An Empirical and Simulated Comparison of Some Tests for Detecting Progressiveness of Response with Increasing Doses of a Compound

Abstract

Abstract Experiments consisting of several doses of a test agent and a zero dose control are often conducted to evaluate the effect of a compound on the response of interest. TUKEY et al. (1985) proposed a trend test procedure which uses the minimum p ‐value from three candidate dose scalings as a sensitive means for detecting a trend in response with increasing dose. Trend is defined here as a progressiveness, either increasing or decreasing, in response with increasing dose of the test agent. In this paper, we take a closer look at the procedure's inflated type I error rate and propose an adjustment based on the multivariate t ‐distribution which preserves the nominal significance level. Application of the adjusted trend test to a number of real data sets indicates that its performance is similar to that observed with Bartholomew's and Williams' tests. An evaluation of these three tests also was conducted on simulated data using an apparently novel approach which takes into account the underlying dosage regimen to genrate the alternative hypotheses for a broad range of dose response relations. The simulation results indicates that the adjusted trend test is overall more powerful than its two competitors, although there are circumstances where each procedure appears superior. This broad‐based power exhibited in both real and simulated settings makes the adjusted trend test an attractive approach.