Weighted Kaplan-Meier estimators for two-stage treatment regimes

In two-stage randomization designs, patients are randomized to one of the initial treatments, and at the end of the first stage, they are randomized to one of the second stage treatments depending on the outcome of the initial treatment. Statistical inference for survival data from these trials uses methods such as marginal mean models and weighted risk set estimates. In this article, we propose two forms of weighted Kaplan-Meier (WKM) estimators based on inverse-probability weighting-one with fixed weights and the other with time-dependent weights. We compare their properties with that of the standard Kaplan-Meier (SKM) estimator, marginal mean model-based (MM) estimator and weighted risk set (WRS) estimator. Simulation study reveals that both forms of weighted Kaplan-Meier estimators are asymptotically unbiased, and provide coverage rates similar to that of MM and WRS estimators. The SKM estimator, however, is biased when the second randomization rates are not the same for the responders and non-responders to initial treatment. The methods described are demonstrated by applying to a leukemia data set.