Estimating survival distributions for time-varying smart designs.

Treatment of complex diseases such as cancer, HIV, leukemia and depression usually follows complex treatment sequences. In two-stage randomization designs, patients are randomized to first-stage treatments, and upon response, a second randomization to the second-stage treatments is done. The clinical goal in such trials is to achieve a response such as complete remission of leukemia, 50 degrees To shrinkage of solid tumor or increase in CD4 count in HIV patients. These responses are presumed to predict longer survival. The focus in two-stage randomization designs with survival endpoints is on estimating survival distributions and comparing different treatment policies. In this article, we propose a parametric approach for estimating survival distributions in time-varying SMART designs. To evaluate the performance of our approach, a simulation study is conducted. The results of the simulation study reveal that the new approach gives survival probabilities that are less biased and more precise than the nonparametric methods. The new method is applied to a data set from a leukemia clinical trial.