Nonparametric Equivalents of Contrasts for Identifying the Minimum Effective Dose

In a one-way layout with general dose-response relationship, the inference about the minimum effective dose (MED) is generally made by using a variety of contrasts of sample means (Ruberg 1989; Tamhane, Hochberg, and Dunnett 1996). This article examines the Mann-Whitney versions of three families of contrasts, and proposes two new nonparametric step-down procedures for identifying the MED. The associated p-value of the estimated MED is then computed. An example is given to illustrate the proposed procedures. The results of a simulation study comparing the relative error rate and power performances for various nonparametric step-down tests are presented.