In the process of developing drugs, proof-of-concept studies can be helpful in determining whether there is any evidence of a dose-response relationship. A global test for this purpose that has gained popularity is a component of the multiple comparisons procedure with modeling techniques (MCP-Mod), which involves the specification of a candidate set of several plausible dose-response models. For each model, a test is performed for significance of an optimally chosen contrast among the sample means. An overall P-value is obtained from the distribution of the maximum of the contrast statistics. This is equivalent to basing the test on the minimum of the P-values arising from these contrast statistics and, hence, can be viewed as a method for combining dependent P-values. We generalize this idea to the use of different statistics for combining the dependent P-values, such as Fisher's combination method or the inverse normal combination method. Simulation studies show that the generalized multiple contrast tests (GMCTs) based on the Fisher and inverse normal methods are generally more powerful than the MCP-Mod procedure based on the minimum of the P-values except for cases where the true dose-response model is, in a sense, near the extremes of the candidate set of dose-response models. The proposed GMCTs can also be used for model selection and dosage selection by employing a closed testing procedure.
Keywords: Fisher's combination method; MCP-Mod; Tippett's combination method; closed testing procedure; inverse normal combination method.
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