Seminar by Dr. Andrew Yiu from Department of Statistics, University of Oxford

Positivity violations constitute one of the two primary challenges of causal inference with observational data, alongside unmeasured confounding. The positivity assumption states that every unit has a strictly positive probability of receiving any treatment on each level of the covariate adjustment set. If positivity is violated, there are regions of the covariate space where we have no outcome information under one of the treatments. In the most serious scenario, our target causal effect is unidentifiable from the data, and we are left with the choice of either changing our target estimand or resorting to the high-risk strategy of extrapolation.

After reviewing some of the existing approaches for handling positivity violations, including the popular method of “trimming”, we address their key limitations by introducing a new method called “overlap approximation”. The idea is to start from a well-known estimand called the “average treatment effect on the overlap population (ATO)”, which we then perturb in the direction of the target causal effect (e.g., the average treatment effect or the average treatment effect on the treated). This produces a class of estimands that progressively approximates our target while remaining identifiable and estimable under positivity violations. We discuss how to perform semiparametric inference for these classes, and we demonstrate the methodology by shedding new light on the famous LaLonde dataset.

Dr. Andrew Yiu is a Postdoctoral Research Fellow at the Department of Statistics, University of Oxford. Prior to this, he completed a PhD at the MRC Biostatistics Unit, University of Cambridge. His research interests include Bayesian semiparametric inference, predictive inference and causal inference.