Efficient estimation in two-stage randomized clinical trials using ranked sets

Clinical trials designed for survival probability estimation of different treatment policies for chronic diseases like cancer, leukemia, and schizophrenia usually need randomization of treatments in two stages. Since complete remission is rare for these diseases, initially an induction therapy is given for patient's remission. Further treatment, which is often an expensive maintenance therapy, is administered only for the patients with remission. If the maintenance therapy is so expensive that the cost of the trial inflates, only a simple random sample of patients will be treated with the expensive maintenance due to budget constraint. In this article, we have implemented a design using ranked sets instead of simple randomization in the second stage and obtained an unbiased estimator of the overall survival distribution for a particular treatment combination. Through simulation studies under different conditions, we have found that the design we developed based on ranked sets gives an unbiased estimate of the population survival probability which is more efficient than the estimate obtained by the usual design.