The Odds Ratio is “portable” across baseline risk but not the Relative Risk: Time to do away with the log link in binomial regression



      In a recent paper we suggest that the relative risk (RR) be replaced with the odds ratio (OR) as the effect measure of choice in clinical epidemiology. In response, Chu, and colleagues raise several points that argue for the status quo. In this paper, we respond to their response.

      Study designs and Settings

      We use the same examples given by Chu and colleagues to recompute estimates of effect and demonstrate the problem with the RR.


      We reaffirm the following findings: a) the OR and RR measure different things and their numerical difference is only important if misinterpreted b) this potential misinterpretation is a trivial issue compared to the lack of portability of the RR c) the same examples reaffirm non-portability of the RR and demonstrate how misleading the results might be in contrast to the OR, which is independent of the baseline risk d) the concept of non-collapsibility for the OR should be expected in the presence of a non-confounding risk factor, and is not a bias e) the log link in regression models that generate RRs as well as the use of RRs in meta-analysis is shown to be problematic using the same examples.


      The OR should replace the RR in clinical research and meta-analyses though there should be conversion of the end product into ratios or differences of risk, solely, for interpretation. To this end we provide a Stata module (logittorisk) for this purpose.


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        • Xiao M
        • Chen Y
        • Cole SR
        • MacLehose R
        • Richardson D
        • Chu H
        Is OR“ portable” in meta-analysis? Time to consider bivariate generalized linear mixed model.
        J Clin Epidemiol. 2020;
        • Doi SA
        • Furuya-Kanamori L
        • Xu C
        • Lin L
        • Chivese T
        • Thalib L
        Questionable utility of the relative risk in clinical research: a call for change to practice.
        J Clin Epidemiol. 2020;
        • Llewelyn H
        The scope and conventions of evidence-based medicine need to be widened to deal with "too much medicine".
        J Eval Clin Pract. 2018; 24: 1026-1032
        • Greenland S
        • Robins JM
        • Pearl J
        Confounding and collapsibility in causal inference.
        Statistical science. 1999; : 29-46
        • Kuha J.
        • Mills C.
        On group comparisons with logistic regression models.
        Sociological Methods & Research. 2020; 49: 498-525
        • Greenland S
        Interpretation and choice of effect measures in epidemiologic analyses.
        American journal of epidemiology. 1987; 125: 761-768
        • Doi SA
        • Barendregt JJ
        • Khan S
        • Thalib L
        • Williams GM
        Advances in the meta-analysis of heterogeneous clinical trials II: The quality effects model.
        Contemp Clin Trials. 2015; 45: 123-129
        • Doi SAR
        • Furuya-Kanamori L
        • Thalib L
        • Barendregt JJ
        Meta-analysis in evidence-based healthcare: a paradigm shift away from random effects is overdue.
        Int J Evid Based Healthc. 2017; 15: 152-160
        • Doi SA
        • Barendregt JJ
        • Khan S
        • Thalib L
        • Williams GM
        Advances in the meta-analysis of heterogeneous clinical trials I: The inverse variance heterogeneity model.
        Contemp Clin Trials. 2015; 45: 130-138
        • Doi SAR
        • Furuya-Kanamori L
        Selecting the best meta-analytic estimator for evidence-based practice: a simulation study.
        Int J Evid Based Healthc. 2020; 18: 86-94
        • GUSTO investigators
        An international randomized trial comparing four thrombolytic strategies for acute myocardial infarction.
        N Engl J Med. 1993; 329: 673-682
        • Lee KL
        • Woodlief LH
        • Topol EJ
        • Weaver WD
        • Betriu A
        • Col J
        • et al.
        Predictors of 30-day mortality in the era of reperfusion for acute myocardial infarction. Results from an international trial of 41,021 patients. GUSTO-I Investigators.
        Circulation. 1995; 91: 1659-1668
        • Furuya-Kanamori L
        • Doi SAR
        • Statistical Software Components, Boston College Department of Economics
        LOGITTORISK: Stata module for conversion of logistic regression output to differences and ratios of risk.
        EconPapers. 2020;