Mengli Xiao1, Haitao Chu2, Stephen R Cole3, Yong Chen4, Richard F MacLehose5, David B Richardson4, Sander Greenland6. 1. Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN 55455, USA. 2. Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN 55455, USA. Electronic address: chux0051@umn.edu. 3. Department of Epidemiology, University of North Carolina, Chapel Hill, NC 27599, USA. 4. Department of Biostatistics, Epidemiology and Informatics, University of Pennsylvania, Philadelphia, PA 19104, USA. 5. Division of Epidemiology and Community Health, School of Public Health, University of Minnesota, Minneapolis, MN 55455, USA. 6. Department of Epidemiology and Department of Statistics, University of California, Los Angeles, 90095, USA.
Abstract
OBJECTIVE: Recently Doi et al. argued that risk ratios should be replaced with odds ratios in clinical research. We disagreed, and empirically documented the lack of portability of odds ratios, while Doi et al. defended their position. In this response we highlight important errors in their position. STUDY DESIGN AND SETTING: We counter Doi et al.'s arguments by further examining the correlations of odds ratios, and risk ratios, with baseline risks in 20,198 meta-analyses from the Cochrane Database of Systematic Reviews. RESULTS: Doi et al.'s claim that odds ratios are portable is invalid because 1) their reasoning is circular: they assume a model under which the odds ratio is constant and show that under such a model the odds ratio is portable; 2) the method they advocate to convert odds ratios to risk ratios is biased; 3) their empirical example is readily-refuted by counter-examples of meta-analyses in which the risk ratio is portable but the odds ratio isn't; and 4) they fail to consider the causal determinants of meta-analytic inclusion criteria: Doi et al. mistakenly claim that variation in odds ratios with different baseline risks in meta-analyses is due to collider bias. Empirical comparison between the correlations of odds ratios, and risk ratios, with baseline risks show that the portability of odds ratios and risk ratios varies across settings. CONCLUSION: The suggestion to replace risk ratios with odds ratios is based on circular reasoning and a confusion of mathematical and empirical results. It is especially misleading for meta-analyses and clinical guidance. Neither the odds ratio nor the risk ratio is universally portable. To address this lack of portability, we reinforce our suggestion to report variation in effect measures conditioning on modifying factors such as baseline risk; understanding such variation is essential to patient-centered practice.
OBJECTIVE: Recently Doi et al. argued that risk ratios should be replaced with odds ratios in clinical research. We disagreed, and empirically documented the lack of portability of odds ratios, while Doi et al. defended their position. In this response we highlight important errors in their position. STUDY DESIGN AND SETTING: We counter Doi et al.'s arguments by further examining the correlations of odds ratios, and risk ratios, with baseline risks in 20,198 meta-analyses from the Cochrane Database of Systematic Reviews. RESULTS: Doi et al.'s claim that odds ratios are portable is invalid because 1) their reasoning is circular: they assume a model under which the odds ratio is constant and show that under such a model the odds ratio is portable; 2) the method they advocate to convert odds ratios to risk ratios is biased; 3) their empirical example is readily-refuted by counter-examples of meta-analyses in which the risk ratio is portable but the odds ratio isn't; and 4) they fail to consider the causal determinants of meta-analytic inclusion criteria: Doi et al. mistakenly claim that variation in odds ratios with different baseline risks in meta-analyses is due to collider bias. Empirical comparison between the correlations of odds ratios, and risk ratios, with baseline risks show that the portability of odds ratios and risk ratios varies across settings. CONCLUSION: The suggestion to replace risk ratios with odds ratios is based on circular reasoning and a confusion of mathematical and empirical results. It is especially misleading for meta-analyses and clinical guidance. Neither the odds ratio nor the risk ratio is universally portable. To address this lack of portability, we reinforce our suggestion to report variation in effect measures conditioning on modifying factors such as baseline risk; understanding such variation is essential to patient-centered practice.
Authors: Suhail A Doi; Luis Furuya-Kanamori; Chang Xu; Tawanda Chivese; Lifeng Lin; Omran A H Musa; George Hindy; Lukman Thalib; Frank E Harrell Journal: J Clin Epidemiol Date: 2021-08-08 Impact factor: 6.437