Chain Procedures: A Class of Flexible Closed Testing Procedures With Clinical Trial Applications

We define a class of multiple testing procedures for testing a family of hypotheses based on a prespecified or data-driven testing sequence. These procedures, termed chain procedures, are characterized by independent sets of parameters which govern the initial allocation of the overall α level among the null hypotheses of interest and the process for iteratively reallocating available (or unspent) α among the remaining eligible null hypotheses. As a result, chain procedures are more flexible than popular stepwise procedures such as the Holm or fallback procedures. While presenting the broad class of chain procedures, this article focuses on the development of parametric chain procedures for problems with a known joint distribution of the hypothesis test statistics. Chain procedures are closed testing procedures and thus control the familywise error rate in the strong sense. Further, we discuss optimal selection of parameters of chain procedures based on clinically relevant application-specific criteria. Finally, we illustrate application of the chain testing method using a clinical trial example aimed at the development of a tailored therapy.

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