Table 6 Estimates of regression parameters and their standard error obtained from MLE and Firth’s procedure by fitting Weibull AFT model for prostate cancer data under separation and near-to-separation
From: On estimation for accelerated failure time models with small or rare event survival data
Separation | Near-to-Separation | |||||||
|---|---|---|---|---|---|---|---|---|
MLE | Firth | MLE | Firth | |||||
Predictors | Estimates | SE | Estimates | SE | Estimates | SE | Estimates | SE |
Treatment | 11.842 | 9,561.118 | 1.129 | 0.409 | 1.146 | 0.600 | 0.846 | 0.271 |
Age | 11.475 | 0.00 | 1.013 | 0.428 | 0.380 | 0.804 | 0.132 | 0.565 |
WT | 0.309 | 0.502 | − 0.112 | 0.199 | − 1.316 | 0.597 | − 0.598 | 0.213 |
PF | -0.895 | 0.888 | -0.981 | 0.388 | -1.138 | 1.417 | -0.854 | 0.720 |
HX | 0.534 | 0.615 | 0.503 | 0.251 | 1.547 | 1.057 | 0.905 | 0.616 |
HG | -1.141 | 0.731 | -1.063 | 0.313 | 13.101 | 7,825.785 | 1.587 | 0.684 |
SZ | -0.537 | 0.778 | -0.054 | 0.259 | 0.506 | 0.918 | 0.389 | 0.591 |
SG | -1.966 | 0.872 | -0.321 | 0.092 | -2.071 | 0.743 | -0.345 | 0.080 |
Intercept | 5.218 | 0.728 | 7.671 | 0.181 | 5.924 | 1.006 | 8.171 | 0.252 |
scale (b) | 0.518 | 0.182 | 0.398 | 0.096 | 0.694 | 0.219 | 0.608 | 0.145 |