Approximate maximum likelihood estimation for logistic regression with covariate measurement error

Abstract

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.

Approximate profile likelihood estimation for Cox regression with covariate measurement error

“…However, the performance of an estimator from RC method in a logistic regression model is good only when odds ratio is 3.0 or less 31 . Cao and Wong 25 obtained the same conclusion that the performance of RC estimator is not good when the regression coefficient is relative large. They also found that an estimator obtained from the second or higher order Taylor expansion for the likelihood function of true covariate given observed covariate has less bias than RC estimator.…”

“…As we point out in Section 1, motivated by the work of Liao et al 29 and Cao and Wong, 25 we propose a new method called APLE for handling multiple covariates measured with highly correlated errors in a Cox model. The key idea of APLE is how to approximate the integral of , where is the full likelihood function of a Cox model.…”

“…They also found that an estimator obtained from the second or higher order Taylor expansion for the likelihood function of true covariate given observed covariate has less bias than RC estimator. Motivated by the work of Liao et al 29 and Cao and Wong, 25 we propose a new method called approximate profile likelihood estimation (APLE) for handling multiple covariates measured with highly correlated errors in a Cox model, which can be regarded as an extension of RC method and also reduce more bias than RC estimator.…”

“…It is well known that measurement errors of some nutrients in the EPIC-InterAct Study are highly correlated. 22,25,26 Agogo et al 27 proposed a two-part regression calibration method on a Cox model for handling covariate measurement error in a single-replicate study design of the EPIC study. But, their measurement error model relied on two strong assumptions: the short-term measurement from the 24-hour dietary recall (24HR) is assumed to be an unbiased measurement of true intake; and errors in the 24HR and the FFQ measurements are uncorrelated.…”

“…Some other references 23,24 also pointed out that biases of estimates caused by measurement error can be in either direction when two or more than two covariates are measured with correlated error terms. It is well known that measurement errors of some nutrients in the EPIC‐InterAct Study are highly correlated 22,25,26 . Agogo et al 27 proposed a two‐part regression calibration method on a Cox model for handling covariate measurement error in a single‐replicate study design of the EPIC study.…”