Weighted causal inference methods with mismeasured covariates and misclassified outcomes.

Inverse probability weighting (IPW) estimation has been widely used in causal inference. Its validity relies on the important condition that the variables are precisely measured. This condition, however, is often violated, which distorts the IPW method and thus yields biased results. In this paper, we study the IPW estimation of average treatment effects for settings with mismeasured covariates and misclassified outcomes. We develop estimation methods to correct for measurement error and misclassification effects simultaneously. Our discussion covers a broad scope of treatment models, including typically assumed logistic regression models and general treatment assignment mechanisms. Satisfactory performance of the proposed methods is demonstrated by extensive numerical studies.