Two-stage randomization designs are becoming common in oncology and AIDS clinical trials. In these designs patients are initially randomized to an induction treatment, followed by randomization to a maintenance treatment conditional on their remission and consent to further participation in the trial. We consider a situation where at the second stage patients can be randomized to either observation or drug maintenance, and the main objective is to compare the induction therapies with respect to a survival endpoint. In practice, two approaches were suggested for such studies which use standard Cox regression analysis and 1) include all patients as if there was no second stage randomization, or 2) include only patients who were not randomized to drug maintenance. We demonstrate that in many cases these approaches can result in biased inference. We propose re-weighted versions of the usual score estimating equation and the score test in the Cox model, where patients randomly assigned to drug maintenance at the second stage receive weight zero, patients randomly assigned to observation receive weight equal to the inverse probability of randomization to observation and patients who were not included in the second randomization receive weight one. We also derive a number of events formula that approximately achieves the desired test power for comparing induction treatments. Large sample properties of our methods are illustrated via a simulation study.(This is joint work with Jeffrey D. Helterbrand of Genentech, Inc.)
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