Stepwise Procedures under Unknown Variances for Toxicological Evaluation

Abstract

Toxicological study is of practical importance in modern drug development. Proper statistical methodologies for toxicological evaluation of new developed drugs are undoubtedly necessary. In toxicological studies, it is practically desirable for a method to not declare the safety of a developed drug at a higher dosage prior to the declaration of the safety at lower dosages. Hsu and Berger's stepwise confidence interval method was recently proposed for this purpose. Unfortunately, their procedure necessitates the homogeneity of variances among dosages, which is seldom satisfied in practice. In this article, via the application of the Stein's two-stage sampling method, we propose a stepwise confidence interval procedure for the same task without the homoscedasticity restriction. In addition, our procedure is shown to control its family-wise type I error rate at the pre-chosen nominal level. A simulation study will be conducted to compare our method, Hsu and Berger's stepwise confidence interval method, and a single stage stepwise testing procedure based on Welch's approximation. Our procedure is empirically shown to outperform Hsu and Berger's procedure under heteroscedasticity and perform similarly with Welch's procedure. An example will be used to illustrate our method.