  Confounding remains one of the major challenges to causal inference with
observational data. This problem is paramount in medicine, where we would like
to answer causal questions from large observational datasets like electronic
health records (EHRs) and administrative claims. Modern medical data typically
contain tens of thousands of covariates. Such a large set carries hope that
many of the confounders are directly measured, and further hope that others are
indirectly measured through their correlation with measured covariates. How can
we exploit these large sets of covariates for causal inference? To help answer
this question, this paper examines the performance of the large-scale
propensity score (LSPS) approach on causal analysis of medical data. We
demonstrate that LSPS may adjust for indirectly measured confounders by
including tens of thousands of covariates that may be correlated with them. We
present conditions under which LSPS removes bias due to indirectly measured
confounders, and we show that LSPS may avoid bias when inadvertently adjusting
for variables (like colliders) that otherwise can induce bias. We demonstrate
the performance of LSPS with both simulated medical data and real medical data.
