Transition Models for Multivariate Longitudinal Binary Data

• Published in: Journal of the American Statistical Association Vol. 102; no. 477; pp. 211 - 223
• Main Authors: Zeng, Leilei, Cook, Richard J
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.03.2007; American Statistical Association; Taylor & Francis Ltd
• Subjects: Analytical estimating; Applications; Binary data; Bleeding; Data analysis; Estimating function; Estimating techniques; Estimation bias; Estimators; Exact sciences and technology; General topics; Longitudinal data; Longitudinal studies; Markov analysis; Markov model; Markov models; Markovian processes; Mathematical methods; Mathematical models; Mathematics; Modeling; Multivariate analysis; Multivariate process; Parametric models; Probability; Probability and statistics; Probability theory and stochastic processes; Regression analysis; Sciences and techniques of general use; Statistical analysis; Statistical methods; Statistics; Stochastic models; Stochastic processes; Theory and Methods; Transition probabilities; Transition probability; Multivariate process; Binary data; Multivariate distribution; Statistical association; Statistical estimation; Probability distribution; Markov model; Longitudinal data; Multivariate analysis; Covariate; Stochastic process; Statistical method; Statistical regression; Regression coefficient; Logistic regression; Categorical data; Estimating function; Marginal distribution; Transition probability; Application
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214506000000889

In many settings with longitudinal binary data, interest lies in modeling covariate effects on transition probabilities of an underlying stochastic process. When data from two or more processes are available, the scientific focus may be on the degree to which changes in one process are associated with changes in another process. Analysis based on independent Markov models permits separate examination of covariate effects on the transition probabilities for each process, but no insight into between-process associations is obtained. We propose a method of estimation and inference based on joint transitional models for multivariate longitudinal binary data using GEE2 or alternating logistic regression that allows modeling of covariate effects on marginal transition probabilities as well as the association parameters. Consistent estimates of regression coefficients and association parameters are obtained, and efficiency gains for the parameters governing the marginal transition probabilities are realized when the association between processes is strong. Extensions to deal with multivariate longitudinal categorical data are indicated.