Two multi-step selection procedures with Possible selection of two treatments of equal prior preference

Abstract

Dunnett's many-one test to compare several experimental treatment means with a control was extended in our previous paper to a decision procedure for selecting a desirable treatment when there is a strictly monotonic prior preference among the multiple treatments due to other consideration such as toxicity or cost. In this paper, we consider the case where two treatments could have equal prior preference. This formulation includes the problem of comparing a combination with its two components, or the comparison of four arms in a 2 by 2 factorial experiment. Our decision procedures will guarantee a high selection probability for the correct treatment(s) when that selection is appropriate. We establish sample size requirements for our decision procedures which can be applied to clinical trials with normal, binomial, or right censored exponential endpoints.