A semiparametric method for evaluating causal effects in the presence of error-prone covariates

The goal of most empirical studies in social sciences and medical research is to determine whether an alteration in an intervention or a treatment will cause a change in the desired outcome response. Unlike randomized designs, establishing the causal relationship based on observational studies is a challenging problem because the ceteris paribus condition is violated. When the covariates of interest are measured with errors, evaluating the causal effects becomes a thorny issue. We propose a semiparametric method to establish the causal relationship, which yields a consistent estimator of the average causal effect. The method we proposed results in locally efficient estimators of the covariate effects. We study their theoretical properties and demonstrate their finite sample performance on simulated data. We further apply the proposed method to the Stroke Recovery in Underserved Populations (SRUP) study by the National Institute on Aging.