Inverse probability weighting estimation under ultrahigh-dimensional error-prone covariates and misclassified treatments

Estimating the average treatment effect (ATE) is one of the fundamental problems in causal inference, as it quantifies the causal impact of a treatment on an outcome of interest. A widely used approach for ATE estimation is the inverse probability weighting method based on propensity scores. However, in practice, datasets often exhibit ultrahigh-dimensional covariates and measurement errors, which can lead to biased or unreliable ATE estimators if not properly addressed. In this paper, we focus on a challenging setting where both covariates and treatments may be measured with error, and the potential outcomes may exhibit nonlinear dependence on the covariates. To tackle these challenges and obtain a more accurate estimator of the ATE, we propose a novel method named FATE, which integrates feature screening, adaptive lasso, treatment adjustment, and error correction for covariates. The proposed feature screening procedure is based on measurement error adjusted data and is designed to accommodate a wide variety of outcome distributions. Furthermore, under appropriate corrections for both treatment misclassification and covariates measurement error, we construct a consistent estimator of the propensity score that accounts for possible collinearity. This leads to a reliable ATE estimator. Theoretical guarantees, including consistency and asymptotic properties, are established. Extensive numerical studies demonstrate that the proposed FATE method performs well and consistently outperforms several competing approaches.