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Abstract:
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Correlated categorical outcomes are common in biomedical applications such as genetics, ophthalmology, and teratology, where repeated measures are made over time, or clusters of subjects are sampled who share common genetic or environmental exposures. While a large body of work has yielded models for analyzing correlated categorical data, these methods generally rely on asymptotics to justify their inferences. We demonstrate how an exponential family model derived by Gourieroux et al (1984) and Zhao and Prentice (1990) allows us to formulate exact correlated-data analogues to conventional exact tests for two-way contingency tables, paying particular attention to tables of several ordered binomials or of two ordered multinomials. We discuss an efficient algorithm to obtain the exact conditional distribution, and illustrate the tests using examples from actual research.
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