Weighted Estimation of Conditional Average Treatment Effect Function With Adjusted Covariate Mismeasurement

Causal inference continues to be a significant mainstay in various fields, and methods have been developed to capture the variability of treatment effects among subpopulations in observational studies. Practically, the validity of standard statistical methods typically depends on the frequently violated assumption that variables are accurately measured. However, distinct studies have demonstrated that naive estimation, which disregards measurement error, leads to seriously biased results, particularly when mismeasured covariates are involved. In this paper, we propose a consistent estimation of the conditional average treatment effect function that accounts for mismeasurement in covariates. The primary task is to construct an appropriate weight function that is unbiased with respect to the unknown correct function and then derive a consistent estimator with mismeasurement adjusted. A numerical study is performed to evaluate the finite sample performance of the methods. Finally, the proposed method is applied to examine the heterogeneity of the effects of smoking cessation on weight gain conditional on age.