An imputation-based solution to using mismeasured covariates in propensity score analysis

Although covariate measurement error is likely the norm rather than the exception, methods for handling covariate measurement error in propensity score methods have not been widely investigated. We consider a multiple imputation-based approach that uses an external calibration sample with information on the true and mismeasured covariates, multiple imputation for external calibration, to correct for the measurement error, and investigate its performance using simulation studies. As expected, using the covariate measured with error leads to bias in the treatment effect estimate. In contrast, the multiple imputation for external calibration method can eliminate almost all the bias. We confirm that the outcome must be used in the imputation process to obtain good results, a finding related to the idea of congenial imputation and analysis in the broader multiple imputation literature. We illustrate the multiple imputation for external calibration approach using a motivating example estimating the effects of living in a disadvantaged neighborhood on mental health and substance use outcomes among adolescents. These results show that estimating the propensity score using covariates measured with error leads to biased estimates of treatment effects, but when a calibration data set is available, multiple imputation for external calibration can be used to help correct for such bias.