Paul R. Rosenbaum

Paul R. Rosenbaum develops the design and analysis of observational studies. His work asks how a study can support a causal inference when investigators cannot assign the exposure by randomization. His research includes matching, sensitivity analysis for unmeasured confounding and ways to design studies whose conclusions withstand larger hidden biases.^[ref]

With Donald B. Rubin, he established the central role of the propensity score $e(X)=P(A=1\mid X)$: conditioning on this score balances measured baseline covariates between treatment groups. Under the required treatment-assignment assumptions and positivity in causal inference, the score permits adjustment for a many-dimensional $X$ through a scalar. Measured balance alone leaves the possibility of unmeasured confounding.^[ref]