Supplementary analysis of probabilities at the termination of a group sequential phase II trial

We consider estimation of various probabilities after termination of a group sequential phase II trial. A motivating example is that the stopping rule of a phase II oncologic trial is determined solely based on response to a drug treatment, and at the end of the trial estimating the rate of toxicity and response is desirable. The conventional maximum likelihood estimator (sample proportion) of a probability is shown to be biased, and two alternative estimators are proposed to correct for bias, a bias‐reduced estimator obtained by using Whitehead's bias‐adjusted approach, and an unbiased estimator from the Rao–Blackwell method of conditioning. All three estimation procedures are shown to have certain invariance property in bias. Moreover, estimators of a probability and their bias and precision can be evaluated through the observed response rate and the stage at which the trial stops, thus avoiding extensive computation. Copyright © 2004 John Wiley & Sons, Ltd.