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

The Use of Subset Selection in Combined-Array Experiments to Determine Optimal Product or Process Designs

. In the quality control literature, a number of authors have advocated the use of combined-arrays in screening experiments to identify robust product designs or robust process designs [Shoemaker, Tsui, and Wu (1991); Nair et al. (1992); Myers, Khuri, and Vining (1992), among others]. This paper considers product design and process design applications in which there are one or more \control" factors that can be modied by the manufacturer, and one or more \environmental" (or \noise") factors that that vary under eld or manufacturing conditions. We show how Gupta's subset selection philosophy can be implemented in such a setting to identify optimal combinations of the levels of the control factors [Gupta (1956, 1965)]. By optimal, we mean those settings of the control factors that yield product designs whose performance is the most robust to variations in environmental factors. For process designs, the optimal settings of the control factors yield a fabrication method whose product qu..