Introduction

Bayesian correction for covariate measurement error: A frequentist evaluation and comparison with regression calibration

“…Alternatively, it is possible to construct sandwich variance estimators by stacking the estimating equations used in the two stages. 1 One drawback with this approach is that the resulting Wald type symmetric confidence intervals do not reflect the asymmetric sampling distribution of the RC estimator, which may lead to confidence interval coverage which deviates from the nominal level.…”

“…ML methods enjoy many favourable frequentist properties – assuming correct model specification the ML estimator is consistent, asymptotically normal, and efficient. In the specific context of adjustment for covariate measurement error, a drawback of ML is that the likelihood function typically involves intractable integrals, 1 such that numerical methods such as numerical integration are required in order to obtain estimates. The same obstacle is overcome in the Bayesian approach through the use of MCMC methods.…”

“…It is well known that error in covariates results in biased estimates of true covariate(s)-outcome associations and in a loss of power to detect such associations. 1 In this paper, we focus on correcting for the effects of measurement error in continuous covariates in three models which are commonly used in epidemiological analysis; linear regression models for continuous outcomes, logistic regression models for binary outcomes, and Cox proportional hazards models for survival or time to event outcomes.…”

“…Many methods have been described for correcting for the effects of measurement error in regression models. 1 The most widely used correction method is regression calibration (RC), which is popular due to its simplicity and applicability in different types of regression models. In RC, the true exposure, which is unobserved in the main study sample, is replaced when fitting the outcome regression model by the expected value of the true exposure, conditional on the measured exposure and the other error-free covariates for each individual.…”

“…Despite excellent book length treatments of covariate measurement error methods, 1 including one specifically focusing on Bayesian methods, 10 in our view it nevertheless continues to be underused by the epidemiological and clinical research communities. This may be for a number of reasons, but principal among them may be the apparent need to move from a frequentist to a Bayesian inferential approach, and the fact that standard statistical packages have (with exceptions) not enabled such Bayesian models to be fitted.…”