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Multiple hypothesis test is critical in late phase clinical studies when multiple endpoints and/or multiple treatment doses are necessary. Closure principle and partitioning principle are fundamental principles in creating and supporting various forms of multiple testing procedures. The essence of these two principles is the parameter space partitioning. However, when constraints in the sample space instead of in the parameter space exist among testing individual hypotheses such as in the gatekeeping test problem, the direct use of the closure and partitioning principles is usually not efficient.
We proposed a new principle called covering principle that decomposes the whole hypothesis family into a few subfamilies in which all the constraints are removed hence either the closure principle or the partitioning principle can be utilized. We proved that multiple testing procedures constructed using the covering principle strongly control the familywise error rate as long as the multiple tests in each subfamiliy all strongly control the type I error. A brief comparison to the popular graphical approach will be provided for illustration purpose.
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