  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.
