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.

翻译：由于纯音听力测试的特性，听力损失数据通常具有复杂的相关结构。广义估计方程（GEE）常用于研究暴露与听力损失之间的关联，因其对相关矩阵的误设具有稳健性。然而，这种稳健性通常在有限样本中导致中等程度的估计效率损失。本文提出对相关系数进行建模，并使用二阶广义估计方程来估计相关参数。在模拟研究中，我们评估了所提方法的有限样本性能，并将其与其他方法（如采用独立、可交换及无结构化相关结构的GEE）进行比较。我们的方法实现了效率提升，其中对应组内变异（如耳级协变量）的协变量系数的效率提升大于组级协变量的系数。当组内相关性为中等至较强时，或与采用无结构化相关结构的GEE相比时，效率提升更为显著。作为实际应用示例，我们将所提方法应用于听觉研究保护项目的听力评估分支数据，并研究了饮食依从性评分与听力损失之间的关联。