Tukey’s Contrast Test Versus Two-Sample Test in a Dose-Response Clinical Trial

Abstract

Tukey, Ciminera, and Heyse (1985) proposed a linear trend test to establish a dose response; or if used sequentially, by eliminating the highest dose at each stage, to select the no-statistical-significance-of-trend (NOSTASOT) dose. The traditional alternatives have been to test the highest dose versus the control, ignoring contributions from the middle doses; or its sequential analog, to establish a minimum effective dose by testing first the highest dose versus the control, and if significant, testing the subsequent doses against the contrast until no significance is observed or doses are exhausted. In dose-response trials and/or in dose-finding trials, clinicians may believe a priori that the ordering of the responses is known, so the efficacy is assumed to increase monotonically with dose. Under order restricted alternatives, that is, under monotonic dose-response assumption, it is generally believed that Tukey’s contrast test, an analog of Tukey’s linear trend test in an analysis of variance set up, is superior to the test based on the highest versus control contrast in most practical or reasonable choices of dose response patterns. In this article we examine these two tests mathematically to establish areas of the parameter space where one is superior to the other in the order restricted parameter space when the number of doses is less than or equal to 7. We demonstrate that the highest versus control test is superior to Tukey’s contrast test only when all the middle doses have identical or near identical responses, which is a region of the alternative parameter space of minimal interest to researchers and dose-response modelers. Hence, we conclude that the traditional wisdom holds that for most of the popular and reasonable dose-response patterns Tukey’s contrast test is superior to the highest versus control test and should be employed by researchers in a typical dose-response trial.