Admissible two-stage designs for phase II cancer clinical trials

In a typical two-stage design for a phase II cancer clinical trial for efficacy screening of cytotoxic agents, a fixed number of patients are initially enrolled and treated. The trial may be terminated for lack of efficacy if the observed number of tumour responses after the first stage is too small, thus avoiding treatment of patient with inefficacious regimen. Otherwise, an additional fixed number of patients are enrolled and treated to accumulate additional information on efficacy as well as safety. The minimax and the so-called 'optimal' designs by Simon have been widely used, and other designs have largely been ignored in the past for such two-stage cancer clinical trials. Recently Jung et al. proposed a graphical method to search for compromise designs with features more favourable than either the minimax or the optimal design. In this paper, we develop a family of two-stage designs that are admissible according to a Bayesian decision-theoretic criterion based on an ethically justifiable loss function. We show that the admissible designs include as special cases the Simon's minimax and the optimal designs as well as the compromise designs introduced by Jung et al. We also present a Java program to search for admissible designs that are compromises between the minimax and the optimal designs.