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. Researchers have found that violation of the assumption can result in substantial bias or increase in variability of estimated treatment effects. To overcome this, we introduce a simple yet novel strategy, mixing, generating a new treated group by mixing the original treated and control units to estimate causal effects. Our strategy has three key advantages: (1) Improvement in estimators' accuracy, regardless of level of positivity, (2) Identical targeting population of treatment effects, and (3) High adaptability for various estimation methods. The mixed sample incorporates propensity scores that are robust to weak overlap and is shown to be useful in balancing covariates with both traditional and modern weighting methods. The estimation of propensity score weighting is done within the M-estimation theory. Implementation into a broader class of weighting estimators is derived through a variation of a resampling algorithm. We illustrate this with several extensive simulation studies and guide the reader with a real-data analysis for practice.