Bias-adjusted estimates of survival following group sequential hypothesis testing.

Abstract

It is known that repeated use of fixed sample hypothesis testing causes inflation of the type one statistical error. Since in a group sequential design a study is stopped preferentially when extreme data have been observed, we expect that the usual estimators are biased toward the extremes. We demonstrate through simulations that the fixed sample survival estimators are biased if computed after stopping a group sequential trial in which stopping is based on survival statistics. The problem is first studied under no censored data and then with the more realistic setting of censoring. In particular, we studied the two sample problem, that is, the estimation of survival following repeatedly testing the equality of two survival distributions. We first investigated some potential measures of bias. Bias-adjusted estimators of survival of the two distributions were suggested first based on the Whitehead (1986, (33), (34)) bias-adjusted estimator. This was done for the proportional hazards model. We found that this approach is not well behaved for the unconditional measures of bias, whereas it behaves well for the conditional measures, provided that the power of the test to detect the true value of the parameter was not too large (< 94%). However, for large powers, it has a tendency to overestimate the absolute difference of the two distributions. A generalized Whitehead bias-adjusted semiparametric estimator was suggested. This is not only applicable to the proportional hazards model, but to other survival data models. The conditional semiparametric estimator was found to behave well for all the data models and powers considered. The unconditional semiparametric estimator produced adjustments of survival in the right direction for the proportional hazards model, but not for the others. It was also seen to be applicable to the two main group sequential designs, namely the Pocock and O'Brien-Fleming designs. Finally, the findings were applied to a leukemia clinical trial. The control treatment (Daunorubicin) was compared to the new treatment (Idarubicin) based on a 0.05-level O'Brien-Fleming group sequential design with a maximum of 4 analyses and equal number of observations per group.