Approximate profile likelihood estimation for Cox regression with covariate measurement error

Abstract

In nutritional epidemiology, measurement error in covariates is a well‐known problem since dietary intakes are usually assessed through self‐reporting. In this article, we consider an additive error model in which error variables are highly correlated, and propose a new method called approximate profile likelihood estimation (APLE) for covariates measured with error in the Cox regression. Asymptotic normality of this estimator is established under regularity conditions, and simulation studies are conducted to examine the finite sample performance of the proposed estimator empirically. Moreover, the popular correction method called regression calibration is shown to be a special case of APLE. We then apply APLE to deal with measurement error in some nutrients of interest in the EPIC‐InterAct Study under a sensitivity analysis framework.

Logistic regression with correlated measurement error and misclassification in covariates

“…41 In addition, more discussion on finding unknown parameters in the additive error model by the moment method can be found in Section 6.2 of Cao and Wong. 16 Applying the method of moments proposed by Cao and Wong 41 on the data from the validation study of the EPIC-InterAct Study, we obtain Σ ^ x x, Σ ^ x w and Σ ^ u u for FFQ measurements of these three nutrients as follows:Covariance matrices Σ ^ u u m a l e and Σ ^ u u .1em f e m a l e show that the correlation coefficients of error variables in FFQ measurements between protein and fat are high (0.741 for males and 0.781 for females), which is consistent with results found in Day et al 17…”

“…These findings are consistent with those of related references. 6,8,9,11,15,16 Table 3. Estimated regression coefficient, standard error, and P-value using different estimation methods under Pt = 0.13, π0 = 0.14, and π1 = 0.23 for male and Pt = 0.11, π0 = 0.14, and π1 = 0.48 for female.…”

“…For example, Ferrari et al 12 applied a linear regression calibration (RC) method 13 to correct the effect of measurement error on the association between fish intake and colorectal cancer; Agogo et al 14 proposed a two-part regression calibration model to investigate the association between intake of vegetable subgroups and all-cause mortality, in which vegetable has excess zero and measurement error. Cao and Wong 15,16 developed an approximate maximum likelihood estimation (AMLE) under a logistic model and an approximate profile likelihood estimation (APLE) under a Cox model when studying the association of type 2 diabetes (T2D) with several error-prone nutrients using the data from the EPIC-InterAct Study. They found that these two methods are extensions of the widely used method RC.…”