Abstract
In this study, we propose a multiple comparison procedure for detecting sequentially a lowest dose having interaction based on the obtained observations by the sequential dose response experiment of cell-wise in the two-way table. For realizing our procedure, we apply group sequential procedure to our procedure that tests sequentially the null hypotheses of no interaction based on tetrad differences. If we can first detect a dose having interaction at an early stage in the sequential test, it is possible to terminate the procedure with a few observations up to the stage. Thus, the procedure is useful from an economical point of view when high costs are involved for obtaining the observations. In the procedure, we induce an integral formula to determine the repeated confidence boundaries for satisfying a predefined type I familywise error rate. Furthermore, we show how to decide the required sample size at each cell with guaranteeing the power of the test in the procedure. In the simulation studies, we compare 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.
