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Abstract:
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In many dose finding studies there are hierarchically ordered endpoints and a given dose is compared with a control on any endpoint conditional on the tests on the higher-ordered endpoints being significant (serial gatekeeping). It is required to control the familywise error rate at a designated level taking into account multiplicity of tests. We give a closed procedure (Marcus, Pertiz and Gabriel 1976) for this problem by applying the general and flexible tree-structured testing approach to gatekeeping problems developed in Dmitrienko, Wiens, Tamhane and Wang (2006). The proposed procedure uses weighted Bonferroni tests for testing intersection hypotheses. For an easier implementation of this closed procedure, we give a stepwise procedure that uses penalized Bonferroni tests for all endpoints except the last, for which it uses a penalized Holm's test.
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