Effect of exposure misclassification on the mean squared error of population attributable risk and prevented fraction estimates

Previous work has considered the effect of exposure misclassification on the bias of population attributable risk (AR) estimates, but little is known about the corresponding effects on their precision or mean squared error (MSE). This paper considers AR estimation in typical scenarios for case-control and cohort studies. The analogous index used when exposure reduces the risk--the prevented fraction (PF)--is also investigated. It is shown, through both theoretical and simulation results, that even with quite modest levels of exposure misclassification, the MSE can increase substantially, relative to the variance of AR estimated without measurement error. When exposure assessment is perfectly sensitive, there is no bias in AR but lack of measurement specificity can still cause a substantial loss of precision. In a few cases, the AR or PF with misclassified exposure can actually have smaller MSE; these exceptional cases arise when sensitivity is poor and the bias in AR or PF is relatively large. We conclude that while bias can be reduced by defining exposure on a highly sensitive basis, one must also consider the deleterious effect on precision by doing so. Loss of precision in the AR and PF estimates can be safely ignored only when the exposure measure is very accurate.