  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.
