A Performance Comparison of Maximum Contrast Methods to Detect Dose Dependency

Abstract

This paper introduces the notion of a maximum contrast method for data analysis on experiments in a one-way layout with levels corresponding to doses of a test chemical. It is defined as the method which uses the maximum of a set of contrast statistics to make decisions for objectives, such as determining the minimum effective dose (MED) in clinical trials, the minimum toxic dose (MTD) in chronic toxicity studies, or a plausible dose-response pattern in dose-response studies, where a contrast statistic is defined as the ratio of a contrast of mean response for dose groups and an estimator of the standard deviation of the numerator. Along with this notion the authors devised an extended Williams method for unequal group sizes and compared the performance of three methods: the Williams method, a modified Williams method, and the max-t method, all of which are often used to identify the MTD based on a newly introduced loss function. They concluded that the modified Williams method is comparatively better for the purpose of identifying the MTD, although each method has its own advantageous pattern.