In nutritional epidemiology, dietary intake assessed with a food frequency questionnaire is prone to measurement error. Ignoring the measurement error in covariates causes estimates to be biased and leads to a loss of power. In this paper, we consider an additive error model according to the characteristics of the European Prospective Investigation into Cancer and Nutrition (EPIC)-InterAct Study data, and derive an approximate maximum likelihood estimation (AMLE) for covariates with measurement error under logistic regression. This method can be regarded as an adjusted version of regression calibration and can provide an approximate consistent estimator. Asymptotic normality of this estimator is established under regularity conditions, and simulation studies are conducted to empirically examine the finite sample performance of the proposed method. We apply AMLE to deal with measurement errors in some interested nutrients of the EPIC-InterAct Study under a sensitivity analysis framework.

中文翻译：

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具有协变量测量误差的逻辑回归的近似最大似然估计

在营养流行病学中，使用食物频率问卷评估的膳食摄入量容易出现测量误差。忽略协变量中的测量误差会导致估计有偏差并导致功效损失。在本文中，我们根据欧洲癌症和营养前瞻性调查 (EPIC)-InterAct 研究数据的特点考虑加性误差模型，并在逻辑回归下推导出具有测量误差的协变量的近似最大似然估计 (AMLE)。这种方法可以看作是回归校准的调整版本，可以提供近似一致的估计量。该估计量的渐近正态性是在规律性条件下建立的，并进行了模拟研究，以实证检验所提出方法的有限样本性能。