DISCUSSION
EVENTS
Phase II/III clinical trials are efficient for testing multiple experimental treatments. However, in simulations based on typical sample sizes in confirmatory trials, we observed that in some scenarios the naive estimator for log hazard ratio has substantial biases arising from adaptation performed at an interim analysis so that it is necessary to have bias adjusted estimators. Brückner et alIn most scenarios, all the bias adjusted estimators we have considered perform better than the naive estimator. The shrinkage estimator does not eradicate much bias but performs best in terms of mean squared error. Our recommendation is to use the shrinkage estimator if the primary aim is to have an estimator whose variability does not exceed that of the naive estimator. The interpretation of shrinkage estimates needs to include an acknowledgement that biases of the shrinkage estimator are only slightly less than those of the naive estimator.The single iteration bias subtracted estimator does not eradicate bias fully, overestimating treatments' effects. From the simulation study, while emphasizing that in practice true treatments' effects are unknown, the overestimation is only noticeable if the experimental treatment selected is not the most desired treatment to continue to stage 2 but even in this case, this estimator is still much less biased compared to the naive estimator. Also, in most scenarios it has smaller mean squared errors than the naive estimator. Thus, the single iteration biased subtracted estimator is preferable if one is ready to accept slight overestimation. Because the bias reduction for this estimator depends on the true values for the log hazard ratios, before conducting a clinical trial, we recommend assessing its properties using a simulation study of plausible hazard functions.Regulators recommend that the magnitude of the bias of a naive point estimator is understood, effort is made to control the bias and the point estimator to be used in the analysis is prespecified.Brückner et alIn simulations, we have used a single treatment selection rule to compare the various estimators. For other selection rules, we expect the UMVCUE to have least biases as it is approximately unbiased by derivation. The shrinkage estimator is likely to have largest biases and least MSEs among the bias adjusted estimators since this has been observed for different selection rules when patient outcomes are normally distributed.The UMVCUE we have derived is not fully unbiased. One reason for this is following stage 1 patients without events before the interim analysis in stage 2 so that the independent increment structure is an approximate assumption. Bias can be reduced by not following stage 1 patients in stage 2. However, this can lead to not including many events which increases RMSE. Therefore, we recommend using a design that follows stage 1 patients in stage 2 but has an approximate independent increment structure.We have considered estimation based on Cox's proportional hazards model and on the log rank score statistic. Trial investigators would need to prespecify the model to use in advance. In general, we recommend estimation based on Cox's proportional hazards model since its estimates have better properties than those based on the logrank score statistic, it is possible to include covariates and using standard statistical packages, it is easier to obtain parameter values for the distribution given by expression (We have not considered confidence intervals with appropriate coverage probabilities. To obtain confidence intervals that adjust for treatment selection, we suggest extending the work of Magirr et alWe have provided a program written in R