A Design for Observational Studies in Which Some People Avoid Treatment

Paul R. Rosenbaum

The American Statistician, 2026, vol. 80, issue 2, 277-285

Abstract: A simple but better design is proposed for observational studies in which receipt of treatment is rare in a large subpopulation defined by measured covariates. In such a subpopulation, few responses to treatment are observed, but there are abundant untreated controls. The design is matched in two ratios, a low ratio—perhaps matched pairs—for the subpopulation where treatment is common, and a high ratio—perhaps 1-to-4—for the subpopulation where treatment is uncommon, retaining this distinction throughout the study, rather than presuming that avoidance of treatment is inconsequential. Theoretical considerations that favor this design are discussed informally with reference to the existing literature on observational studies. These include: increased design sensitivity, possible effect modification and its possible consequences for design sensitivity, counterfactual low risk in relation to design sensitivity, and the degree to which conclusions may be generalized. The design is exemplified by a study with 1212 treatment-control matched pairs and 213 sets matched 1-to-4, so that more than 30% of the 3489=2×1212+213+4×213 study subjects come from the subpopulation that rarely receives treatment. The R package aamatch contains the unmatched data, reconstructs the matched data, and replicates the analyses.

Date: 2026
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DOI: 10.1080/00031305.2026.2623909

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