INTRODUCTION
EVENTS, EVENT
Phase II/III clinical trials are efficient two‐stage designs that test multiple experimental treatments. In stage 1, patients are allocated to the control and all experimental treatments, with the data collected from them used to select experimental treatments to continue to stage 2. Patients recruited in stage 2 are allocated to the selected treatments and the control. Combined data of stage 1 and stage 2 are used for a confirmatory phase III analysis. Appropriate analysis needs to adjust for selection bias of the stage 1 data. Point estimators exist for normally distributed outcome data. Extending these estimators to time to event data is not straightforward because treatment selection is based on correlated treatment effects and stage 1 patients who do not get events in stage 1 are followed‐up in stage 2. We have derived an approximately uniformly minimum variance conditional unbiased estimator (UMVCUE) and compared its biases and mean squared errors to existing bias adjusted estimators. In simulations, one existing bias adjusted estimator has similar properties as the practically unbiased UMVCUE while the others can have noticeable biases but they are less variable than the UMVCUE. For confirmatory phase II/III clinical trials where unbiased estimators are desired, we recommend the UMVCUE or the existing estimator with which it has similar properties.

Phase II/III clinical trials are efficient since they can answer objectives of phases II and III in a single two‐stage trial.When outcomes are normally distributed, several point estimators that adjust for using stage 1 data for treatment selection have been proposed. The statistical methods used to develop the estimators can be grouped into three based on statistical techniques used to adjust for treatment selection. For the first, estimated bias is subtracted from the naive point estimate.There are two main features that make extension of estimators for normally distributed outcomes to TTE outcomes complex. Treatment selection may be based on treatment differences that are correlated so that there is need to determine the joint distribution of these differences that do not have a diagonal covariance matrix. The covariance matrix for TTE outcomes is not as well established in literature and as straightforward as for normally distributed outcomes and so it is important to describe it in detail. Secondly, it is more efficient for patients without events in stage 1 to be followed further in stage 2. However, this induces correlation between stage 1 and stage 2 data. Brückner et alWe have extended the UMVCUE for normally distributed outcomes to derive a new approximately UMVCUE for TTE outcomes and have compared the new estimator to the estimators by Brückner et al. We have derived expressions that encompass several treatment selection rules and that include the possibility of stopping for futility, which give more general estimators compared to Brückner et al who considered a single selection rule and assumed that the trial always continued to stage 2. Also, unlike Brückner et al, we have proposed how to reduce the impact of correlation between stage 1 and stage 2 data and have incorporated these in the estimators.