Bayesian Analysis of Sparse Multivariate Matched Proportions
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Multivariate matched proportions (MMP) data appears in a variety of contexts—including post-market surveillance of adverse events in pharmaceuticals, disease classification, and agreement between care providers—and consists of multiple sets of paired binary measurements taken on the same subject. While recent work proposes non-Bayesian methods to address the complexities of MMP data, the issue of sparsity, where no or very few responses are recorded for one or more sets, is unaddressed. However, the presence of sparse sets results in underestimates of variance, loss of coverage, and bias in existing methods. Additionally, Bayesian methods have not previously been considered for MMP data. In this work, we propose a Bayesian marginal probability model for MMP data with robust t-priors that adjusts for sparsity using targeted informative priors on the variance components of sparse sets and half-Cauchy priors on non-sparse sets. In simulation, we demonstrate our method's ability to handle sparsity and show that it outperforms existing methods in terms of coverage and bias, while maintaining comparable power. Finally, we analyze data from a study of care coordination within a System of Care framework and provide additional insights that the original univariate analysis missed.
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