Bayesian adjustment for covariate measurement errors: A flexible parametric approach

In most epidemiological investigations, the study units are people, the outcome variable (or the response) is a health‐related event, and the explanatory variables are usually environmental and/or socio‐demographic factors. The fundamental task in such investigations is to quantify the association between the explanatory variables (covariates/exposures) and the outcome variable through a suitable regression model. The accuracy of such quantification depends on how precisely the relevant covariates are measured. In many instances, we cannot measure some of the covariates accurately. Rather, we can measure noisy (mismeasured) versions of them. In statistical terminology, mismeasurement in continuous covariates is known as measurement errors or errors‐in‐variables. Regression analyses based on mismeasured covariates lead to biased inference about the true underlying response–covariate associations. In this paper, we suggest a flexible parametric approach for avoiding this bias when estimating the response–covariate relationship through a logistic regression model. More specifically, we consider the flexible generalized skew‐normal and the flexible generalized skew‐t distributions for modeling the unobserved true exposure. For inference and computational purposes, we use Bayesian Markov chain Monte Carlo techniques. We investigate the performance of the proposed flexible parametric approach in comparison with a common flexible parametric approach through extensive simulation studies. We also compare the proposed method with the competing flexible parametric method on a real‐life data set. Though emphasis is put on the logistic regression model, the proposed method is unified and is applicable to the other generalized linear models, and to other types of non‐linear regression models as well. Copyright © 2009 John Wiley & Sons, Ltd.