Optimizing Propensity Score Trimming via Bootstrapping: Addressing Limited Overlap in Observational Studies

Oregon Convention Center 

The inverse propensity score weighting (IPW) plays a central role in Causal Inference. It gets challenged by the limited overlap under which propensity scores are close to zero or one. Although trimming extreme propensity scores is common in practice, the related asymptotic theory is inadequate, and there is little theoretical guidance on choosing the cut-off value.
Using propensity scores estimated from a parametric model, instead of fixing the cut-off value, we propose estimating the average potential outcome trimmed with all possible cut-off values, which renders a stochastic process parametrized by the trimming cut-off values. We characterize the asymptotic behavior of the estimated stochastic process and show the asymptotic consistency of the bootstrap procedure. We propose using a bootstrap estimator to choose the cut-off value that balances the bias-variance trade-off. With simulation studies, we further provide practical guidance for selecting the optimal cut-off value.

Inverse propensity score weighting

Limited overlap

Non-smoothness

Asymptotic distribution 

IMS