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Propensity score methods are an important tool to help reduce confounding in non-experimental studies and produce more accurate causal effect estimates. Most propensity score methods assume that covariates are measured without error. However, covariates are often measured with error. Recent work has shown that ignoring such error could lead to bias in treatment effect estimates. In this paper, we consider an additional complication: that of differential measurement error across treatment groups, such as can occur if a covariate is measured differently in the treatment and control groups. We propose two flexible Bayesian approaches for handling differential measurement error when estimating average causal effects using propensity score methods. We consider three scenarios: systematic (i.e., a location shift), heteroscedastic (i.e., different variances), and mixed (both systematic and heteroscedastic) measurement errors. We also explore various prior choices (i.e., weakly informative or point mass) on the sensitivity parameters related to the differential measurement error. We present results from simulation studies evaluating the performance of the proposed methods and apply these approaches to an example estimating the effect of neighborhood disadvantage on adolescent drug use disorders.

Bayesian Approach for Addressing Differential Covariate Measurement Error in Propensity Score Methods