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Some Counterclaims Undermine Themselves in Observational Studies

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  • Paul R. Rosenbaum

Abstract

Claims based on observational studies that a treatment has certain effects are often met with counterclaims asserting that the treatment is without effect, that associations are produced by biased treatment assignment. Some counterclaims undermine themselves in the following specific sense: presuming the counterclaim to be true may strengthen the support that the original data provide for the original claim, so that the counterclaim fails in its role as a critique of the original claim. In mathematics, a proof by contradiction supposes a proposition to be true en route to proving that the proposition is false. Analogously, the supposition that a particular counterclaim is true may justify an otherwise unjustified statistical analysis, and this added analysis may interpret the original data as providing even stronger support for the original claim. More precisely, the original study is sensitive to unmeasured biases of a particular magnitude, but an analysis that supposes the counterclaim to be true may be insensitive to much larger unmeasured biases. The issues are illustrated using data from the U.S. Fatal Accident Reporting System. Supplementary materials for this article are available online.

Suggested Citation

  • Paul R. Rosenbaum, 2015. "Some Counterclaims Undermine Themselves in Observational Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1389-1398, December.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:512:p:1389-1398
    DOI: 10.1080/01621459.2015.1054489
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    References listed on IDEAS

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    1. Jesse Y. Hsu & Dylan S. Small, 2013. "Calibrating Sensitivity Analyses to Observed Covariates in Observational Studies," Biometrics, The International Biometric Society, vol. 69(4), pages 803-811, December.
    2. Paul R. Rosenbaum, 2007. "Sensitivity Analysis for m-Estimates, Tests, and Confidence Intervals in Matched Observational Studies," Biometrics, The International Biometric Society, vol. 63(2), pages 456-464, June.
    3. Paul R. Rosenbaum, 2014. "Weighted M -statistics With Superior Design Sensitivity in Matched Observational Studies With Multiple Controls," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1145-1158, September.
    4. Peter B. Gilbert & Ronald J. Bosch & Michael G. Hudgens, 2003. "Sensitivity Analysis for the Assessment of Causal Vaccine Effects on Viral Load in HIV Vaccine Trials," Biometrics, The International Biometric Society, vol. 59(3), pages 531-541, September.
    5. Paul R. Rosenbaum, 2013. "Impact of Multiple Matched Controls on Design Sensitivity in Observational Studies," Biometrics, The International Biometric Society, vol. 69(1), pages 118-127, March.
    6. Jesse Y. Hsu & Dylan S. Small & Paul R. Rosenbaum, 2013. "Effect Modification and Design Sensitivity in Observational Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 135-148, March.
    7. Paul R. Rosenbaum, 2015. "Bahadur Efficiency of Sensitivity Analyses in Observational Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 205-217, March.
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