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We propose a class of continuous-time Markov counting processes for analyzingcorrelated binary data and establish a correspondence between these models andsums of exchangeable Bernoulli random variables. Our approach generalizes manyprevious models for correlated outcomes, admits easily interpretableparameterizations, allows different cluster sizes, and incorporatesascertainment bias in a natural way. We demonstrate several new models fordependent outcomes and provide algorithms for computing maximum likelihoodestimates. We show how to incorporate cluster-specific covariates in aregression setting and demonstrate improved fits to well-known datasets fromfamilial disease epidemiology and developmental toxicology.

Markov counting models for correlated binary responses