Background
Methods
Basic notations
Overview of the multiple failure time models
Andersen and Gill (AG) independent increment model
Prentice, Williams and Peterson (PWP) conditional model
Wei, Lin, and Weissfeld (WLW) marginal model
Simulation
Simulation of within-subject dependence
Computation of the correlation ρ0
Software simulation
Results
ρ
| Events | Model | Relative bias | Naive var | Robust var | Coverage |
---|---|---|---|---|---|---|
0.1 | 3 | AG | -0.193 | 0.008 | 0.006 | 0.308 |
PWP | -0.030 | 0.010 | 0.011 | 0.930 | ||
WLW | 0.320 | 0.009 | 0.021 | 0.415 | ||
6 | AG | -0.254 | 0.004 | 0.003 | 0.003 | |
PWP | -0.042 | 0.006 | 0.007 | 0.897 | ||
WLW | 0.666 | 0.005 | 0.021 | 0.004 | ||
9 | AG | -0.278 | 0.003 | 0.002 | 0.000 | |
PWP | -0.048 | 0.005 | 0.006 | 0.871 | ||
WLW | 0.929 | 0.004 | 0.022 | 0.000 | ||
12 | AG | -0.291 | 0.002 | 0.001 | 0.000 | |
PWP | -0.050 | 0.004 | 0.005 | 0.861 | ||
WLW | 1.151 | 0.003 | 0.022 | 0.000 | ||
0.45 | 3 | AG | -0.296 | 0.008 | 0.007 | 0.069 |
PWP | -0.201 | 0.009 | 0.011 | 0.491 | ||
WLW | 0.166 | 0.009 | 0.022 | 0.806 | ||
6 | AG | -0.343 | 0.004 | 0.004 | 0.001 | |
PWP | -0.291 | 0.005 | 0.006 | 0.055 | ||
WLW | 0.358 | 0.005 | 0.022 | 0.318 | ||
9 | AG | -0.350 | 0.003 | 0.003 | 0.000 | |
PWP | -0.324 | 0.004 | 0.004 | 0.008 | ||
WLW | 0.514 | 0.003 | 0.021 | 0.058 | ||
12 | AG | -0.349 | 0.002 | 0.002 | 0.000 | |
PWP | -0.338 | 0.003 | 0.003 | 0.002 | ||
WLW | 0.657 | 0.003 | 0.022 | 0.005 | ||
0.8 | 3 | AG | -0.381 | 0.008 | 0.008 | 0.016 |
PWP | -0.339 | 0.009 | 0.011 | 0.124 | ||
WLW | 0.051 | 0.009 | 0.024 | 0.936 | ||
6 | AG | -0.448 | 0.004 | 0.005 | 0.000 | |
PWP | -0.509 | 0.005 | 0.005 | 0.000 | ||
WLW | 0.110 | 0.004 | 0.023 | 0.892 | ||
9 | AG | -0.462 | 0.003 | 0.004 | 0.000 | |
PWP | -0.574 | 0.003 | 0.003 | 0.000 | ||
WLW | 0.157 | 0.003 | 0.023 | 0.829 | ||
12 | AG | -0.462 | 0.002 | 0.004 | 0.000 | |
PWP | -0.605 | 0.002 | 0.003 | 0.000 | ||
WLW | 0.205 | 0.002 | 0.022 | 0.727 |
Example
Number of events | ||||||||
---|---|---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | 4 | 5 | 6-10 | Total | |
N. of subjects (%) | 260 (54.7) | 101 (21.3) | 53 (11.2) | 21 (4.4) | 21 (4.4) | 10 (2.1) | 9 (1.9) | 475 (100) |
Model | Covariate | Beta | Naive S.E. | Robust S.E. | Robust 95% CI | |
---|---|---|---|---|---|---|
AG | Smoking | 0.158 | 0.059 | 0.089 | -0.016, 0.332 | |
Asthma | 0.276 | 0.111 | 0.155 | -0.028, 0.579 | ||
PWP | Smoking | 0.147 | 0.060 | 0.088 | -0.025, 0.319 | |
Asthma | 0.251 | 0.113 | 0.148 | -0.039, 0.540 | ||
WLW | Smoking | 0.162 | 0.058 | 0.102 | -0.037, 0.362 | |
Asthma | 0.407 | 0.111 | 0.189 | 0.036, 0.778 |