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Biometrika 2008 95(2):481-488; doi:10.1093/biomet/asn004
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© 2008 Biometrika Trust

Articles

The prognostic analogue of the propensity score

Ben B. Hansen

Statistics Department, University of Michigan 439 West Hall, Ann Arbor, Michigan 48109, U.S.A. ben.b.hansen{at}umich.edu

Received for publication 1 June 2006. Revision received 1 November 2007.
  Abstract

The propensity score collapses the covariates of an observational study into a single measure summarizing their joint association with treatment conditions; prognostic scores summarize covariates' association with potential responses. As with propensity scores, stratification on prognostic scores brings to uncontrolled studies a concrete and desirable form of balance, a balance that is more familiar as an objective of experimental control. Like propensity scores, prognostic scores can reduce the dimension of the covariate, yet causal inferences conditional on them are as valid as are inferences conditional only on the unreduced covariate. As a method of adjustment unto itself, prognostic scoring has limitations not shared with propensity scoring, but it holds promise as a complement to the propensity score, particularly in certain designs for which unassisted propensity adjustment is difficult or infeasible.

Key Words: Covariate balance • Matched sampling • Matching • Observational study • Quasi-experiment • Regression discontinuity • Subclassification


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