Generalized estimating equations with stabilized working correlation structure

Generalized estimating equations (GEE) proposed by Liang and Zeger (1986) yield a consistent estimator for the regression parameter without correctly specifying the correlation structure of the repeatedly measured outcomes. It is well known that the efficiency of regression coefficient estimator increases with correctly specified working correlation and thus unstructured correlation could be a good candidate. However, lack of positive-definiteness of the estimated correlation matrix in unbalanced case causes practitioners to choose independent, autoregressive or exchangeable matrices as working correlation structure. Our goal is to broaden practical choices of working correlation structure to unstructured correlation matrix or any other matrices by proposing a GEE with a stabilized working correlation matrix via linear shrinkage method in which the minimum eigenvalue is forced to be bounded below by a small positive number. We show that the resulting regression estimator of GEE is asymptotically equivalent to that of the original GEE. Simulation studies show that the proposed modification can stabilize the variance of the GEE regression estimator with unstructured working correlation, and improve efficiency over popular choices of working correlation. Two real data examples are presented where the standard error of the regression coefficient estimator can be reduced using the proposed method.