The parallel gatekeeping strategy proposed by Dmitrienko et al. (Statist. Med. 2003; 22:2387-2400) provides a flexible framework for the pursuit of strong control on study wise type I error rate. This paper further explores the application of the weighted Simes parallel gatekeeping procedure recommended by Dmitrienko et al. and proposes some modifications to it to better incorporate the interrelationships of different hypotheses in actual clinical trials and to achieve better power performance. We first propose a simple method to quantitatively control the impact of secondary tests on the testing of primary hypotheses. We then introduce a matched gatekeeping procedure to exemplify how to address special relationships between individual primary and secondary tests following the parallel gatekeeping framework. Our simulation study demonstrates that the enhanced gatekeeping procedures generally result in more powerful tests than the parallel gatekeeping procedure in Dmitrienko et al. whenever applicable.

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.

To minimize potential controversies in determining the need for multiplicity adjustment for multiple hypotheses, we propose a decision rule based multiplicity adjustment strategy in this paper. Resorting to a predefined decision rule of a clinical trial, one may link the different hypotheses by their logical relationships and divide them into different families. A proper multiplicity adjustment procedure can then be developed by maintaining strong control of Type I error rate within each family. The paper applies the proposed multiplicity adjustment strategy to a published raloxifene clinical trial.

A statistical technique useful in the analysis of experiments involving time-response curves is presented. This procedure, known as growth curves analysis, uses the techniques of multivariate linear models to estimate parameters and test hypotheses. Examples of experimental designs to which this procedure can be applied and a worked out example are presented.

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