Markov-Dependent Models for Correlated Binary Responses

• Activity Number: 304
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Forrest Crawford*+ and Daniel Zelterman
• Companies: Yale University and Yale University Biostatistics
• Keywords: Correlated outcomes ; binary data ; dependent data ; Markov process ; Poisson

Abstract

Methods for analysis of correlated binary data often suffer from analytic intractability, problems with fitting, restrictive assumptions, or difficulty of interpretation of inferred parameters. In this paper, we establish a correspondence between Markov arrival processes and sums of dependent Bernoulli random variables using a technique called "probabilistic embedding". Our approach generalizes many previous models for correlated outcomes, admits easily interpretable parameterizations, allows different cluster sizes, incorporates ascertainment bias in a natural way, and dramatically simplifies likelihood-based inference. We show how incorporate cluster-specific covariates in a regression setting and apply our method to a dataset of familial chronic obstructive pulmonary disease incidence.