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A note on a sensitivity analysis for unmeasured confounding, and the related E-value

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  • Sjölander Arvid

    (Department of Medical Epidemiology and Biostatistics, Karolinska Institute, Solna, Sweden)

Abstract

Unmeasured confounding is one of the most important threats to the validity of observational studies. In this paper we scrutinize a recently proposed sensitivity analysis for unmeasured confounding. The analysis requires specification of two parameters, loosely defined as the maximal strength of association that an unmeasured confounder may have with the exposure and with the outcome, respectively. The E-value is defined as the strength of association that the confounder must have with the exposure and the outcome, to fully explain away an observed exposure-outcome association. We derive the feasible region of the sensitivity analysis parameters, and we show that the bounds produced by the sensitivity analysis are not always sharp. We finally establish a region in which the bounds are guaranteed to be sharp, and we discuss the implications of this sharp region for the interpretation of the E-value. We illustrate the theory with a real data example and a simulation.

Suggested Citation

  • Sjölander Arvid, 2020. "A note on a sensitivity analysis for unmeasured confounding, and the related E-value," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 229-248, January.
    • Handle: RePEc:bpj:causin:v:8:y:2020:i:1:p:229-248:n:6
    DOI: 10.1515/jci-2020-0012
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    References listed on IDEAS

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    1. Zhihong Cai & Manabu Kuroki & Judea Pearl & Jin Tian, 2008. "Bounds on Direct Effects in the Presence of Confounded Intermediate Variables," Biometrics, The International Biometric Society, vol. 64(3), pages 695-701, September.
    2. Keisuke Hirano & Jack R. Porter, 2012. "Impossibility Results for Nondifferentiable Functionals," Econometrica, Econometric Society, vol. 80(4), pages 1769-1790, July.
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