Correcting the Odds Ratio in Cohort Studies of Common Outcomes

McNutt, Louise‐Anne; Hafner, Jean-Paul; Xue, Xiaonan

doi:10.1001/jama.282.6.529

Cited by 39 publications

(29 citation statements)

References 2 publications

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“…If the Poisson method is in turn problematic because individual probabilities have to be estimated and those estimates become larger than 1 for some individuals, there may be no other solution than the doubling-of-cases method with robust standard error estimation, but this needs extra programming and statistical expertise. In line with other commentators, 7,10 we discourage the use of the Zhang and Yu method, despite its ease of application and its appealing conceptual simplicity.…”

Section: Recommendations For Clinical Researcherssupporting

confidence: 63%

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

Knol

Cessie

Algra

et al. 2011

CMAJ

395

319

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L ogistic 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 Yu 5 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.In this paper, we illustrate the difference between risk ratios and odds ratios using clinical examples, and describe the magnitude of the problem in the literature. We also review methods to obtain adjusted risk ratios and evaluate these methods by means of simulations. We conclude with practical details on these methods and recommendations on their application. Misuse of odds ratios in cohort studies and RCTsAn odds ratio is calculated as the ratio of the odds of the outcome in the patients with the treatment or exposure and the odds of the outcome in the patients without the treatment or exposure. The risk ratio, also referred to as the relative risk, is calculated as the ratio of the risk of the outcome in these two groups. In this article, we illustrate, by means of two empirical examples, that use of odds ratios in cohort studies and RCTs can lead to misinterpretation of results.Clinical example 1: cohort study A cohort study evaluated the relation between changes in marital status of mothers and cannabis use by their children.11 Use of cannabis was reported by 48.6% of the participants at age 21. Table 1 presents the crude and adjusted odds ratios as reported in the paper for one to two changes in maternal marital status and the risk of cannabis use, and for three or more changes in maternal marital status and the risk of cannabis use. We calculated the corresponding crude and adjusted risk ratios (Table 1) based on the data provided in the article. The odds ratios and risk ratios were quite different: a modest increase of the risk by 50% (adjusted risk ratio is 1.5) was observed, whereas the "risk" seemed more than doubled when the odds ratio was interpreted as a risk ratio (adjusted odds ratio is 2.3). Analysis CMAJ • Odds ratios, often used in cohort studies and randomized controlled trials (RCTs), are often interpreted as risk ratios but always overestimate the risk ratio. Clinical example 2: RCT• We evaluated alterna...

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Section: Recommendations For Clinical Researcherssupporting

confidence: 63%

“…[6][7][8][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.…”

mentioning

confidence: 99%

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

Knol

Cessie

Algra

et al. 2011

CMAJ

395

319

View full text Add to dashboard Cite

show abstract

“…This method of estimating a confidence interval, known as the ''method of substitution'', has been applied to other measures of association [10]. Subsequent criticism suggested, however, that the proposed confidence interval for relative risk would be too narrow because of its failure to account for variability in the baseline risk [11,12]. Others arrived at the same conclusion independently in similar contexts [13].…”

Section: Introductionmentioning

confidence: 99%

Relative risks and confidence intervals were easily computed indirectly from multivariable logistic regression

Localio¹,

Margolis²,

Berlin³

2007

Journal of Clinical Epidemiology

229

219

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“…Recently, there has been much discussion and interest in the literature concerning the appropriateness of estimating relative risk (RR) versus odds ratio (OR) in cross-sectional and cohort studies, for example, Schouten et al [1], Axelson et al [2], McNutt et al [3,4], Skov et al [5] and Zhang and Yu [6], among others. In case-control studies, the OR may be preferable because of the different sampling fractions in the case and control groups.…”

Section: Introductionmentioning

confidence: 99%

Estimating relative risks for common outcome using PROC NLP

Yu¹,

Wang²

2008

Computer Methods and Programs in Biomedicine

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In cross-sectional or cohort studies with binary outcomes, it is biologically interpretable and of interest to estimate the relative risk or prevalence ratio, especially when the response rates are not rare. Several methods have been used to estimate the relative risk, among which the log-binomial models yield the maximum likelihood estimate (MLE) of the parameters. Because of restrictions on the parameter space, the log-binomial models often run into convergence problems. Some remedies, e.g., the Poisson and Cox regressions, have been proposed. However, these methods may give outof-bound predicted response probabilities. In this paper, a new computation method using the SAS Nonlinear Programming (NLP) procedure is proposed to find the MLEs. The proposed NLP method was compared to the COPY method, a modified method to fit the log-binomial model. Issues in the implementation are discussed. For illustration, both methods were applied to data on the prevalence of microalbuminuria (micro-protein leakage into urine) for kidney disease patients from the Diabetes Control and Complications Trial. The sample SAS macro for calculating relative risk is provided in the appendix.

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Correcting the Odds Ratio in Cohort Studies of Common Outcomes

Cited by 39 publications

References 2 publications

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

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

Relative risks and confidence intervals were easily computed indirectly from multivariable logistic regression

Estimating relative risks for common outcome using PROC NLP

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