|
1.3489
|
1.5245
|
0.0164*
|
dist*phone(Ref.=Yes)
|
No
|
-0.4821
|
0.1104
|
0.6175
|
0.4232
|
0.8982
|
0.0324*
|
dist*education (Ref.=Tertiary)
|
No educ.
|
-0.7837
|
0.1245
|
0.4567
|
0.22315
|
0.6982
|
0.04532*
|
Primary
|
-0.0263
|
0.0365
|
0.9740
|
0.72315
|
0.9982
|
0.0254*
|
Secondary
|
-0.6321
|
0.1432
|
0.5315
|
0.42315
|
0.6982
|
0.3821*
|
dist*income (Ref.= Low)
|
High
|
0.3554
|
0.0128
|
1.4268
|
1.3489
|
1.7245
|
0.0182*
|
Middle
|
1.7951
|
0.1123
|
6.0201
|
1.3489
|
4.3245
|
0.0134*
|
Visiting time*dist
|
0.0521
|
0.0145
|
1.0513
|
1.0245
|
1.1542
|
0.0123*
|
Follow up times/visits *dist* ownership of cell phone(Ref.=Yes)
|
No
|
-0.0332
|
0.03341
|
0.9704
|
0.7342
|
0.9989
|
0.0324*
|
Follow up times/visits *dist*gender (Ref.= Male)
|
Female
|
0.0421
|
0.0343
|
1.0408
|
1.0184
|
1.1893
|
0.0324*
|
Age*dist*gendr (Ref.=Male)
|
Female
|
-0.0122
|
0.01224
|
0.9900
|
0.6543
|
0.9998
|
0.0324*
|
*stands for statistically significant variables