Regression calibration provides a way to obtain unbiased estimators of fixed effects in regression models when one or more predictors are measured with error. Recent development of measurement error methods has focused on models that include interaction terms between measured-with-error predictors, and separately, methods for estimation in models that account for correlated data. In this work, we derive explicit and novel forms of regression calibration estimators and associated asymptotic variances for longitudinal models that include interaction terms, when data from instrumental and unbiased surrogate variables are available but not the actual predictors of interest. The longitudinal data are fit using linear mixed models that contain random intercepts and account for serial correlation and unequally spaced observations. The motivating application involves a longitudinal study of exposure to two pollutants (predictors) - outdoor fine particulate matter and cigarette smoke - and their association in interactive form with levels of a biomarker of inflammation, leukotriene E4 (LTE 4 , outcome) in asthmatic children. Because the exposure concentrations could not be directly observed, we used measurements from a fixed outdoor monitor and urinary cotinine concentrations as instrumental variables, and we used concentrations of fine ambient particulate matter and cigarette smoke measured with error by personal monitors as unbiased surrogate variables. We applied the derived regression calibration methods to estimate coefficients of the unobserved predictors and their interaction, allowing for direct comparison of toxicity of the different pollutants. We used simulations to verify accuracy of inferential methods based on asymptotic theory.

译文

回归校准提供了一种方法,当测量一个或多个预测变量时,可以获得回归模型中固定效应的无偏估计量。测量误差方法的最新发展集中在模型上,该模型包括有误差的测量预测因子之间的交互项,以及分别用于考虑相关数据的模型中的估计方法。在这项工作中,当有工具和无偏替代变量的数据可用但没有实际的预测变量时,我们将得出包含交互项的纵向模型的回归校准估计量和相关的渐近方差的显式和新颖形式。使用线性混合模型拟合纵向数据,该模型包含随机截距,并考虑了序列相关性和不等间距的观测值。激励应用包括纵向研究暴露于两种污染物 (预测因子)-户外细颗粒物和香烟烟雾-以及它们与哮喘儿童炎症生物标志物白三烯E4 (LTE 4,结果) 水平的交互关系。由于无法直接观察到暴露浓度,因此我们使用固定室外监测器的测量值和尿可替宁浓度作为仪器变量,并且我们使用个人监测器错误测量的细环境颗粒物和香烟烟雾的浓度作为无偏替代变量。我们应用派生的回归校准方法来估计未观察到的预测因子及其相互作用的系数,从而可以直接比较不同污染物的毒性。我们使用模拟来验证基于渐近理论的推理方法的准确性。

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