title: Markov counting models for correlated binary responses.
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.
authors: Yale School of Public Health, Biostatistics, PO Box 208034, New Haven, CT 06510, USA forrest.crawford@yale.edu.
authors: Forrest W
authors: FW
authors: Crawford
authors: Yale School of Public Health, Biostatistics, PO Box 208034, New Haven, CT 06510, USA.
authors: Daniel
authors: D
authors: Zelterman
mesh_terms: D000465:Algorithms; D016010:Binomial Distribution; D056808:Biostatistics; D001938:Brazil / Q000453:epidemiology; D002648:Child; D016000:Cluster Analysis; D030342:Genetic Diseases, Inborn / Q000453:epidemiology; D006801:Humans; D054990:Idiopathic Pulmonary Fibrosis / Q000453:epidemiology; D016013:Likelihood Functions; D008390:Markov Chains; D015233:Models, Statistical; D009026:Mortality; D009369:Neoplasms / Q000453:epidemiology / Q000235:genetics; D029424:Pulmonary Disease, Chronic Obstructive / Q000453:epidemiology; D018600:Teratology / Q000706:statistics & numerical data
keywords: Bernoulli trials; Developmental toxicity; Familial disease; Markov process; Teratology