A Likelihood Paradigm for Clinical Trials
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Given the prominent role of clinical trials in evidence-based medicine, proper interpretation of clinical data as statistical evidence is not just a philosophical question but also has important practical implications. It has been recognized for some time that the likelihood paradigm, founded on the law of likelihood, provides an appropriate framework for representing and interpreting statistical evidence. As stated, the law of likelihood is limited to simple hypotheses and not applicable to composite hypotheses, despite the tremendous relevance of composite hypotheses in clinical trials and other applications. This article proposes a generalization of the law of likelihood for composite hypotheses, which helps expand the likelihood paradigm to cover clinical trials. The generalized law is developed in an axiomatic fashion, illustrated with real examples, and examined in an asymptotic analysis. Its implications are explored by making comparisons with common frequentist concepts, by drawing connections with Wald-type procedures, and by noting its utility for interpreting hypothesis tests as reduced data.
KeywordsApproximate likelihood Law of likelihood Likelihood ratio Statistical evidence Support interval Support set
AMS Classification62A01 62P10
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