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Abstract:
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We examine tests for monotonic and umbrella-ordered dose-response for binary data. This is an important issue of interest in many research areas, including clinical trials, preclinical animal studies, toxicology studies, and observational studies. For example, these methods may be of use in the analysis of efficacy parameters (e.g., tumor repose or other dichotomized efficacy or pharmacodynamic endpoints) in randomized, multi-dose phase II trials. We examine two tests for monotonic dose-response for binary data (Dosemeci and Benichou (1998) (DB) and Peddada (2001)), and we propose two new tests for the umbrella-ordered case: a contrast-based test and a quasi-likelihood ratio test. We utilize the E+M method of Lloyd (2008) to make these tests exact, which make the tests more appropriate for small samples. We also examine an exact version of a test by Peddada (2001) for umbrella orders. We compare the power of the different tests, and compare the E+M approach with the maximization approach.
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