Table 3.
Simulation studies of the performance of auxiliary-variable estimator (θ̃C) compared to the local evaluation (LE), a full (complete-case) BICR, and a simple estimator (θ̂CA) based on an audit of 19%, 20%, 21% and 22%, for the null, small, moderate and large, effect sizes, respectively. Average estimates are provided with standard deviations in parenthesis. gives the simulated mean standard errors based on the proposed variance estimator described section 2.2. The true log-hazard ratio is the parameter used to generate continuous event times. The true BICR log-hazard was computed empirically by generating 1 million observations per treatment group.
| Reader Bias | Effect Size | True True log-HR | BICR log-HR | LE Estimator θ̂L (SD) | Full BICR Estimator θ̂C (SD) | Simple BICR Estimator θ̂CA (SD) | Auxiliary-Variable Estimator | Rel. Eff.† | |
|---|---|---|---|---|---|---|---|---|---|
| θ̃C (SD) | |||||||||
| None | Null | 0.000 | −0.002 | 0.000 (0.084) | 0.000 (0.095) | 0.001 (0.222) | 0.000 (0.144) | 0.146 | 2.36 |
| None | Small | −0.288 | −0.287 | −0.283 (0.087) | −0.289 (0.097) | −0.291 (0.203) | −0.289 (0.147) | 0.148 | 1.91 |
| None | Moderate | −0.511 | −0.515 | −0.503 (0.091) | −0.512 (0.101) | −0.514 (0.221) | −0.511 (0.150) | 0.151 | 2.17 |
| None | Large | −0.773 | −0.783 | −0.765 (0.094) | −0.778 (0.106) | −0.782 (0.232) | −0.777 (0.154) | 0.156 | 2.26 |
| Small | Null | 0.000 | 0.232 | −0.122 (0.084) | 0.234 (0.103) | 0.237 (0.231) | 0.239 (0.171) | 0.172 | 1.82 |
| Small | Small | −0.288 | −0.047 | −0.400 (0.086) | −0.048 (0.105) | −0.049 (0.210) | −0.046 (0.176) | 0.176 | 1.43 |
| Small | Moderate | −0.511 | −0.265 | −0.615 (0.090) | −0.267 (0.110) | −0.268 (0.241) | −0.264 (0.177) | 0.178 | 1.85 |
| Small | Large | −0.773 | −0.522 | −0.871 (0.095) | −0.527 (0.115) | −0.532 (0.246) | −0.525 (0.182) | 0.182 | 1.84 |
| Large | Null | 0.000 | 0.421 | −0.194 (0.083) | 0.418 (0.112) | 0.422 (0.257) | 0.425 (0.207) | 0.201 | 1.55 |
| Large | Small | −0.288 | 0.189 | −0.467 (0.087) | 0.140 (0.115) | 0.139 (0.236) | 0.146 (0.200) | 0.200 | 1.39 |
| Large | Moderate | −0.511 | −0.078 | −0.681 (0.089) | −0.076 (0.117) | −0.078 (0.259) | −0.071 (0.200) | 0.201 | 1.67 |
| Large | Large | −0.773 | −0.331 | −0.935 (0.094) | −0.330 (0.119) | −0.327 (0.264) | −0.324 (0.203) | 0.204 | 1.69 |
†
Relative Efficiency=SD(θ̂C)2/SD(θ̃C)2