Efficient Estimation of The Survival Distribution and Related Quantities of Treatment Policies in Two-Stage Randomization Designs in Clinical Trials

Abstract

Two-stage designs are common in therapeutic clinical trials such as Cancer or AIDS treatments. In a two-stage design, patients are initially treated with one induction (primary) therapy and then depending upon their response and consent, are treated by a maintenance therapy, sometimes to intensify the effect of the first stage therapy. The goal is to compare different combinations of primary and maintenance (intensification) therapies to find the combination that is most beneficial. To achieve this goal, patients are initially randomized to one of several induction therapies and then if they are eligible for the second-stage randomization, are offered to be randomized to one of several maintenance therapies. In practice, the analysis is usually conducted in two separate stages which does not directly address the major objective of finding the best combination. Recently Lunceford et al. (2002, Biometrics, 58, 48-57) introduced ad hoc estimators for the survival distribution and mean restricted survival time under different treatment policies. These estimators are consistent but not efficient, and do not include information from auxiliary covariates. In this dissertation study we derive estimators that are easy to compute and are more efficient than previous estimators. We also show how to improve efficiency further by taking into account additional information from auxiliary variables. Large sample properties of these estimators are derived and comparisons with other estimators are made using simulation. We apply our estimators to a leukemia clinical trial data set that motivated this study.