Markov counting models for correlated binary responses

TL;DR

This paper introduces a flexible class of continuous-time Markov counting models for analyzing correlated binary data, providing interpretability, accommodating various cluster sizes, and handling ascertainment bias, with applications in epidemiology and toxicology.

Contribution

It generalizes existing models for correlated outcomes, offers new models, and includes algorithms for maximum likelihood estimation and covariate incorporation.

Findings

Models fit well to epidemiological data

Improved modeling of dependent binary outcomes

Algorithms for efficient parameter estimation

Abstract

We propose a class of continuous-time Markov counting processes for analyzing correlated binary data and establish a correspondence between these models and sums of exchangeable Bernoulli random variables. Our approach generalizes many previous models for correlated outcomes, admits easily interpretable parameterizations, allows different cluster sizes, and incorporates ascertainment bias in a natural way. We demonstrate several new models for dependent outcomes and provide algorithms for computing maximum likelihood estimates. We show how to incorporate cluster-specific covariates in a regression setting and demonstrate improved fits to well-known datasets from familial disease epidemiology and developmental toxicology.