The bias of the sample proportion following a group sequential phase II clinical trial

Group sequential testing procedures have seen wide use in Phase II clinical trials. The sample proportion p of responders is the commonly used estimator for the binomial response probability p. It can be shown that p is the maximum likelihood estimator (MLE) of p. It is well known that MLE can be in general (Whitehead) and p in particular (Dupont) biased estimators, if ther computation follows a group sequential procedure. In this paper we numerically investigate the bias of p. We find that the magnitude of the bias of p is less than 0.025 in all cases we investigated. We apply the idea in Whitehead to propose a bias-adjusted estimator that reduces the bias substantially and reduces the mean square error as well in a certain range of p. We also evaluate the uniformly minimum variance unbiased (UMVU) estimator. If one does not mind a bias of 0.025, one may find the sample proportion a suitable estimator for p because of its simplicity and easy explanation. If one is concerned with bias, the bias-adjusted estimator may be a good choice.