A detailed evaluation of adjustment methods for multiplicative measurement error in linear regression with...

It is often appropriately assumed, based on both theoretical and empirical considerations, that airborne exposures in the workplace are lognormally distributed, and that a worker's mean exposure over a reference time period is a key predictor of subsequent adverse health effects for that worker. Unfortunately, it is generally impossible to accurately measure a worker's true mean exposure. We begin by introducing a familiar model for exposure that views this true mean, as well as logical surrogates for it, as lognormal random variables. In a more general context, we then consider the linear regression of a continuous health outcome on a lognormal predictor measured with multiplicative error. We discuss several candidate methods of adjusting for the measurement error to obtain consistent estimators of the true regression parameters. These methods include a simple correction of the ordinary least squares estimator based on the surrogate regression, the regression of the outcome on the covariates and on the conditional expectation of the true predictor given the observed surrogate, and a quasi-likelihood approach. By means of a simulation study, we compare the various methods for practical sample sizes and discuss important issues relevant to both estimation and inference. Finally, we illustrate promising adjustment strategies using actual lung function and dust exposure data on workers in the Dutch animal feed industry.