Multiplicity adjustment for multiple endpoints in clinical trials with multiple doses of an active treatment

Frequently, multiple doses of an active treatment and multiple endpoints are simultaneously considered in the designs of clinical trials. For these trials, traditional multiplicity adjustment procedures such as Bonferroni, Hochberg and Hommel procedures can be applied when treating the comparisons of different doses to the control on all endpoints at the same level. However, these approaches will not take into account the possible dose-response relationship on each endpoint, and therefore are less specific and may have lower power. To gain power, in this paper, we consider the problem as a two-dimensional multiplicity problem: one dimension concerns the multiple doses and the other dimension concerns the multiple endpoints. We propose procedures which consider the dose order to form the closure of the procedures and control the family-wise type I error rate in a strong sense. For this two-dimensional problem, numerical examples show that procedures proposed in this paper in general have higher power than the commonly used procedures (e.g. the regular Hochberg procedure) especially for comparing the higher dose to the control.