Multivariate longitudinal models for complex change processes

Longitudinal studies offer us an opportunity to develop detailed descriptions of the process of growth and development or of the course of progression of chronic diseases. Most longitudinal analyses focus on characterizing change over time in a single outcome variable and identifying predictors of growth or decline. Both growth and degenerative diseases, however, are complex processes with multiple markers of change, so that it may be important to model more than one outcome measure and to understand their relationship over time. We consider random effects models for the association between the trajectories of two outcomes over time, and then compare their properties to approaches based on separate ordinary least-squares estimates of change. We then illustrate with an example from the Religious Orders Study, a longitudinal cohort study of more than 900 members of Catholic religious orders who have had up to eight annual clinical examinations.