A boundary‐optimized rejection region test for the two‐sample binomial problem |
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| Authors: | Erin E. Gabriel Martha Nason Michael P. Fay Dean A. Follmann |
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| Affiliation: | 1. Unit of Biostatistics at the Institute of Environmental Medicine, Karolinska Institutet, Stockholm, Sweden;2. Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, Rockville, MD, USA |
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| Abstract: | Testing the equality of 2 proportions for a control group versus a treatment group is a well‐researched statistical problem. In some settings, there may be strong historical data that allow one to reliably expect that the control proportion is one, or nearly so. While one‐sample tests or comparisons to historical controls could be used, neither can rigorously control the type I error rate in the event the true control rate changes. In this work, we propose an unconditional exact test that exploits the historical information while controlling the type I error rate. We sequentially construct a rejection region by first maximizing the rejection region in the space where all controls have an event, subject to the constraint that our type I error rate does not exceed α for any true event rate; then with any remaining α we maximize the additional rejection region in the space where one control avoids the event, and so on. When the true control event rate is one, our test is the most powerful nonrandomized test for all points in the alternative space. When the true control event rate is nearly one, we demonstrate that our test has equal or higher mean power, averaging over the alternative space, than a variety of well‐known tests. For the comparison of 4 controls and 4 treated subjects, our proposed test has higher power than all comparator tests. We demonstrate the properties of our proposed test by simulation and use our method to design a malaria vaccine trial. |
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| Keywords: | animal models challenge trials Fisher's exact most powerful test unconditional exact test |
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