Propensity score-based estimators with multiple error-prone covariates

Propensity score methods are an important tool to help reduce confounding in non-experimental studies. Most propensity score methods assume that covariates are measured without error. However, covariates are often measured with error, which leads to biased causal effect estimates if the true underlying covariates are the actual confounders. Although some studies have investigated the impact of a single mismeasured covariate on estimating a causal effect and proposed methods for handling the measurement error, almost no work exists investigating the case where multiple covariates are mismeasured. In this paper, we examine the consequences of multiple error-prone covariates when estimating causal effects using propensity score-based estimators via extensive simulation studies and real data analyses. We find that causal effect estimates are less biased when the propensity score model includes mismeasured covariates whose true underlying values are strongly correlated with each other. However, when the measurement \emph{errors} are correlated with each other, additional bias is introduced. In addition, it is beneficial to include correctly measured auxiliary variables that are correlated with confounders whose true underlying values are mismeasured in the propensity score model.