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Overestimation of risk ratios by odds ratios in trials and cohort studies: alternatives to logistic regression

Canadian Medical Association journal (CMAJ), 2012-05, Vol.184 (8), p.895-899 [Peer Reviewed Journal]

COPYRIGHT 2012 Joule Inc. ;COPYRIGHT 2012 CMA Joule Inc. ;Copyright Canadian Medical Association May 15, 2012 ;1995-2012, Canadian Medical Association 2012 ;ISSN: 0820-3946 ;EISSN: 1488-2329 ;DOI: 10.1503/cmaj.101715 ;PMID: 22158397 ;CODEN: CMAJAX

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  • Title:
    Overestimation of risk ratios by odds ratios in trials and cohort studies: alternatives to logistic regression
  • Author: Knol, Mirjam J ; Le Cessie, Saskia ; Algra, Ale ; Vandenbroucke, Jan P ; Groenwold, Rolf H H
  • Subjects: Analysis ; Clinical trials ; Cohort Studies ; Data Interpretation, Statistical ; Humans ; Logistic Models ; Logistic regression ; Methods ; Odds Ratio ; Randomized Controlled Trials as Topic - methods ; Regression analysis ; Risk assessment ; Studies
  • Is Part Of: Canadian Medical Association journal (CMAJ), 2012-05, Vol.184 (8), p.895-899
  • Description: Logistic regression analysis, which estimates odds ratios, is often used to adjust for covariables in cohort studies and randomized controlled trials (RCTs) that study a dichotomous outcome. In case-control studies, the odds ratio is the appropriate effect estimate, and the odds ratio can sometimes be interpreted as a risk ratio or rate ratio depending on the sampling method.1-4 However, in cohort studies and RCTs, odds ratios are often interpreted as risk ratios. This is problematic because an odds ratio always overestimates the risk ratio, and this overestimation becomes larger with increasing incidence of the outcome.5 There are alternatives for logistic regression to obtain adjusted risk ratios, for example, the approximate adjustment method proposed by Zhang and Yu5 and regression models that directly estimate risk ratios (also called "relative risk regression").6-9 Some of these methods have been compared in simulation studies.7,9 The method by Zhang and Yu has been strongly criticized,7,10 but regression models that directly estimate risk ratios are rarely applied in practice. We found eight methods to estimate adjusted risk ratios in the literature (Table 35,7-9,14-19). The Mantel-Haenszel risk ratio method is straightforward and gives a weighted risk ratio over strata of covariables.14,15 This method is only practica- ble if adjusting for a small number of categorical covariables (i.e., continuous covariables first need to be categorized). Log-binomial and Poisson regression are generalized linear models that directly estimate risk ratios.7,8 The default standard errors obtained by Poisson regression are typically too large; therefore, calculation of robust standard errors for Poisson regression may be needed to obtain a correct confidence interval around the risk ratio.9 The other four methods use odds ratios or logistic regression to estimate risk ratios. The Zhang and Yu method is a simple formula that calculates the risk ratio based on the odds ratio and the incidence of the outcome in the unexposed group.5 The doublingof- cases method concerns changing the data set in such a way that logistic regression yields a risk ratio instead of an odds ratio.17 Again, calculation of robust standard errors may be needed to obtain a correct confidence interval around the risk ratio.18 Lastly, the method proposed by Austin uses the predicted probabilities obtained from a logistic regression model to estimate risk ratios.19 A recent review article of methods to estimate risk ratios and risk differences in cohort studies illustrated several of these eight methods using empirical data.20 We showed in the clinical examples and simulations that an odds ratio can substantially overestimate the risk ratio. In fact, both are correct, but when an odds ratio is interpreted as a risk ratio, serious misinterpretation with potential consequences for treatment decisions and policymaking can occur, as illustrated by the two clinical examples. Therefore, any misinterpretation of odds ratios should be avoided with calculation and presentation of adjusted risk ratios in both cohort studies and RCTs. Also, if adjustment for baseline covariates is not done, which is often the case in RCTs, the risk ratio is the preferred measure of association in case of dichotomous outcomes.21 Note that in case-control studies, the odds ratio is the appropriate effect estimate and the odds ratio can be interpreted as a risk ratio or rate ratio depending on the sampling method.1-4 Of course, if data of cohort studies or RCTs are collected so that a time-dependent analysis is possible, Cox regression yielding hazard ratios is recommended because it estimates relative hazards and does not involve problems related to odds ratios.
  • Publisher: Canada: Joule Inc
  • Language: English
  • Identifier: ISSN: 0820-3946
    EISSN: 1488-2329
    DOI: 10.1503/cmaj.101715
    PMID: 22158397
    CODEN: CMAJAX
  • Source: ProQuest One Psychology
    GFMER Free Medical Journals
    MEDLINE
    PubMed Central
    Alma/SFX Local Collection
    ProQuest Central
    DOAJ Directory of Open Access Journals
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