Single-stage Contrast Families for Identifying the Minimum Effective Dose under Unequal Variances

Under unequal variances on normally distributed responses, the problem of detecting the lowest dose level of treatment for which the mean response is greater than that of Placebo is considered. A general framework of single-stage contrast combined family is constructed, which can be used to remove the influence of unequal variances. Based on this framework, several such families are considered and their percentiles are tabulated using extensive Monte-Carlo techniques. The corresponding singlestage contrast procedures are proposed to identify the minimum effective dose (MinED). Among the four proposed procedures, simulation results reveal that the single-stage Helmert procedure is the best with the highest average power. It works especially well for cases of weak to medium dose response. The single-stage Reverse Helmert procedure performs best for the case of strong dose response although it has the lowest average power. A numerical example in a Phase II clinical trial setting is given to illustrate the applications of the four procedures.