Causal inference for observational studies with an external control group

What is it about?

The notion of propensity score plays a central role in traditional causal inference for non-randomized comparative studies. Propensity score is defined as the conditional probability of assignment to a particular treatment given a vector of observed covariates. This definition makes it difficult to apply to studies with external controls such as a historical control. In such studies subjects are not "assigned" to treatments. There is not an assignment mechanism. This paper introduces the concept of proto-propensity ratio, a one-dimensional summary of covariates that plays essentially the same role as propensity score but does not presume that subjects are assigned to treatments. We also tweak the definition of unconfoundedness, traditionally an attribute of the assignment mechanism, so that it applies to studies with an external control group. With these modifications, we show that causal interpretation is possible for externally controlled studies, thereby providing a clear theoretical foundation for such studies.

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Why is it important?

This work provides a clear theoretical foundation for analyzing studies that rely on external control groups, which are increasingly important in medical product evaluation. It reassures researchers and decision-makers that, under transparent and reasonable assumptions, these studies can still support causal conclusions—while also clarifying what those assumptions are and how standard methods should be adapted. In short, the paper explains how to think rigorously and responsibly about cause-and-effect when randomization is not an option, using tools that remain familiar but are interpreted in a more appropriate way for external control studies.