Pareto-smoothed inverse propensity weighing for causal inference

Causal inference has received great attention across different fields ranging from economics, statistics, biology, medicine, to machine learning. Observational causal inference is challenging because confounding variables may influence both the treatment and outcome. Propensity score based methods are theoretically able to handle this confounding bias problem. However, in practice, propensity score estimation is subject to extreme values, leading to small effective sample size and making the estimators unstable or even misleading. Two strategies– truncation and normalization – are usually adopted to address this problem. In this paper, we propose a new Pareto-smoothing strategy to tackle this problem. Simulations and a real-world example validate the effectiveness.