A SEQUENTIAL MULTIPLE COMPARISON PROCEDURE FOR DETECTING A LOWEST DOSE HAVING INTERACTION IN A DOSE-RESPONSE TEST

Abstract

In this study, we propose a multiple comparison procedure for detecting sequentially a lowest dose level having interaction based on two dose sample means on two treatments with increasing dose levels in a dose-response test. We apply a group sequential procedure in order to realize our method that tests sequentially the null hypotheses of no interaction based on tetrad differences. If we can first detect a dose level having interaction at an early stage in the sequential test, since we can terminate the procedure with just the few observations up to that stage, the procedure is useful from an economical point of view. In the procedure, we present an integral formula to determine the repeated confidence boundaries for satisfying a predefined type I familywise error rate. Furthermore, we show how to decide a required sample size in each cell so as to guarantee the power of the test. In the simulation studies, we evaluate the superiority among the procedures based on three α spending functions in terms of the power of the test and the required sample size for various configurations of population means.