Estimation of survival distributions of treatment policies in two-stage randomization designs in clinical trials

Some clinical trials follow a design where patients are randomized to a primary therapy at entry followed by another randomization to maintenance therapy contingent upon disease remission. Ideally, analysis would allow different treatment policies, i.e., combinations of primary and maintenance therapy if specified up-front, to be compared. Standard practice is to conduct separate analyses for the primary and follow-tip treatments, which does not address this issue directly. We propose consistent estimators for the survival distribution and mean restricted survival tune for each treatment policy in such two-stage studies and derive large-sample properties. The methods are demonstrated on a leukemia clinical trial data set and through simulation.