Conditional mix-GEE models for longitudinal data with unspecified random-effects distributions

In the longitudinal studies, the mixture generalized estimation equation (mix-GEE) was proposed to improve the efficiency of the fixed-effects estimator for addressing the working correlation structure misspecification. When the subject-specific effect is one of interests, mixed-effects models were widely used to analyze longitudinal data. However, most of the existing approaches assume a normal distribution for the random effects, and this could affect the efficiency of the fixed-effects estimator. In this article, a conditional mixture generalized estimating equation (cmix-GEE) approach based on the advantage of mix-GEE and conditional quadratic inference function (CQIF) method is developed. The advantage of our new approach is that it does not require the normality assumption for random effects and can accommodate the serial correlation between observations within the same cluster. The feature of our proposed approach is that the estimators of the regression parameters are more efficient than CQIF even if the working correlation structure is not correctly specified. In addition, according to the estimates of some mixture proportions, the true working correlation matrix can be identified. We establish the asymptotic results for the fixed-effects parameter estimators. Simulation studies were conducted to evaluate our proposed method.