Sample size selection in clinical trials when population means are subject to a partial order: one-sided ordered alternatives

The statistical methodology under order restriction is very mathematical and complex. Thus, we provide a brief methodological background of order-restricted likelihood ratio tests for the normal theoretical case for the basic understanding of its applications, and relegate more technical details to the appendices. For data analysis, algorithms for computing the order-restricted estimates and computation of p-values are described. A two-step procedure is presented for obtaining the sample size in clinical trials when the minimum power, say 0.80 or 0.90 is specified, and the normal means satisfy an order restriction. Using this approach will result in reduction of 14–24% in the sample size required when one-sided ordered alternatives are used, as illustrated by several examples.