Testing a sequence of pre-ordered hypotheses to decide which of these can be rejected or accepted while controlling the familywise error rate (FWER) is of importance in many scientific studies such as clinical trials. In this paper, we first introduce a generalized fixed sequence procedure whose critical values are defined by using a function of the numbers of rejections and acceptances, and which allows follow-up hypotheses to be tested even if some earlier hypotheses are not rejected. We then construct the least favorable configuration for this generalized fixed sequence procedure and present a sufficient condition for the FWER control under arbitrary dependence. Based on the condition, we develop three new generalized fixed sequence procedures controlling the FWER under arbitrary dependence. We also prove that each generalized fixed sequence procedure can be described as a specific closed testing procedure. Through simulation studies and a clinical trial example, we compare the power performance of these proposed procedures with those of the existing FWER controlling procedures. Finally, when the pairwise joint distributions of the true null p-values are known, we further improve these procedures by incorporating pairwise correlation information while maintaining the control of the FWER. Copyright © 2015 John Wiley & Sons, Ltd.

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There are challenges in designing pediatric trials arising from special ethical issues and the relatively small accessible patient population. The application of conventional phase 3 trial designs to pediatrics is not realistic in some therapeutic areas. To address this issue, we propose various approaches for designing pediatric trials that incorporate data available from adult studies using James-Stein shrinkage estimation, empirical shrinkage estimation, and Bayesian methods. We also apply the concept of consistency used in multi-regional trials to pediatric trials. The performance of these methods is assessed through representative scenarios and an example using actual Type 2 diabetes mellitus (T2DM) trials.