Generalized Estimating Equations for Hearing Loss Data with Specified Correlation Structures

Due to the nature of pure-tone audiometry test, hearing loss data often has a complicated correlation structure. Generalized estimating equation (GEE) is commonly used to investigate the association between exposures and hearing loss, because it is robust to misspecification of the correlation matrix. However, this robustness typically entails a moderate loss of estimation efficiency in finite samples. This paper proposes to model the correlation coefficients and use second-order generalized estimating equations to estimate the correlation parameters. In simulation studies, we assessed the finite sample performance of our proposed method and compared it with other methods, such as GEE with independent, exchangeable and unstructured correlation structures. Our method achieves an efficiency gain which is larger for the coefficients of the covariates corresponding to the within-cluster variation (e.g., ear-level covariates) than the coefficients of cluster-level covariates. The efficiency gain is also more pronounced when the within-cluster correlations are moderate to strong, or when comparing to GEE with an unstructured correlation structure. As a real-world example, we applied the proposed method to data from the Audiology Assessment Arm of the Conservation of Hearing Study, and studied the association between a dietary adherence score and hearing loss.