Descriptive statistics were used to summarize baseline characteristics of participants in the study area. The baseline characteristics of respondents were summarized as indicated in Table1.
Table1 indicated that out of a sample of 226 patients, 80.1% were females, 70.4% of the infected patients were with working functional status, (i.e., an individual able to perform usual work in and out of the house), and 6.6% were unable to perform activities (bedridden patients). Regarding the clinical stage of patients, 36.3% were at clinical stage1, 30.1% at clinical stage2, and 23.0% at clinical stage3.
Among the patients, 92.9% were adherent to the prescribed medication and the rest were non-adherent, 60.6% were from rural area, 59.7% patients were free from opportunistic infectious disease. The body mass index of patients revealed that 58% were at normal level, 28.3% at underweight, and others were overweight level, 28.8% of them were unemployment status. Among the HIV positive patients included under current investigation, 26.6% had also TB.
At enrolment, the average (std.dev) baseline age of study participants was 33.15(7.79) years. The average (Std.dev) baseline weight was 53.19(9.55) kg and average (Std.dev) baseline hemoglobin was 11.73 (2.46). Finally, the average (Std.dev) of baseline CD4 cell count was 363.38(227.68) cells per mm3.
Among the different covariance structures, UN had smallest AIC and BIC and selected for data analysis in current investigation.
Table1: Baseline characteristics of potential predictors for HIV/AIDS patients
Characteristics
|
Category
|
TB Status
|
Mean CD4 cell count
|
Percent
|
Yes
|
No
|
Sex
|
Male
|
15
|
30
|
327.07
|
19.9
|
Female
|
38
|
143
|
372.42
|
80.1
|
Marital status
|
Single
|
15
|
33
|
378.64
|
21.2
|
Married
|
21
|
86
|
393.21
|
47.3
|
Separated
|
2
|
14
|
297.35
|
7.2
|
Divorced
|
11
|
29
|
309.57
|
17.7
|
Widow
|
4
|
11
|
315.80
|
6.6
|
Residence area
|
Urban
|
12
|
77
|
381.24
|
39.4
|
Rural
|
41
|
95
|
351.79
|
60.6
|
Educational level
|
No education
|
21
|
49
|
416.92
|
31.0
|
primary
|
11
|
47
|
379.42
|
25.7
|
secondary
|
14
|
42
|
305.62
|
24.8
|
Tertiary
|
7
|
35
|
335.62
|
18.5
|
Religion
|
Muslim
|
35
|
62
|
383.98
|
42.9
|
Orthodox
|
14
|
100
|
360.28
|
50.4
|
Others
|
4
|
11
|
253.79
|
6.6
|
Occupation
|
unemployed
|
17
|
49
|
388.59
|
28.8
|
employed
|
23
|
73
|
334.93
|
42.5
|
others
|
14
|
51
|
379.89
|
28.7
|
Functional status
|
Ambulatory
|
4
|
12
|
194.49
|
7.1
|
Bedridden
|
6
|
9
|
135.68
|
6.6
|
working
|
123
|
36
|
401.26
|
70.4
|
Others
|
7
|
29
|
366.57
|
15.9
|
Opportunistic infectious
|
No
|
38
|
97
|
391.12
|
59.7
|
Yes
|
15
|
76
|
322.24
|
40.3
|
WHO stages
|
Stage 1
|
4
|
78
|
408.02
|
36.3
|
Stage2
|
4
|
64
|
356.22
|
36.3
|
Stage3
|
25
|
27
|
325.25
|
23
|
Stage4
|
18
|
6
|
315.15
|
10.6
|
Adherence status
|
No
|
6
|
10
|
108.32
|
7.1
|
Yes
|
46
|
164
|
383.35
|
92.9
|
BMI
|
Under weight
|
26
|
38
|
316.4
|
28.3
|
Normal
|
25
|
106
|
366.7
|
58
|
Overweight
|
3
|
28
|
444.9
|
13.7
|
Social support
|
No
|
28
|
81
|
444.9
|
48.2
|
Yes
|
25
|
92
|
366.75
|
51.8
|
TB Status
|
No
|
60
|
|
26.55
|
Yes
|
166
|
|
73.45
|
Mean age(Std.dev)
|
33.15(7.79)
|
Mean weight(Std.dev)
|
53.19(9.55)
|
Mean Hemoglobin(Std. dev)
|
11.73(2.46)
|
Mean CD4 cell count(Std.dev)
|
363.38(227.68)
|
Table2: Parameter Estimates of CD4 cell count, with (UN) covariance structure
Effect
|
Estimate
|
std.err
|
95% CI
|
p-value
|
Intercept
|
13.593
|
3.163
|
(7.359,19.837)
|
<0.0001*
|
Time(months)
|
0.200
|
0.037
|
(0.177,0.273)
|
<0.0001*
|
Age
|
-0.128
|
0.033
|
(-0.194,-0.063)
|
0.0001*
|
Educational level (ref=tertiary
|
No education
|
3.619
|
3.318
|
(-2.893, 10.131)
|
0.2757
|
Primary
|
-4.327
|
3.027
|
(-10.268, 1.615)
|
0.1533
|
Secondary
|
-6.712
|
3.091
|
(-12.780, -0.645)
|
0.0302
|
Func.st. (ref=working)
|
Ambulatory
|
-3.053
|
0.946
|
(-4.911, -1.196)
|
0.0013*
|
Bedridden
|
-3.750
|
1.077
|
(-5.863, -1.638)
|
0.0005*
|
Medication adherence (ref=non-adherent)
|
Adherent
|
4.632
|
0.570
|
(3.514, 5.751)
|
<0.0001*
|
Dietary adherence(Ref. =no)
|
yes
|
2.632
|
0.970
|
(1.514, 4.751)
|
<0.0001*
|
Social support(Ref.= no)
|
yes
|
1.832
|
0.380
|
(1.314, 5.651)
|
<0.0001*
|
Ownership of Cell phone(Ref.=no)
|
yes
|
1.832
|
0.380
|
(1.314, 5.651)
|
<0.0001*
|
BMI(Ref.=Normal)
|
over or under weighted)
|
-0.114
|
0.512
|
(-1.218,- 0.891)
|
0.0246*
|
Weight
|
0.068
|
0.026
|
(0.016, 0.120)
|
0.0097*
|
WHO stage(Ref= st.4)
|
Stage 1
|
2.194
|
0.572
|
(1.071, 3.317)
|
0.0001*
|
Stage2
|
1.748
|
0.574
|
(0.622, 2.874)
|
0.0024*
|
Stage3
|
0.374
|
0.112
|
(0.155,0.593)
|
0.0008*
|
Hemoglobin
|
1.201
|
0.382
|
(0.451, 1.952)
|
0.0017*
|
TB (Ref=no)
|
yes
|
-2.340
|
0.443
|
(-3.209, -1.471)
|
<0.0001*
|
Disclosure of disease(Ref.= no)
|
yes
|
1.201
|
0.382
|
(0.451, 1.952)
|
0.0017*
|
Opportunistic infections(Ref.=no)
|
yes
|
-2.340
|
0.443
|
(-3.209, -1.471)
|
< 0.0001*
|
Sex (Ref.= female)
|
Male
|
-2.340
|
0.443
|
(-3.209, -1.471)
|
< 0.0001*
|
Residence area(Ref.=rural)
|
Urban
|
1.201
|
0.382
|
(0.451, 1.952)
|
0.0017*
|
*stands for statistically significant at 5% level of confidence
The result in Table2 shows that there was significant effect of TB status on CD4 cell count. Hence, the expected number of CD4 cell count of HIV patients who were co-infected with TB was decreased by 2.34 as compared to HIV patients who were free from TB. As age increased by one year, the expected number of CD4 cell count was decreased by 0.128, given that the other variables constant. The expected number of CD4 cell count for ambulatory and bedridden HIV patients was decreased by 3.1 and 3.8 respectively as compared to those of working functional status. Similarly, the expected number of CD4 cell count for medication adherent and dietary adherent HIV patients were increased by 4.6 and 2.6 respectively as compared to those of non-adherent patients, given the other variables constant.
Patients who got social support and those who had cell phone had good improvements in their expected number of CD4 cell count as compared to their counterparts. Patients’ BMI, WHO stages Hemoglobin levels, disclosure level of the disease, opportunistic disease infection and residence area had significant effect on the expected number of CD4 cell count.
The generalized linear mixed effect model (Binary logistic regression model) was implemented for the analysis of the levels of TB status as indicated in Table3. Table3 revealed that the odds of rural HIV patients being infected by TB were 6.3 times higher than those of urban patients. The odds of ambulatory HIV patients being co-infected by TB were greater by 14.6 % as compared to patients at working status, given the other variables constant.
In Table3, it is observed that TB infection was lower for patients whose WHO stages’ were 1, 2, and 3 compared to stage 4, and patients whose religion was orthodox compared to others. Weight and CD4 cell count has a negative relationship with the event of HIV/TB co-infection. In Table3 it is indicated that TB infection was higher for those who were bedridden functional status compared to working status, for patients whose marital status was separated compared to widowed status. In this separate longitudinal data analysis intra-class correlation was not investigated. To conduct such correlation between the two responses, joint data analysis was employed. According to the results of longitudinal sub models under separate analysis in Table3, the random effect estimates depicted that intercepts and slopes vary significantly, which suggests that there was significant considerable variation among HIV/AIDS patients from visit to visit.
When the number of CD4 cell count increased, its average effect for odds of a patient being co-infected with TB was around 0.004 times lower for ART treatment [AOR= 0.996; 95%CI: 0.994, 0.998]. And the amount of variability among patients due to the effect of time per month in each visit was 0.011. And the correlation was -0.176 which indicates that there was negative correlation between intercept and slope (when a patient’s intercept increase by one unit of standard deviation, that patient’s slope decreased by 0.176 standard deviations).Table3 also shows the covariance parameter estimates for separate longitudinal analysis for TB status.
Table3: Parameter Estimates of TB status, binary logistic regression models data analysis
Effect
|
Estimate
|
Std. Err
|
95% CI for AOR
|
p - Value
|
Intercept
|
3.136
|
2.011
|
23.01(4.19, 212.94)
|
0.0017*
|
Residence area(Ref=urban)
|
Rural
|
1.839
|
0.644
|
6.29(1.78, 22.25)
|
0.0043*
|
Fun.st. (Ref=working)
|
Ambulatory
|
0.136
|
1.125
|
1.146(0.126, 10.423)
|
0.036*
|
Bedridden
|
3.171
|
1.037
|
23.831(3.121, 182.00)
|
0.0022*
|
Marital status. (Ref= living without partner)
|
Living with partner
|
-0.698
|
1.164
|
0.498(0.051, 4.879)
|
0.5486
|
WHO stage (Ref=st.4)
|
Stage 1
|
-7.896
|
0.728
|
0.04(0.01, 0.02)
|
< 0.01*
|
Stage 2
|
-7.550
|
0.694
|
0.005(0.0001, 0.002)
|
<0.01*
|
Stage 3
|
-3.729
|
0.667
|
0.024(0.006, 0.089)
|
<0.01)*
|
Weight
|
-0.101
|
0.024
|
0.904(0.862, 0.946)
|
<0.0001 *
|
CD4 cell count
|
-0.004
|
0.001
|
0.996(0.994, 0.998)
|
<0.0001*
|
Medication adherence(Ref.=no)
|
yes
|
-0.004
|
0.001
|
0.996(0.994, 0.998)
|
<0.0001*
|
Dietary adherence(Ref.=no)
|
yes
|
-0.004
|
0.001
|
0.996(0.994, 0.998)
|
<0.0001*
|
*stands for statistically significant variable
|
To have an appropriate joint model that represents the longitudinally measured of CD4 count and TB status of the HIV patients, different candidate joint models with different random effect for the joint modeling were considered. The AIC and BIC were used as a guideline in selecting covariates for the model. A smaller AIC and BIC values were generally indicates a better model.
In joint modeling of longitudinal outcomes, we have two types of modeling techniques those are marginal model and conditional independency random effects model. Marginal models were not functional in this study because, it did not consider the random parts, where individual effects on the variable of interests can be identified. Table4 revealed that the joint model with random intercept effects with the inclusion of random linear slopes was the best model as compared to random intercept only.
Therefore, the joint model with random intercept and linear slope was considered as an appropriate model. Table4 also shows that the value of fit statistics (AIC and BIC) for all joint models were less than that of the separate models. In this study, both separate and joint models were fitted because in separate analysis one response was considered as linear predictor for the other. Moreover, when we compared the two models (separate and joint), joint model was fitting better the data as compared to the separate model. The result of selected appropriate joint models for the longitudinally measured CD4 count and TB status of HIV infected patients and indicated in Table4.
The result in Table4 shows that time of follow ups visits, residence area, and functional status, adherence to medication, WHO clinical stages, weight, hemoglobin level and social support were significantly associated with both CD4 cell count and TB status. In addition, one way interaction terms (time * educational level) was also associated with both outcomes. Unstructured covariance structure was also applied for joint longitudinal data analysis as was done for in separate model analyses.
The random effects for the two outcomes were significantly and negatively associated (Table4). This translates in to a negative correlation between HAART CD4 cell and TB status. This means that increasing the average CD4 cell count per mm3 tends to decrease the chance of being co-infected with TB.
Table4: Parameter estimates of CD4 cell count and TB status using joint model.
Effect
|
TB status
|
CD4 cell count
|
Estimate
|
Std.Err
|
P-value
|
Estimate
|
Std. Err
|
P- value
|
Intercept
Time
Age
Residence(ref=urban)
Rural
Educ.Level (ref=tertiary)
No education
Primary
Secondary
Func.Stat (ref=working)
Ambulatory
Bedridden
Other
Ols(ref=yes)
No
Adherence(ref= non-adherent)
Adherent
WHOst.(ref=stage4)
Stage1
Stage2
Stage3
Weight
Hemoglobin
BMI(ref=underweight)
Normal
Overweight
Social sup.(ref=yes)
No
Time*educational level(Ref.=Tertiary)
Time*no education
Time*primary
Time*secondary
|
|
6.467
-0.054
-0.025
1.307
0.104
-1.387
1.701
0.568
3.002
1.160
0.613
-1.010
-9.131
-8.960
-4.048
-0.146
-0.402
-0.528
-1.286
0.531
0.155
0.144
0.003
|
2.687
0.018
0.031
0.531
0.881
0.901
0.952
0.941
0.864
0.689
0.574
0.657
0.698
0.674
0.610
0.032
0.097
0.433
0.233
0.488
0.031
0.042
0.043
|
0.0162
0.0025*
0.026*
0.0139*
0.9064
0.1240
0.0739
0.0458*
0.0005*
0.0925*
0.2849
0.1046*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
0.2224
0.1963
0.0260*
<0.0001*
0.0007*
0.0455*
|
7.857
0.205
-0.099
-0.050
1.459
-0.200
-1.017
-3.915
-4.617
-1.637
1.542
4.379
2.481
1.107
0.030
0.030
0.587
0.690
1.856
-1.100
0.190
0.246
0.203
|
1.863
0.010
0.022
0.401
0.633
0.630
0.645
0.677
0.695
0.516
0.429
0.427
0.370
0.364
0.372
0.018
0.073
0.279
0.500
0.371
0.016
0.019
0.021
|
<0.0001
<0.01*
<0.0001*
0.1013*
0.0212
0.7513
0.1150
<0.0001*
<0.0001*
0.0015*
0.0003
<0.0001*
<0.0001*
0.0016
0.0162*
<0.0001*
<0.0001*
0.0134
0.0002
0.0033*
<0.0001*
<0.0001*
<0.0001*
|
|
|
|
|
|
|
|
|
According to the results of longitudinal model under joint analysis in Table4, the random effect estimates indicated that intercepts and slopes vary significantly, which suggests that there was significant considerable variation among HIV/AIDS patients from visit to visit.
As visiting times of patients to hospitals for treatment increased by one unit, the odds of being co-infected with TB was decreased by 0.05 and the expected number of CD4 cell count was increased by 0.2 given the other variables constant.
As weight of patients increased by one unit, the odds of being co-infected with TB was decreased by 1.3 and the expected number of CD4 cell count was increased by 0.03 given the other variables constant. As patient’s age increased by one year the expected number of CD4 cell count was decreased by 0.099 and the odds of being co-infected with TB was increased by 0.025 controlling other variables constant.
The expected number of CD4 cell count for patients whose functional status were ambulatory, was decreased by 3.9 as compared to those patients whose functional status was working status. But, the odds of an ambulatory patients being co-infected with TB was increased by 0.6 as compared to those patients at working status. Similarly, the expected number of CD4 cell count for bedridden patients was decreased by 4.6 as compared to patients with working status and the odds of bedridden patients being co-infected with TB was increased by 3 as compared to patients with working status.
Patients’ adherence status was also another important variable for CD4 cell count and TB status and the result showed that, the expected number of CD4 cell count for adherent patients was 4.4 times that of non-adherent patients and the odds of being co-infected with TB for adherent patients was decreased by1.0 given the other variables constant..
The expected number of CD4 cell count for patients who did not get social support was decreased by 1.1 as compared to those who got social support but the odds of being co-infected with TB for patients who did not get social support was increased by 0.5 controlling the other variables constant.
As hemoglobin level of patients increased by one unit, the expected number of CD4 cell count of HIV patients increased by 0.59 cell per/mm3 but the odds of being co-infected with TB for such patients decreased by 0.4 keeping the other variables constant.
The expected number of CD4 cell count for patients whose WHO of stage1 was greater by 2.5 cells per mm3 as compared to stage4 but the odds of being co-infected with TB for WHO stage1 patients was decreased by 9.1 as compared to stage4. Similarly, the expected number of CD4 cell count of WHO stage2 patients was greater by 1.1 and the odds of being co-infected with TB for WHO stage2 patients was decreased by 8,9 as compared to those of patient whose WHO stages were stage4 given the other variables constant..
In Table4, it is also indicated that the expected number of CD4 cell count for rural patients was decreased by 0.05 as compared to urban patients but the odds of being co-infected with TB for rural patients was increased by 1.3 as compared to urban patients given the other variables constant.
The interaction effect in Table4 indicates that, as visiting time of a patient increased by one unit, the expected number of CD4 cell count for non-educated patients was decreased by 0.2 but the odds of being co-infected with TB for such patients was increased by 0.15 as compared to tertiary educated patients, keeping the other variables constant. Similarly, as visiting time of patients increased by one unit, the expected number of CD4 cell count for primary educated patients was decreased by 0.24 cells per mm3 and the odds of being co-infected with TB was increased by 0.14 as compared to tertiary educated patients keeping the other variables constant.