Statistica Sinica 17(2007), 1567-1589

DESIGNED EXTENSION OF SURVIVAL STUDIES:

APPLICATION TO CLINICAL TRIALS

WITH UNRECOGNIZED HETEROGENEITY

Yi Li$^1$, Mei-Chiung Shih$^2$ and Rebecca A. Betensky$^1$

$^1$Harvard University and $^2$Standford University

Abstract: It is well known that unrecognized heterogeneity among patients, such as is conferred by genetic subtype, can undermine the power of a randomized trial, designed under the assumption of homogeneity, to detect a truly beneficial treatment. We consider the conditional power approach to allow for recovery of power under unexplained heterogeneity. While Proschan and Hunsberger (1995) confined the application of conditional power design to normally distributed observations, we consider more general and difficult settings in which the data are in the framework of continuous time and are subject to censoring. In particular, we derive a procedure appropriate for the analysis of the weighted log rank test under the assumption of a proportional hazards frailty model. The proposed method is illustrated through application to a brain tumor trial.

Key words and phrases: Adaptive design, conditional power, frailty model.