The performance of functional methods for correcting non‐Gaussian measurement error within Poisson regression: corrected excess risk of lung cancer mortality in relation to radon exposure among French uranium miners

Abstract

A broad variety of methods for measurement error (ME) correction have been developed, but these methods have rarely been applied possibly because their ability to correct ME is poorly understood. We carried out a simulation study to assess the performance of three error-correction methods: two variants of regression calibration (the substitution method and the estimation calibration method) and the simulation extrapolation (SIMEX) method. Features of the simulated cohorts were borrowed from the French Uranium Miners' Cohort in which exposure to radon had been documented from 1946 to 1999. In the absence of ME correction, we observed a severe attenuation of the true effect of radon exposure, with a negative relative bias of the order of 60% on the excess relative risk of lung cancer death. In the main scenario considered, that is, when ME characteristics previously determined as most plausible from the French Uranium Miners' Cohort were used both to generate exposure data and to correct for ME at the analysis stage, all three error-correction methods showed a noticeable but partial reduction of the attenuation bias, with a slight advantage for the SIMEX method. However, the performance of the three correction methods highly depended on the accurate determination of the characteristics of ME. In particular, we encountered severe overestimation in some scenarios with the SIMEX method, and we observed lack of correction with the three methods in some other scenarios. For illustration, we also applied and compared the proposed methods on the real data set from the French Uranium Miners' Cohort study.

Simulation–Extrapolation for Bias Correction with Exposure Uncertainty in Radiation Risk Analysis Utilizing Grouped Data

“…SIMEX is known to provide an approximately unbiased estimator when the extrapolating function is appropriately chosen and the classical measurement error is not large. Extrapolation by using a quadratic function is widely used and performs well in terms of bias reduction (Allodji et al, 2012;Carroll et al, 2006;Stefanski and Cook, 1995), although undercorrection of bias could also be associated with the choice of range of ζ (Stefanski and Cook, 1995). In the application to real data, we presented the result based on a linear extrapolating function as well because it might be important to consider uncertainty in the extrapolation step, although of course we should not subjectively base our choice of extrapolation function on the value of the bias-corrected estimate derived.…”

“…Then, simple regression analysis was applied to averaged estimates as a function of ζ j . Often a linear-quadratic function of the form b 0 + b 1 ζ j + b 2 ζ 2 j , where the b 0 , b 1 and b 2 are the coefficients to be estimated by the regression analysis, is used to conduct the extrapolation (Cook and Stefanski, 1994;Allodji et al, 2012), and the parameter value for the case of no measurement error, ζ = −1, is estimated.…”

Bilan de la surveillance épidémiologique des travailleurs du cycle électronucléaire en France

“…Des développements méthodologiques ont permis de prendre en compte la structure complexe des erreurs de mesure sur l'exposition au radon, identifiée dans cette cohorte, afin d'obtenir une estimation affinée de la relation entre cette exposition et le risque de décès par cancer du poumon (Allodji et al, 2012 ;Hoffmann et al, 2017). La persistance de l'association entre radon et cancer du poumon a été confirmée.…”

Measurement Error and Environmental Epidemiology: a Policy Perspective

“…In addition, under each measurement error scenario, β may be estimated with standard models and statistical software (49). In a simulation study based on historical radon exposures in miners, Allodji et al showed that SIMEX compared favorably with other likelihood based approaches to estimate a relative rate parameter (45). The authors used the approach to correct for both Berkson and classical error, which they suggest may have resulted in large biases in previously estimated exposure response parameters in occupational studies of radon exposure (41).…”