On the potential of measurement error to induce differential bias on odds ratio estimates:: an example from radon epidemiology

It is well established that odds ratios estimated by logistic regression are subject to bias if exposure is measured with error. The dependence of this bias on exposure parameter values, particularly for multiplicative measurement error, and its implications in epidemiology are not, however, as fully acknowledged. We have been motivated by a German West case-control study on lung cancer and residential radon, where restriction to a subgroup exhibiting larger mean and variance of exposure than the entire group has shown higher odds ratio estimates as compared to the full analysis. By means of correction formulae and simulations, we show that bias from additive classical type error depends on the exposure variance, not on the exposure mean, and that bias from multiplicative classical type error depends on the geometric standard deviation (in other words on the coefficient of variation of exposure), but not on the geometric mean of exposure. Bias from additive or multiplicative Berkson type error is independent of exposure distribution parameters. This indicates that there is a potential of differential bias between groups where these parameters vary. Such groups are commonly compared in epidemiology: for example when the results of subgroup analyses are contrasted or meta-analyses are performed. For the German West radon study, we show that the difference of measurement error bias between the subgroup and the entire group exhibits the same direction but not the same dimension as the observed results. Regarding meta-analysis of five European radon studies, we find that a study such as this German study will necessarily result in smaller odds ratio estimates than other studies due to the smaller exposure variance and coefficient of variation of exposure. Therefore, disregard of measurement error can not only lead to biased estimates, but also to inconsistent results and wrongly concluded effect differences between groups. Copyright (C) 2002 John Wiley Sons, Ltd.