A Two-Stage Design for Comparative Clinical Trials: the Heteroscedastic Solution

The problem of comparing several experimental treatments to a control arises frequently in clinical trials. Various multi-stage randomized phase II/III designs have been proposed for the purpose of selecting one or more promising experimental treatments and comparing them with a control, while controlling overall Type I and Type II error rates. In this paper, a hybrid selection and testing design for comparing the means of several experimental normal populations among themselves and with the mean of a control normal population is proposed. It is assumed that the variances of the experimental and the control normal populations are unknown and unequal. A Stein-type two-sample selection approach is used at both the selection and testing stages to solve the heteroscedastic problems caused by the unknown variances. The hybrid two-stage design allows for dropping the poorly performing treatments early on the basis of interim analysis results and for early termination if none of the experimental treatments seems promising. Numerical computations are given to show the advantage of the proposed procedure over a pure selection procedure. An example is provided to illustrate the use of the new procedure.