A common goal in environmental epidemiologic studies is to undertake logistic regression modeling to associate a continuous measure of exposure with binary disease status, adjusting for covariates. A frequent complication is that exposure may only be measurable indirectly, through a collection of subject-specific variables assumed associated with it. Motivated by a specific study to investigate the association between lung function and exposure to metal working fluids, we focus on a multiplicative-lognormal structural measurement error scenario and approaches to address it when external validation data are available. Conceptually, we emphasize the case in which true untransformed exposure is of interest in modeling disease status, but measurement error is additive on the log scale and thus multiplicative on the raw scale. Methodologically, we favor a pseudo-likelihood (PL) approach that exhibits fewer computational problems than direct full maximum likelihood (ML) yet maintains consistency under the assumed models without necessitating small exposure effects and/or small measurement error assumptions. Such assumptions are required by computationally convenient alternative methods like regression calibration (RC) and ML based on probit approximations. We summarize simulations demonstrating considerable potential for bias in the latter two approaches, while supporting the use of PL across a variety of scenarios. We also provide accessible strategies for obtaining adjusted standard errors to accompany RC and PL estimates.

中文翻译：

---

使用外部验证数据对日志暴露进行建模的逻辑回归的近似和伪似然分析。

环境流行病学研究的一个共同目标是进行逻辑回归模型，以将连续暴露测量与二元疾病状态相关联，并针对协变量进行调整。一个常见的并发症是，暴露可能只能通过一系列假设与之相关的特定主题变量来间接测量。受一项调查肺功能与接触金属加工液之间关联的特定研究的启发，我们专注于乘法对数正态结构测量误差场景以及在外部验证数据可用时解决该问题的方法。从概念上讲，我们强调真实未转化暴露对疾病状态建模感兴趣的情况，但测量误差在对数尺度上是相加的，因此在原始尺度上是相乘的。在方法论上，我们赞成伪似然 (PL) 方法，它比直接完全最大似然 (ML) 表现出更少的计算问题，但在假设模型下保持一致性，而无需小暴露效应和/或小测量误差假设。诸如回归校准 (RC) 和基于概率近似的 ML 等计算方便的替代方法需要此类假设。我们总结了在后两种方法中显示出相当大的偏差潜力的模拟，同时支持在各种场景中使用 PL。我们还提供了可获取的策略来获得调整后的标准误差以伴随 RC 和 PL 估计。