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Optimal approximate conversions of odds ratios and hazard ratios to risk ratios

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  • Tyler J. VanderWeele

Abstract

Odds ratios approximate risk ratios when the outcome under consideration is rare but can diverge substantially from risk ratios when the outcome is common. In this paper, we derive optimal analytic conversions of odds ratios and hazard ratios to risk ratios that are minimax for the bias ratio when outcome probabilities are specified to fall in any fixed interval. The results for hazard ratios are derived under a proportional hazard assumption for the exposure. For outcome probabilities specified to lie in symmetric intervals centered around 0.5, it is shown that the square‐root transformation of the odds ratio is the optimal minimax conversion for the risk ratio. General results for any nonsymmetric interval are given both for odds ratio and for hazard ratio conversions. The results are principally useful when odds ratios or hazard ratios are reported in papers, and the reader does not have access to the data or to information about the overall outcome prevalence.

Suggested Citation

  • Tyler J. VanderWeele, 2020. "Optimal approximate conversions of odds ratios and hazard ratios to risk ratios," Biometrics, The International Biometric Society, vol. 76(3), pages 746-752, September.
    • Handle: RePEc:bla:biomet:v:76:y:2020:i:3:p:746-752
    DOI: 10.1111/biom.13197
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    References listed on IDEAS

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    1. Yelland Lisa N & Salter Amy B & Ryan Philip, 2011. "Relative Risk Estimation in Randomized Controlled Trials: A Comparison of Methods for Independent Observations," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-31, January.
    2. Mirjam J Knol & Ruben G Duijnhoven & Diederick E Grobbee & Karel G M Moons & Rolf H H Groenwold, 2011. "Potential Misinterpretation of Treatment Effects Due to Use of Odds Ratios and Logistic Regression in Randomized Controlled Trials," PLOS ONE, Public Library of Science, vol. 6(6), pages 1-5, June.
    3. Thomas S. Richardson & James M. Robins & Linbo Wang, 2017. "On Modeling and Estimation for the Relative Risk and Risk Difference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1121-1130, July.
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