Statistical Methods for Selecting Maximum Effective Dose and Evaluating Treatment Effect When Dose-Response is Monotonic

The maximum effective dose (MaxED) is an important quantity for therapeutic drugs. The MaxED for therapeutic drugs is defined as the dose above which no improvement in efficacy is obtained. In this article, we propose two experimental designs and analytic methods (one single-stage design and one two-stage design) to select the MaxED among several fixed doses and to compare the therapeutic effect of the selected MaxED with a control. The selection of MaxED is based on the isotonic regression under the restriction of monotonicity. In the single-stage design, both the selection of the MaxED and assessing its efficacy are carried out at the end of experiment. In the two-stage design, the selection of the MaxED and assessment of its efficacy are carried out at the interim analysis (first stage), the experiment in the second stage is carried out only at the selected MaxED and control if the first-stage test is not significant. Thus, the two-stage design enables selection of the MaxED at an earlier stage and stopping the trial earlier if the treatment effect at MaxED is extreme. Williams' test (1972) is applied to test whether the selected MaxED is significantly different from control for the single-stage design and the first-stage test of the two-stage design. The sample size calculation for each design is provided. Extensive simulations are carried out to illustrate the performances of the proposed methods.