Comparison of treatments in a combination therapy trial

Although the min test proposed by Laska and Meisner (1) for testing superiority of a combination to each of its components is the uniformly most powerful monotone test, it is conservative in the neighborhood of origin. Considering a restricted null hypothesis, we analyze a general linear model. The p value associated with the proposed test and a confidence interval for the shortest distance between the combination therapy and component therapies are computed. Analysis of a design with two or more combinations is proposed. A numerical example is given and a problem of optimal allocation of the sample sizes and other relevant design issues are discussed.