Distribution-Free Assessment of Population Overlap in Observational Studies

Overlap in baseline covariates between treated and control groups, also known as positivity or common support, is a common assumption in observational causal inference. Assessing this assumption is often ad hoc, however, and can give misleading results. For example, the common practice of examining the empirical distribution of estimated propensity scores is heavily dependent on model specification and has poor uncertainty quantification. In this paper, we propose a formal statistical framework for assessing the extrema of the population propensity score; e.g., the propensity score lies in [0.1,0.9] almost surely. We develop a family of upper confidence bounds, which we term O-values, for this quantity. We show these bounds are valid in finite samples so long as the observations are independent and identically distributed, without requiring any further modeling assumptions on the data generating process. Finally, we demonstrate this approach using benchmark observational studies, showing how to build our proposed method into the observational causal inference workflow.