Consistent Estimation of Propensity Score Functions with Oversampled Exposed Subjects

Observational cohort studies with oversampled exposed subjects are typically implemented to understand the causal effect of a rare exposure. Because the distribution of exposed subjects in the sample differs from the source population, estimation of a propensity score function (i.e., probability of exposure given baseline covariates) targets a nonparametrically nonidentifiable parameter. Consistent estimation of propensity score functions is an important component of various causal inference estimators, including double robust machine learning and inverse probability weighted estimators. This paper develops the use of the probability of exposure from the source population in a flexible computational implementation that can be used with any algorithm that allows observation weighting to produce consistent estimators of propensity score functions. Simulation studies and a hypothetical health policy intervention data analysis demonstrate low empirical bias and variance for these propensity score function estimators with observation weights in finite samples.