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Abstract:
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In medical studies, prior knowledge can often be used to constrain inference to clinically or biologically relevant alternative hypotheses, leading to substantial power gains relative to an unconstrained approach. For example, in cancer pharmacogenomic studies, researchers may be interested in markers for which the gene effect is present only when exposed to drug. Often the space of interesting alternatives can be described by the boundary or closure of a double cone. While single cone alternatives have been well-studied, previous studies of double cone alternatives have been limited to empirical investigations of the type I error. Here we present a detailed treatment of inference for double cone alternatives. We derive explicit mathematical formulas for calculating type I and type II error rates and illustrate how these rates relate to geometric features of the acceptance region. We provide numerical algorithms for approximating the error rates and evaluate their performance through simulations studies.
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