Multivariate methods for binary longitudinal data with heterogeneous correlation over time

Clustered binary data occur frequently in biostatistical work. One particular application is in binary longitudinal data, where several visits are available for the same individual. Several approaches have been proposed for the analysis of clustered binary data. In Rosner, a polychotomous logistic regression model was proposed which is a generalization of the beta-binomial distribution and allows for person- and visit-specific covariates, while controlling for clustering effects. One assumption of this model is that all pairs of visits within an individual are equally correlated, which may be inappropriate if several visits are available over a long follow-up period. In this paper, this approach is extended to allow for heterogeneous correlation over time. The total time period is divided into subintervals and a beta-binomial mixture model is introduced to estimate odds ratios relating outcomes for pairs of visits both within a subinterval as well as in different subintervals. To include covariates, an extension of the polychotomous logistic regression model is proposed, which allows one to estimate effects of person-, subinterval-, and visit-specific covariates, while controlling for clustering using the beta-binomial mixture model. This model is applied to the analysis of respiratory symptom data in children collected over a 14-year period in East Boston, MA, in relation to maternal and child smoking, where the unit is the child and symptom history is divided into early-adolescent and late-adolescent symptom experience.