Sensitivity Analysis on Odds Ratios
Leppälä, Kalle (2023-06-13)
Oxford University Press
13.06.2023
Kalle Leppälä, Sensitivity Analysis on Odds Ratios, American Journal of Epidemiology, Volume 192, Issue 11, November 2023, Pages 1882–1886, https://doi.org/10.1093/aje/kwad137.
https://creativecommons.org/licenses/by/4.0/
© The Author(s) 2023. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
https://creativecommons.org/licenses/by/4.0/
© The Author(s) 2023. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
https://creativecommons.org/licenses/by/4.0/
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202312214007
https://urn.fi/URN:NBN:fi:oulu-202312214007
Tiivistelmä
Abstract
The classical Cornfield inequalities state that if a third confounding variable is fully responsible for an observed association between the exposure and the outcome variables, then the association between both the exposure and the confounder, and the confounder and the outcome, must be at least as strong as the association between the exposure and the outcome, as measured by the risk ratio. The work of Ding and VanderWeele on assumption-free sensitivity analysis sharpens this bound to a bivariate function of the 2 risk ratios involving the confounder. Analogous results are nonexistent for the odds ratio, even though the conversion from odds ratios to risk ratios can sometimes be problematic. We present a version of the classical Cornfield inequalities for the odds ratio. The proof is based on the mediant inequality, dating back to ancient Alexandria. We also develop several sharp bivariate bounds of the observed association, where the 2 variables are either risk ratios or odds ratios involving the confounder.
The classical Cornfield inequalities state that if a third confounding variable is fully responsible for an observed association between the exposure and the outcome variables, then the association between both the exposure and the confounder, and the confounder and the outcome, must be at least as strong as the association between the exposure and the outcome, as measured by the risk ratio. The work of Ding and VanderWeele on assumption-free sensitivity analysis sharpens this bound to a bivariate function of the 2 risk ratios involving the confounder. Analogous results are nonexistent for the odds ratio, even though the conversion from odds ratios to risk ratios can sometimes be problematic. We present a version of the classical Cornfield inequalities for the odds ratio. The proof is based on the mediant inequality, dating back to ancient Alexandria. We also develop several sharp bivariate bounds of the observed association, where the 2 variables are either risk ratios or odds ratios involving the confounder.
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