Bayesian Analysis of Multivariate Matched Proportions with Sparse Response

Multivariate matched proportions (MMP) data appear in a variety of contexts including post-market surveillance of adverse events in pharmaceuticals, disease classification, and agreement between care providers. It consists of multiple sets of paired binary measurements taken on the same subject. While recent work proposes methods to address the complexities of MMP data, the issue of sparse response, where no or very few “yes” responses are recorded for one or more sets, is unaddressed. The presence of sparse response sets results in the underestimation of variance components, loss of coverage, and lowered power in existing methods. Bayesian methods, which have not previously been considered for MMP data, provide a useful framework when sparse responses are present. In particular, the Bayesian probit model in combination with mean model prior specifications provides an elegant solution to the problem of variance underestimation. We examine a multivariate probit-based approach using hierarchical horseshoe-like priors along with a Bayesian functional principal component analysis (FPCA) to model the latent covariance. We show that our approach performs well on MMP data with sparse responses and outperforms existing methods. In a re-examination of a study on the system of care (SOC) framework for children with mental and behavioral disorders, we are able to provide a more complete picture of the relationships in the data. Our analysis provides additional insights into the functioning on the SOC that a previous univariate analysis missed.