In dose-response studies, one of the most important issues is the identification of the minimum
effective dose (MED), where the MED is defined as the lowest dose such that the
mean response is better than the
mean response of a zero-dose control by a clinically significant difference.
Dose-response curves are sometimes monotonic in nature. To find the MED, various authors have proposed step-down test procedures based on contrasts among the
sample means. In this article, we improve upon the method of
Marcus and Peritz (1976, Journal of the Royal
Statistical Society, Series B 38, 157-165) and implement the dose-response method of Hsu and Berger (1999, Journal of the American
Statistical Association 94, 468-482) to construct the lower confidence bound for the difference between the
mean response of any nonzero-dose level and that of the control under the monotonicity assumption to identify the MED. The proposed method is illustrated by numerical examples, and simulation studies on power comparisons are presented.
