Doubly robust outlier resistant inference on causal treatment effect

Outliers can severely distort causal effect estimation in observational studies, yet this issue has received limited attention in the literature. Their influence is especially pronounced in small sample sizes, where detecting and removing outliers becomes increasingly difficult. Therefore, it is essential to estimate treatment effects robustly without excluding these influential data points. To address this, we propose a doubly robust point estimator for the average treatment effect under a contaminated model that includes outliers. Robustness in outcome regression is achieved through a robust estimating equation, while covariate balancing propensity scores (CBPS) ensure resilience in propensity score modeling. To prevent model overfitting due to the inclusion of numerous parameters, we incorporate variable selection. All these components are unified under a penalized empirical likelihood framework. For confidence interval estimation, most existing approaches rely on asymptotic properties, which may be unreliable in finite samples. We derive an optimal finite-sample confidence interval for the average treatment effect using our proposed estimating equation, ensuring that the interval bounds remain unaffected by outliers. Through simulations and a real-world application involving hypertension data with outliers, we demonstrate that our method consistently outperforms existing approaches in both accuracy and robustness.