A Performance Comparison of Maximum Contrast Methods to Detect Dose Dependency
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0092-8615/97 Copyright 0 1997 Drug Information Association Inc.
A PERFORMANCE COMPARISON OF MAXIMUM CONTRAST METHODS TO DETECT DOSE DEPENDENCY ISAO YOSHIMURA AND AKIRAWAKANA Faculty of Engineering, Science University of Tokyo, Tokyo, Japan
CHIKUMA HAMADA School of Medicine, The University of Tokyo, Tokyo, Japan
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 doseresponse 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 o f e n 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. Key Words: Contrast; Max-t method; Minimum toxic dose; One-way layout; Williams method
INTRODUCTION ONE OF THE TYPICAL forms of experiments adopted to biomedical or toxicological studies is to measure a response variable in animals or human beings at several doses of a test chemical or a drug. One purpose of such experiments is to evaluate the dose-response relationship, or, in special cases, to identify a key dose such as the minimum effective dose, the minimum toxic dose, the no adverse effect level (NOAEL), or the highest effective dose step (HEDS). Although numerous methods to analyze data in such experiments have been proposed in the biostatistics literature, those using contrast play a particularly important role, as is realized, for example, through Scheffk’s multiple comparison procedure (1) or the maximum contrast test explained by Robertson et al. (2). Concerning the usefulness of contrasts, Ruberg (3) pointed out that widely used potential methods to identify MED such as the Dunnett method (4) and the Williams method (5,6)
Reprint address: Isao Yoshimura, Department of Management Science, Faculty of Engineering, Science University of Tokyo, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162, Japan, E-mail: [email protected].
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are based o n a family of ti - 1 contrasts. As a consequence of this insight. he considered using other families of contrasts. subsequently comparing them t o lead to the conclusion that each family had its own advantageous dose-response pattern. A similar conclusion was reached by Tamhane et al. (7). In
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