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Biometrika 1998 85(4):907-920; doi:10.1093/biomet/85.4.907
© 1998 by Biometrika Trust
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Dual and simultaneous sensitivity analysis for matched pairs

JOSEPH L. GASTWIRTH, ABBA M. KRIEGER and PAUL R. ROSENBAUM

Department of Statistics, George Washington University Washington, DC 20052, U.S.A.jlgast{at}gwuvm.gwu.edu
Department of Statistics, University of Pennsylvania Philadelphia, Pennsylvania 19104-6302, U.S.A.jlawless{at}setosa.uwaterloo.ca
Department of Statistics, University of Pennsylvania Philadelphia, Pennsylvania 19104-6302, U.S.A.rosenbaum{at}stat.wharton.upenn.edu

When a study shows an association between a treatment and a response, before concluding that there is a causal relationship it is useful to assess whether or not an unobserved variable, U, might explain the observed association. Sensitivity analysis clarifies the properties U must have in terms of its relationship to the response and its imbalance in the groups being compared. A substantial literature has investigated the imbalance or association between U and group assignment. This paper develops a dual sensitivity analysis for matched pairs, focusing on the strength of the relationship between U and the response required to reduce an observed association to non-significance. A third simultaneous form of sensitivity analysis models both relationships between U and treatment assignment and U and response. The simultaneous form allows one to compare results from the sensitivity analysis to subject matter knowledge about both relationships. The methods are illustrated by several examples.

Key Words: Causal inference • Exponential family • Matched sampling • McNemar's test • Observational study • Sensitivity analysis • Signed-rank test


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