Multivariate mix-GEE models for longitudinal data with multiple outcomes

Multivariate longitudinal studies often involve two or more outcomes of interest mea-sured repeatedly across time for each subject. A main challenge in the analysis of such data is the complex correlation structure. Appropriate modeling of the covariance matrix can provide more efficient parameter estimators. In this paper, multivariate finite mixture models are built for the working correlation matrix of the generalized estimating equations (GEE). A new procedure is proposed to estimate the parameters while ensuring the positive definiteness of the estimated working correlation matrix. Moreover, the consistency and the asymptotic normality of the parameter estimates are derived theoretically. Furthermore, if data are from a Gaussian mixture model, the estimators can be proved to be asymptotically efficient. In addition, the proposed method is illustrated through several simulation studies and a real data example of transportation safety.& COPY; 2023 Elsevier Inc. All rights reserved.