When a randomized, concurrently controlled study is unethical or impractical, researchers often turn to a single-armed, historically controlled study (HCS) as a practical alternative. Causal inference in an HCS is usually carried out using methods designed for a typical observational study (TOS). This paper points out the differences between a TOS and an HCS and attempts to conceptualize the latter in clinically meaningful terms. In particular, it is noted that the current treatment effect, the average of individual treatment effects over the patient population for the current study, may be a more relevant estimand than the quantity estimated by standard TOS methods, which is a weighted average of individual effects over current and historical patients. The current treatment effect can be estimated under an outcome regression model or a covariate density model, the latter corresponding to a propensity score model from a TOS perspective. Augmenting both estimators leads to a doubly robust estimator that is consistent and asymptotically normal if either model is correctly specified. Simulation experiments are conducted to evaluate the finite sample performance of the proposed methods. Practical recommendations are given in regard to the design and analysis of an HCS.

causal inference, density ratio, double robustness, historical control, outcome regression, propensity score.