Flexible designs for phase II comparative clinical trials involving two response variables

The aim of phase II clinical trials is to determine whether an experimental treatment is sufficiently promising and safe to justify further testing. The need for reduced sample size arises naturally in phase II clinical trials owing to both technical and ethical reasons, motivating a significant part of research in the field during recent years, while another significant part of the research effort is aimed at more complex therapeutic schemes that demand the consideration of multiple endpoints to make decisions. In this paper, our attention is restricted to phase II clinical trials in which two treatments are compared with respect to two dependent dichotomous responses proposing some flexible designs. These designs permit the researcher to terminate the clinical trial when high rates of favorable or unfavorable outcomes are observed early enough requiring in this way a small number of patients. From the mathematical point of view, the proposed designs are defined on bivariate sequences of multi-state trials, and the corresponding stopping rules are based on various distributions related to the waiting time until a certain number of events appear in these sequences. The exact distributions of interest, under a unified framework, are studied using the Markov chain embedding technique, which appears to be very useful in clinical trials for the sample size determination. Tables of expected sample size and power are presented. The numerical illustration showed a very good performance for these new designs.