1 Background of the Study
2 Materials and Methods
2.1 Data Source
2.2 Ethical Consideration
2.3 Variables of the Study
Variable name | Values of the variable | Type |
---|---|---|
Age | Years (baseline) | Continuous |
Marital status | Single, married, separated, windowed, divorced | Categorical |
Residence | Rural, urban | Categorical |
Educational level | Not educated, primary, secondary, tertiary | Categorical |
Working time | Partimer, working full time, unemployed | Categorical |
Use of alcohol | Use, do not use | Categorical |
Smoking | Smoker, nonsmoker | Categorical |
Use of soft drug | Use, do not use | Categorical |
Type of TB | Pulmonary TB, extra pulmonary TB | Categorical |
Clinical stage | Stage-I, stage-II, stage-III, stage-IV | Categorical |
Functional status | Working, ambulatory, bed ridden | Categorical |
Religion | Muslim, orthodox, protestant | Categorical |
Sex | Female, male | Categorical |
Status of patients | Active, missed, died, transferred | Categorical |
2.4 Model Specification
2.4.1 Univariate Linear Mixed Effects Model
2.4.2 Methods of Parameter Estimation
2.4.3 Multivariate Linear Mixed Model
2.4.4 Special Cases for the Random Effect Variance Matrix
2.4.5 Association of the Evolutions (AOE)
2.4.6 Evolution of the Association (EOA)
2.4.7 Joint Model Estimation Techniques
2.4.8 Model Selection Criteria
Variable | Active | % | Died | % | Missed | % | Transferred | % | Total | % |
---|---|---|---|---|---|---|---|---|---|---|
Sex | ||||||||||
Female | 61 | 48.41 | 14 | 43.75 | 24 | 42.86 | 16 | 40.00 | 115 | 45.28 |
Male | 65 | 51.59 | 18 | 56.25 | 32 | 57.14 | 24 | 60.00 | 139 | 54.72 |
Religion | ||||||||||
Muslim | 43 | 34.13 | 15 | 46.88 | 17 | 30.36 | 16 | 40.00 | 91 | 35.83 |
Orthodox | 75 | 59.52 | 15 | 46.88 | 37 | 66.07 | 19 | 47.50 | 146 | 57.48 |
Protestant | 8 | 6.35 | 2 | 6.25 | 2 | 3.57 | 5 | 12.50 | 17 | 6.69 |
Educational level | ||||||||||
Not educated | 26 | 20.63 | 8 | 25.00 | 13 | 23.21 | 12 | 30.00 | 59 | 23.23 |
Primary | 56 | 44.44 | 14 | 43.75 | 20 | 35.71 | 18 | 45.00 | 108 | 42.52 |
Secondary | 37 | 29.37 | 8 | 25.00 | 19 | 33.93 | 6 | 15.00 | 70 | 27.56 |
Tertiary | 7 | 5.56 | 2 | 6.25 | 4 | 7.14 | 4 | 10.00 | 17 | 6.69 |
Residence | ||||||||||
Rural | 21 | 16.67 | 4 | 12.50 | 7 | 12.50 | 6 | 15.00 | 38 | 14.96 |
Urban | 105 | 83.33 | 28 | 87.50 | 49 | 87.50 | 34 | 85.00 | 216 | 85.04 |
Marital status | ||||||||||
Divorced | 6 | 4.76 | 2 | 6.25 | 7 | 12.50 | 6 | 15.00 | 21 | 8.27 |
Married | 65 | 51.59 | 12 | 37.50 | 18 | 32.14 | 16 | 40.00 | 111 | 43.70 |
Separated | 8 | 6.35 | 9 | 28.13 | 10 | 17.86 | 1 | 2.50 | 28 | 11.02 |
Single | 33 | 26.19 | 8 | 25.00 | 19 | 33.93 | 13 | 32.50 | 73 | 28.74 |
Widowed | 14 | 11.11 | 1 | 3.13 | 2 | 3.57 | 4 | 10.00 | 21 | 8.27 |
Clinical stage | ||||||||||
Stage-I | 4 | 3.17 | 0 | 0 | 1 | 1.79 | 3 | 7.14 | 8 | 3.15 |
Stage-II | 16 | 12.70 | 2 | 6.25 | 2 | 3.57 | 3 | 7.14 | 23 | 9.06 |
Stage-III | 61 | 48.41 | 14 | 43.75 | 27 | 48.21 | 21 | 50.00 | 123 | 48.43 |
Stage-IV | 45 | 35.71 | 16 | 50.00 | 26 | 46.43 | 13 | 30.95 | 100 | 39.37 |
Functional status | ||||||||||
Ambulatory | 53 | 42.06 | 13 | 40.63 | 37 | 66.07 | 23 | 57.50 | 126 | 49.61 |
Bedridden | 5 | 3.97 | 9 | 28.13 | 7 | 12.50 | 5 | 12.50 | 26 | 10.24 |
Working | 68 | 53.97 | 10 | 31.25 | 12 | 21.43 | 12 | 30.00 | 102 | 40.16 |
Alcohol | ||||||||||
No | 91 | 72.22 | 15 | 46.88 | 28 | 50.00 | 22 | 55.00 | 156 | 61.42 |
Yes | 35 | 27.78 | 17 | 53.13 | 28 | 50.00 | 18 | 45.00 | 98 | 38.58 |
Smoke | ||||||||||
No | 108 | 85.71 | 17 | 53.13 | 38 | 67.86 | 29 | 72.50 | 192 | 75.59 |
Yes | 18 | 14.29 | 15 | 46.88 | 18 | 32.14 | 11 | 27.50 | 62 | 24.41 |
Type of TB | ||||||||||
Extra pulmonary | 60 | 47.62 | 17 | 53.13 | 25 | 44.64 | 20 | 50.00 | 122 | 48.03 |
Pulmonary | 66 | 52.38 | 15 | 46.88 | 31 | 55.36 | 20 | 50.00 | 132 | 51.97 |
3 Results and Discussion
3.1 Descriptive Statistics
Measurement time | Sample points | Square root of CD4 | Weight | ||
---|---|---|---|---|---|
Mean | SD | Mean | SD | ||
0 | 254 | 11.965 | 5.430 | 48.407 | 10.608 |
6 | 156 | 16.102 | 5.309 | 52.994 | 10.818 |
12 | 134 | 18.094 | 4.852 | 54.795 | 9.6920 |
18 | 105 | 19.419 | 5.004 | 55.771 | 10.066 |
24 | 65 | 19.386 | 5.148 | 56.854 | 11.300 |
30 | 43 | 19.842 | 5.499 | 57.465 | 11.023 |
36 | 23 | 18.884 | 5.295 | 56.609 | 8.6380 |
42 | 9 | 16.777 | 3.653 | 58.556 | 12.136 |
48 | 3 | 14.824 | 1.181 | 64.333 | 13.614 |
3.2 Exploring Individual Profile and the Mean Structure
3.3 The Separate Longitudinal Analysis
No. | Random effects | Square root of CD4 | Weight | ||
---|---|---|---|---|---|
AIC | BIC | AIC | BIC | ||
1 | Only intercept | 5195.162 | 5274.305 | 4533.621 | 4594.209 |
2 | Intercept and linear time slope | 5137.415 | 5225.869 | 4523.083 | 4592.991 |
3 | Only linear time slope | 5630.983 | 5710.125 | 4724.709 | 4785.297 |
4 | Intercept and quadratic time slope | 5175.464 | 5263.917 | 4536.473 | 4606.382 |
5 | Only quadratic time slope | 5711.422 | 5790.564 | 4794.546 | 4855.133 |
6 | Linear and quadratic time slope | 5583.500 | 5671.953 | 4670.797 | 4740.706 |
7 | Intercept linear and quadratic time slopes | 5093.714 | 5196.134 | 4486.242 | 4570.133 |
Fixed effects | Weight | Square root of CD4 | |||
---|---|---|---|---|---|
Estimate | 95 % CI | Fixed effects | Estimate | 95 % CI | |
Intercept | 35.999 | [30.94, 41.057]\(^\dag \)
| Intercept | 11.844 | [10.744, 12.943] |
Sex | Alcohol | ||||
Female (ref) | Non-user (ref) | ||||
Male | 6.330 | [4.040, 8.620]\(^\dag \)
| Users |
\(-\)0.622 | [−1.764, 0.520] |
Age | 0.244 | [0.111, 0.376]\(^\dag \)
| |||
Time | 0.656 | [0.530, 0.783]\(^\dag \)
| Time | 0.560 | [0.479, 0.642]\(^\dag \)
|
Time\(^2\)
|
\(-\)0.011 | [−0.01, −0.007]\(^\dag \)
| Time\(^2\)
|
\(-\)0.010 | [−0.011, −0.008]\(^\dag \)
|
Functional status | |||||
Ambulatory (ref) | |||||
Bedridden | 1.543 | [−2.496, 5.582] | Bedridden |
\(-\)3.347 | [−5.447, −1.248]\(^\dag \)
|
Working | 3.334 | [0.870, 5.799] | Working | 2.236 | [0.982, 3.490] |
Patient status | |||||
Active (ref) | |||||
Died |
\(-\)3.604 | [−7.256, 0.047] | Died |
\(-\)0.741 | [−2.579,1.098] |
Missed |
\(-\)3.530 | [−6.362, −0.697]\(^\dag \)
| Missed |
\(-\)0.448 | [−1.907, 1.012] |
Transferred |
\(-\)1.170 | [−4.344, 2.004] | Transferred | 1.461 | [−0.170, 3.093] |
Educational level | |||||
Not educated (ref) | |||||
Primary |
\(-\)0.653 | [−3.539, 2.233] | |||
Secondary | 4.671 | [1.555, 7.788]\(^\dag \)
| |||
Tertiary | 3.906 | [−1.042, 8.853] | |||
Time \(\times \) functional status | |||||
Time \(\times \) bedridden |
\(-\)0.233 | [−0.480, 0.013] | Time \(\times \) bedridden | 0.042 | [−0.134, 0.217] |
Time \(\times \) working |
\(-\)0.138 | [−0.226, −0.051]\(^\dag \)
| Time \(\times \) working |
\(-\)0.046 | [−0.105, 0.013] |
Random-effects | Estimate | 95 % CI | Random-effects | Estimate | 95 % CIs |
---|---|---|---|---|---|
\(\hat{\sigma }_{b_0}\)
| 8.901 | [8.046, 9.847] |
\(\hat{\sigma }_{b_0}\)
| 4.206 | [3.715, 4.761] |
\(\hat{\sigma }_{b_1}\)
| 0.633 | [0.525, 0.765] |
\(\hat{\sigma }_{b_1}\)
| 0.364 | [0.290, 0.457] |
\(\hat{\sigma }_{b_2}\)
| 0.015 | [0.012, 0.020] |
\(\hat{\sigma }_{b_2}\)
| 0.007 | [0.005, 0.010] |
\(\hat{\sigma }_{b_{10}b_{11}}\)
|
\(-\)0.350 | [−0.525, −0.147] |
\(\hat{\sigma }_{b_{10}b_{11}}\)
|
\(-\)0.301 | [−0.464, −0.118] |
\(\hat{\sigma }_{b_{10}b_{12}}\)
| 0.292 | [−0.009, 0.545] |
\(\hat{\sigma }_{b_{10}b_{12}}\)
| 0.334 | [0.090, 0.540] |
\(\hat{\sigma }_{b_{10}b_{22}}\)
|
\(-\)0.996 | [−1.00, −0.784] |
\(\hat{\sigma }_{b_{10}b_{22}}\)
|
\(-\)0.983 | [−0.995, −0.944] |
\(\hat{\sigma }_{\varepsilon }\)
| 3.174 | [2.931, 3.436] |
\(\hat{\sigma }_{\varepsilon }\)
| 2.682 | [2.491, 2.887] |
3.4 Joint Analysis of Square Root of CD4 Count and Weight
Type of model | Random effect considered | AIC | BIC |
---|---|---|---|
Joint | Intercept only | 9717.900 | 9739.100 |
Joint | Intercept and linear slope | 9543.100 | 9676.000 |
Joint | Intercept linear and quadratic slopes | 9673.900 | 9719.900 |
Univariate (separate) | Intercept and linear slope | 13,989.00 | 13,999.70 |
Fixed effects | Weight | Square root of CD4 | |||
---|---|---|---|---|---|
Estimate | 95 % CI | Fixed effects | Estimate | 95 % CI | |
Intercept | 57.644 | [52.331, 62.957] | Intercept | 14.968 | [13.208, 16.728] |
Transferred (ref) | |||||
Active | 1.503 | [−1.659, 4.665] | Active |
\(-\)1.134 | [−2.747, 0.479] |
Died |
\(-\)1.852 | [−6.128, 2.424] | Died |
\(-\)2.083 | [−4.226, 0.059] |
Missed |
\(-\)2.122 | [−5.746, 1.502] | Missed |
\(-\)2.012 | [−3.843, −0.180] |
Sex | Alcohol | ||||
Male (ref) | User(ref) | ||||
Female |
\(-\)7.197 | [−9.452, −4.941]\(^\dag \)
| Non-users | 0.530 | [−0.602, 1.662] |
Educational level | |||||
Tertiary (ref) | |||||
Not educated |
\(-\)4.230 | [−9.204, 0.744] | |||
Primary |
\(-\)5.406 | [−10.108, −0.704]\(^\dag \)
| |||
Secondary |
\(-\)0.260 | [−5.127, 4.608] | |||
Time | 0.423 | [0.319, 0.528]\(^\dag \)
| Time | 0.431 | [0.357, 0.506] |
Time\(^2\)
|
\(-\)0.007 | [−0.010, −0.005]\(^\dag \)
| Time\(^2\)
|
\(-\)0.008 | [−0.010, −0.006]\(^\dag \)
|
Functional status | |||||
Working (ref) | |||||
Ambulatory |
\(-\)4.265 | [−6.778, −1.752]\(^\dag \)
| Ambulatory |
\(-\)2.329 | [−3.591, −1.068]\(^\dag \)
|
Bedridden |
\(-\)1.838 | [−6.070, 2.395] | Bedridden |
\(-\)5.606 | [−7.764, −3.448]\(^\dag \)
|
Time \(\times \) functional status | |||||
Working \(\times \) time (ref) | |||||
Ambulatory \(\times \) time | 0.198 | [0.086, 0.311]\(^\dag \)
| Ambulatory \(\times \) time | 0.110 | [0.042 , 0.178]\(^\dag \)
|
Bedridden \(\times \) time |
\(-\)0.046 | [\(-\)0.338, 0.245] | Bedridden \(\times \) time | 0.112 | [−0.073, 0.297] |