Semiparametric efficient estimation of survival distributions in two-stage randomisation designs in clinical trials with censored data

Two-stage randomisation designs are useful in the evaluation of combination therapies where patients are initially randomised to an induction therapy and then, depending upon their response and consent, are randomised to a maintenance therapy. In this paper we derive the best regular asymptotically linear estimator for the survival distribution and related quantities of treatment regimes. We propose an estimator which is easily computable and is more efficient than existing estimators. Large-sample properties of the proposed estimator are derived and comparisons with other estimators are made using simulation.