Finding the Maximum Safe Dose Level for Heteroscedastic Data

Abstract

In this article we extend to the heteroscedastic setting the multiple stepwise test procedures proposed in Tamhane et al. [Tamhane. A. C., Dunnett, C. W., Green, J. W., Wetherington, J. F. (2001). Multiple test procedures for identifying a safe dose. J. Am. Statist. Assoc. 96:835–843] for finding the maximum safe dose. Toxicological data are often heteroscedastic; therefore, the extensions given herein should be highly useful in practice. Simulations are performed to study the Type I familywise error rate and power properties of the procedures. A real data example is given to illustrate the procedures.

Key Words:

• Dose–response
• Multiple comparisons
• Toxicology
• Unequal variances

Mathematics Subject Classification:

• 62J15
• 62P10

Acknowledgments

This research was partially supported by an educational grant from DuPont. We thank Dr. John Green of DuPont Safety, Health and Environmental Excellence Center, Haskell Laboratory for Toxicology and Industrial Medicine for providing the data for the problem and helpful discussions. We also thank two referees for useful suggestions.