A determinant-based criterion for working correlation structure selection in generalized estimating equations

In generalized estimating equations (GEE), the correlation between the repeated observations on a subject is specified with a working correlation matrix. Correct specification of the working correlation structure ensures efficient estimators of the regression coefficients. Among the criteria used, in practice, for selecting working correlation structure, Rotnitzky-Jewell, Quasi Information Criterion (QIC) and Correlation Information Criterion (CIC) are based on the fact that if the assumed working correlation structure is correct then the model-based (naive) and the sandwich (robust) covariance estimators of the regression coefficient estimators should be close to each other. The sandwich covariance estimator, used in defining the Rotnitzky-Jewell, QIC and CIC criteria, is biased downward and has a larger variability than the corresponding model-based covariance estimator. Motivated by this fact, a new criterion is proposed in this paper based on the bias-corrected sandwich covariance estimator for selecting an appropriate working correlation structure in GEE. A comparison of the proposed and the competing criteria is shown using simulation studies with correlated binary responses. The results revealed that the proposed criterion generally performs better than the competing criteria. An example of selecting the appropriate working correlation structure has also been shown using the data from Madras Schizophrenia Study.