Multivariate conditional mix-GEE method for mixed-effect models with multivariate longitudinal data

Multivariate longitudinal data refers to the repeated measurements of multiple outcomes of interest over time. The covariance matrix of such data holds paramount importance, as neglecting the correlation structure can result in inefficient estimators of the mean parameter. Random effects models are extensively employed in analysis of multivariate longitudinal data, particularly individual-specific effects is one of interests. However, most existing approaches assume a normal distribution for random effects, which can undermine the efficiency of fixed-effects estimator, potentially causing inaccurate inferences. In this article, multivariate conditional mix-GEE model is proposed to analyze longitudinal data. Our new approach offers several advantages: First, it accounts for the correlations among different responses, serial correlation from repeated measurements and heterogeneous variation across individuals. Significantly, it relaxes normality assumptions for random effects. Moreover, a key feature of our proposed method lies in the estimation of mixture proportions, which enables the identification of the complex true covariance structure in multivariate longitudinal data. Additionally, the theoretical derivations establish the consistency and asymptotic normality of the parameter estimators. Simulation studies and a real data example of Health and Retirement Study(HRS) are conducted to evaluate our proposed method.