Statistics and Its Interface

Volume 2 (2009)

Number 2

Simultaneous sensitivity analysis for observational studies using full matching or matching with multiple controls

Pages: 203 – 211

DOI: http://dx.doi.org/10.4310/SII.2009.v2.n2.a10

Authors

Joseph L. Gastwirth (Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, Penn., U.S.A.)

Abba M. Krieger (Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, Penn., U.S.A.)

Paul R. Rosenbaum (Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, Penn., U.S.A.)

Dylan Small (Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, Penn., U.S.A.)

Abstract

In a matched observational study, a sensitivity analysis asks how the conclusions of the study would change if the matching had failed to adjust for an unobserved covariate with particular attributes. A ‘simultaneous’ sensitivity analysis characterizes the unobserved covariate $u$ in terms of two sensitivity parameters which relate $u$ to treatment and to response. In a previous paper, we proposed a simultaneous sensitivity analysis for matched pairs. The current paper extends this to matching with multiple controls and to full matching, using the technique of asymptotic separability. An example concerns the possibility that the military caused an increase in smoking by soldiers by various programs that subsidized cigarettes.

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