Modeling association in longitudinal binary outcomes: a brief review

In order to better understand aging, longitudinal studies are run in which participants are evaluated repeatedly and selected end-points (e.g., score on a cognitive screen, falls, occurrence/reoccurrence of a condition) are examined. The objective of the present paper is primarily to describe the methods available that take into account correlation between binary outcomes, and in particular to model the association of binary outcomes after controlling for covariates by using an implementation of generalized estimating equations (GEE) called 'alternating logistic regression' (ALR). In GEE, association within longitudinal outcomes is accounted for but not estimated. Alternating logistic regression, however, basically enables simultaneous estimation of pair-wise odds ratios of outcomes within a cluster, while accounting for the dependence of the outcome on covariates. A sub-sample (n=2458) from a community-based sample of Duke Established Populations for Epidemiologic Studies of the Elderly is used. In the example used here, logistic regression using GEE and ALR is used to model binary outcomes at three time points (baseline, three and six years later) and to control for covariates in a representative community-based sample 65 years of age and older (n=2458). The outcomes indicate any problem versus no problem on a five-item activities of daily living (ADL) scale in a community sample. The ALR model, however, provides insight into decline in ADL from baseline to each of the time-points whereas GEE does not. In both controlled and uncontrolled analyses, decline in ADL over three and six-year intervals (baseline to three years later, baseline to six years and three years post-baseline to six years post-baseline) is significant.