Improving Causal Estimation by Mixing Samples to Address Weak Overlap in Observational Studies

Sufficient overlap of propensity scores is one of the most critical assumptions in observational studies. In this article, we will cover the severity in statistical inference under such assumption failure with weighting, one of the most dominating causal inference methodologies. Then we propose a simple, yet novel remedy: "mixing" the treated and control groups in the observed dataset. We state that our strategy has three key advantages: (1) Improvement in estimators' accuracy especially in weak overlap, (2) Identical targeting population of treatment effect, (3) High flexibility. We introduce a property of mixed sample that offers a safer inference by implementing onto both traditional and modern weighting methods. We illustrate this with several extensive simulation studies and guide the readers with a real-data analysis for practice.