Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, USA.
Wilmer Eye Institute, Johns Hopkins School of Medicine, Baltiomre, Maryland, USA.
Ophthalmic Epidemiol. 2023 Jun;30(3):307-316. doi: 10.1080/09286586.2022.2098984. Epub 2022 Jul 15.
Both linear regression with generalized estimating equations (GEE) and linear mixed-effects models (LMEM) can be used to estimate the marginal association of an exposure with clustered continuous outcomes. This study compares their performance for bivariate continuous outcomes which are common in eye studies.
Parametric and non-parametric simulations were used to compare the GEE models including independent, exchangeable, and unstructured working correlation structures and LMEM including random intercept only and random intercept and slope models in R and SAS. Data generation referenced the data distributions from a real-world study for estimating ocular structure-visual function relationships in patients with retinitis pigmentosa.
From both parametric and non-parametric simulations, comparing the random intercept LMEM and GEE exchangeable model, bias was similar; coverage probability of the 95% confidence interval (CI) from the random intercept LMEM was often closer to 95%, especially when the sample size was small; the power for testing the association of the exposure was higher from the GEE exchangeable model, but its type-I error rate might be inflated especially when the sample size was small. The type-I error rate from the random intercept LMEM was closer to 0.05, but it might be under 0.05 and coverage probability might be over 95%. The GEE independent model performed worst and the LMEM with both random intercept and slope might not converge.
To estimate marginal exposure-outcome association with bivariate continuous outcomes, the random intercept LMEM may be preferred. It has the best coverage probability of 95% CI and is the only model with correct type-I error rates in this study. However, it may have low power and overly wide CI in studies with small sample size or low inter-eye correlation.
线性回归的广义估计方程（GEE）和线性混合效应模型（LMEM）都可用于估计暴露与聚类连续结果的边缘关联。本研究比较了它们在眼科研究中常见的二元连续结果中的表现。
使用参数和非参数模拟比较 GEE 模型，包括独立、可交换和非结构化工作相关结构，以及包括仅随机截距和随机截距和斜率模型的 LMEM，在 R 和 SAS 中进行。数据生成参考了来自现实世界研究的数据分布，用于估计色素性视网膜炎患者的眼部结构-视觉功能关系。
来自参数和非参数模拟，比较随机截距 LMEM 和 GEE 可交换模型，偏差相似；随机截距 LMEM 的 95%置信区间（CI）覆盖率通常更接近 95%，尤其是当样本量较小时；GEE 可交换模型检验暴露关联的效能更高，但当样本量较小时，其Ⅰ型错误率可能会膨胀。随机截距 LMEM 的Ⅰ型错误率更接近 0.05，但可能低于 0.05，覆盖率可能超过 95%。GEE 独立模型表现最差，同时具有随机截距和斜率的 LMEM 可能无法收敛。
要估计二元连续结果的边缘暴露-结果关联，随机截距 LMEM 可能是首选。在本研究中，它具有最佳的 95%CI 覆盖率，是唯一具有正确Ⅰ型错误率的模型。然而，在样本量较小或双眼间相关性较低的研究中，它可能具有较低的效能和过度宽的 CI。
