Table 3 Estimates, standard error (SE) and simulation standard error (Sim.SE) of β0 and b from Maximum Likelihood Estimation and Firth’s Penalized Likelihood Estimation under Weibull Distribution in case of separation and near-to separation. Maximum convergence failure by MLE is 26.6% when separation occur over 1000 simulations in case of 80% censoring
From: On estimation for accelerated failure time models with small or rare event survival data
MLE | Firth | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
Sample Size (n) | Cens.% | True Coefficients | Estimates | Bias | SE | Sim.SE | Estimates | Bias | SE | Sim.SE |
Separation | ||||||||||
50 | 20 | βc=0.5 | 0.481 | -0.019 | 0.109 | 0.115 | 0.479 | -0.021 | 0.103 | 0.115 |
50 | 0.587 | 0.087 | 0.151 | 0.195 | 0.575 | 0.075 | 0.138 | 0.184 | ||
80 | 0.568 | 0.068 | 0.259 | 0.831 | 0.492 | -0.008 | 0.223 | 0.397 | ||
20 | βb=1.9 | 1.943 | 0.043 | 0.211 | 0.197 | 1.928 | 0.028 | 0.198 | 0.195 | |
50 | 14.187 | 12.287 | 6,559.531 | 1.566 | 3.071 | 1.171 | 0.879 | 0.175 | ||
80 | 104.371 | 102.471 | 7020.086 | 700.557 | 2.764 | 0.864 | 0.813 | 9.344 | ||
Near-to-Separation | ||||||||||
50 | 20 | βc=0.5 | 0.503 | 0.003 | 0.111 | 0.117 | 0.500 | 0.000 | 0.105 | 0.117 |
50 | 0.494 | -0.006 | 0.146 | 0.149 | 0.485 | -0.015 | 0.134 | 0.146 | ||
80 | 1.682 | 1.182 | 0.244 | 23.939 | 0.484 | -0.016 | 0.203 | 0.264 | ||
20 | βb=1.9 | 1.904 | 0.004 | 0.216 | 0.229 | 1.890 | -0.010 | 0.202 | 0.227 | |
50 | 2.030 | 0.130 | 0.354 | 0.348 | 1.934 | 0.034 | 0.309 | 0.315 | ||
80 | 2.855 | 0.955 | 0.636 | 21.649 | 1.433 | -0.467 | 0.468 | 0.459 | ||