Background
Methods
Study design
Inference based on generalized estimating equations
Inference based on a mixture Cox model with time-dependent covariate
Assumption on career as female sex worker
Observed values of the variables
Model and method
Comparison of the methods by simulation
Consistent | Probability of condom | Rate of condom |
---|---|---|
condom use | use at the beginning | acquisition during |
of career | career | |
Low |
π = 0.2 |
h = 0.05 |
Medium |
π = 0.5 |
h = 0.10 |
High |
π = 0.8 |
h = 0.25 |
Consistent condom use | Proportion of samples leading to rejection of H
0
| |||
---|---|---|---|---|
Pre 1-1-2004 | Post 1-1-2004 | GEE-linear | GEE-logit | Cox-binomial |
Low
|
Low
|
0.067
*
|
0.059
|
0.059
|
Low | Medium | 0.883 | 0.916 | 0.998 |
Low | High | 1.000 | 1.000 | 1.000 |
Medium
|
Medium
|
0.056
|
0.068
*
|
0.062
|
Medium | High | 0.734 | 0.984 | 1.000 |
High
|
High
|
0.056
|
NA
|
0.050
|
Cox-binomial model | GEE method | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
District |
n
Cox
|
p
Cox
|
n
logit
|
p
logit
|
p
Total
| %Diff |
p<0.05 | ||||
Belgaum | 199 | 0.069 | 0.295 | <0.001 | 397 | 0.366 | 0.775 | <0.001 | <0.001 | −0.5 | NO |
Bellary | 234 | 0.090 | 0.274 | <0.001 | 398 | 0.183 | 0.760 | <0.001 | <0.001 | −2.7 | NO |
Chennai | 265 | 0.073 | 0.446 | <0.001 | 349 | 0.143 | 0.413 | <0.001 | <0.001 | 13.6 | YES |
Chitoor | 360 | 0.012 | 0.107 | <0.001 | 395 | 0.026 | 0.230 | <0.001 | <0.001 | 7.7 | YES |
Coimbatore | 306 | 0.006 | 0.144 | <0.001 | 325 | 0.020 | 0.117 | <0.001 | <0.001 | 12.2 | YES |
Dharmapuri | 306 | 0.020 | 0.262 | <0.001 | 387 | 0.049 | 0.657 | <0.001 | <0.001 | 16.5 | YES |
East Godavari | 303 | 0.067 | 0.314 | <0.001 | 392 | 0.149 | 0.518 | <0.001 | <0.001 | 4.5 | NO |
Guntur | 324 | 0.012 | 0.345 | <0.001 | 386 | 0.068 | 0.532 | <0.001 | <0.001 | 21.9 | YES |
Madurai | 269 | 0.044 | 0.263 | <0.001 | 319 | 0.097 | 0.304 | <0.001 | <0.001 | 12.1 | YES |
Mumbai BB | 156 | 0.069 | 0.112 | 0.578 | 379 | 0.576 | 0.629 | 0.369 | 0.573 | −0.9 | NO |
Mumbai NBB | 144 | 0.064 | 0.072 | 0.983 | 354 | 0.557 | 0.711 | 0.011 | 0.041 | −0.8 | NO |
Mysore | 328 | 0.031 | 0.191 | <0.001 | 420 | 0.120 | 0.377 | <0.001 | <0.001 | 8.7 | YES |
Prakasam | 374 | 0.003 | 0.123 | <0.001 | 402 | 0.026 | 0.204 | <0.001 | <0.001 | 10.1 | YES |
Pune BB | 74 | 0.202 | 0.261 | 0.884 | 399 | 0.769 | 0.942 | <0.001 | <0.001 | −3.9 | YES |
Pune NBB | 60 | 0.112 | 0.130 | 0.054 | 251 | 0.689 | 0.870 | <0.001 | <0.001 | 0.0 | NO |
Salem | 249 | 0.035 | 0.313 | <0.001 | 319 | 0.106 | 0.364 | <0.001 | <0.001 | 13.9 | YES |
Shimoga | 192 | 0.059 | 0.225 | <0.001 | 338 | 0.158 | 0.641 | <0.001 | <0.001 | 2.9 | NO |
Thane BB | 54 | 0.337 | 0.500 | 0.752 | 397 | 0.847 | 0.913 | 0.082 | 0.209 | −5.6 | YES |
Thane NBB | 64 | 0.241 | 0.311 | 0.662 | 377 | 0.735 | 0.894 | <0.001 | <0.001 | −3.5 | NO |
Visakhapatnam | 350 | 0.042 | 0.386 | <0.001 | 405 | 0.043 | 0.500 | <0.001 | <0.001 | 18.8 | YES |
Yevatmal | 57 | 0.131 | 0.435 | <0.001 | 148 | 0.328 | 0.800 | <0.001 | <0.001 | 0.6 | NO |
Results
Simulation study
Application to the Indian data
GEE method with linear link
Re-analysis with the Cox-binomial method
Analysis with the Cox-binomial model combining all districts and with additional covariates
Model with intervention effect only
|
Estimate
|
Robust s.e. |
p-value
|
Binomial part
| |||
Intervention | 1.297 | 0.23 | <0.0001 |
Cox part
| |||
Intervention | 1.496 | 0.16 | <0.0001 |
Model with intervention and year
| |||
Binomial part
| |||
Intervention | −0.255 | 0.17 | 0.13 |
Year | 0.444 | 0.09 | <0.0001 |
Cox part
| |||
Intervention | 0.723 | 0.24 | 0.0026 |
Year | 0.298 | 0.07 | <0.0001 |