= Paul R. Rosenbaum
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<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.https://statistics.wharton.upenn.edu/profile/rosenbap/[Official research profile and authored book descriptions]{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>.<The central role of the propensity score in observational studies for causal effects by Paul R. Rosenbaum and Donald B. Rubin>[Balancing-score results and treatment-effect assumptions]{ref}
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