Propensity score methods are a popular tool to control for confounding in observational data, but their bias-reduction properties are threatened by covariate measurement error. There are few easy-to-implement methods to correct for such bias. We describe and demonstrate how existing sensitivity analyses for unobserved confounding---propensity score calibration, Vanderweele and Arah's bias formulas, and Rosenbaum's sensitivity analysis---can be adapted to address this problem. In a simulation study, we examined the extent to which these sensitivity analyses can correct for several measurement error structures: classical, systematic differential, and heteroscedastic covariate measurement error. We then apply these approaches to address covariate measurement error in estimating the association between depression and weight gain in a cohort of adults in Baltimore City. We recommend the use of Vanderweele and Arah's bias formulas and propensity score calibration (assuming it is adapted appropriately for the measurement error structure), as both approaches perform well for a variety of propensity score estimators and measurement error structures.
Rudolph, Kara E. and Stuart, Elizabeth A., "Using Sensitivity Analyses for Unobserved Confounding to Address Covariate Measurement Error in Propensity Score Methods" (November 2016). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 283.