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A second evidence factor for a second control group

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  • Paul R. Rosenbaum

Abstract

In an observational study of the effects caused by a treatment, a second control group is used in an effort to detect bias from unmeasured covariates, and the investigator is content if no evidence of bias is found. This strategy is not entirely satisfactory: two control groups may differ significantly, yet the difference may be too small to invalidate inferences about the treatment, or the control groups may not differ yet nonetheless fail to provide a tangible strengthening of the evidence of a treatment effect. Is a firmer conclusion possible? Is there a way to analyze a second control group such that the data might report measurably strengthened evidence of cause and effect, that is, insensitivity to larger unmeasured biases? Evidence factor analyses are not commonly used with a second control group: most analyses compare the treated group to each control group, but analyses of that kind are partially redundant; so, they do not constitute evidence factors. An alternative analysis is proposed here, one that does yield two evidence factors, and with a carefully designed test statistic, is capable of extracting strong evidence from the second factor. The new technical work here concerns the development of a test statistic with high design sensitivity and high Bahadur efficiency in a sensitivity analysis for the second factor. A study of binge drinking as a cause of high blood pressure is used as an illustration.

Suggested Citation

  • Paul R. Rosenbaum, 2023. "A second evidence factor for a second control group," Biometrics, The International Biometric Society, vol. 79(4), pages 3968-3980, December.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:4:p:3968-3980
    DOI: 10.1111/biom.13921
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    References listed on IDEAS

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    1. Michael J. Daniels & Jason A. Roy & Chanmin Kim & Joseph W. Hogan & Michael G. Perri, 2012. "Bayesian Inference for the Causal Effect of Mediation," Biometrics, The International Biometric Society, vol. 68(4), pages 1028-1036, December.
    2. Jesse Y. Hsu & José R. Zubizarreta & Dylan S. Small & Paul R. Rosenbaum, 2015. "Strong control of the familywise error rate in observational studies that discover effect modification by exploratory methods," Biometrika, Biometrika Trust, vol. 102(4), pages 767-782.
    3. P R Rosenbaum & D B Rubin, 2023. "Propensity scores in the design of observational studies for causal effects," Biometrika, Biometrika Trust, vol. 110(1), pages 1-13.
    4. 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.
    5. B Karmakar & B French & D S Small, 2019. "Integrating the evidence from evidence factors in observational studies," Biometrika, Biometrika Trust, vol. 106(2), pages 353-367.
    6. Matteo Bonvini & Edward H. Kennedy, 2022. "Sensitivity Analysis via the Proportion of Unmeasured Confounding," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(539), pages 1540-1550, September.
    7. S R Howard & S D Pimentel, 2021. "The uniform general signed rank test and its design sensitivity [A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations]," Biometrika, Biometrika Trust, vol. 108(2), pages 381-396.
    8. Paul R. Rosenbaum, 2007. "Confidence Intervals for Uncommon but Dramatic Responses to Treatment," Biometrics, The International Biometric Society, vol. 63(4), pages 1164-1171, December.
    9. 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.
    10. Rosenbaum, Paul R. & Silber, Jeffrey H., 2009. "Amplification of Sensitivity Analysis in Matched Observational Studies," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1398-1405.
    11. Paul R. Rosenbaum, 2010. "Evidence factors in observational studies," Biometrika, Biometrika Trust, vol. 97(2), pages 333-345.
    12. B. Zhang & D. S. Small & K. B. Lasater & M. McHugh & J. H. Silber & P. R. Rosenbaum, 2023. "Matching One Sample According to Two Criteria in Observational Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(542), pages 1140-1151, April.
    13. Colin B. Fogarty & Dylan S. Small, 2016. "Sensitivity Analysis for Multiple Comparisons in Matched Observational Studies Through Quadratically Constrained Linear Programming," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1820-1830, October.
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