What's the Relative Risk? A Method to Directly Estimate Risk Ratios in Cohort Studies of Common Outcomes

doi:10.1016/S1047-2797(01)00278-2

Annals of Epidemiology

Volume 12, Issue 7, October 2002, Pages 452-454

https://doi.org/10.1016/S1047-2797(01)00278-2 Get rights and content

Abstract

PURPOSE: In cohort studies of common outcomes, odds ratios (ORs) may seriously overestimate the true effect of an exposure on the outcome of interest (as measured by the risk ratio [RR]). Since few study designs require ORs (most frequently, case-control studies), their popularity is due to the widespread use of logistic regression. Because ORs are used to approximate RRs so frequently, methods have been published in the general medical literature describing how to convert ORs to RRs; however, these methods may produce inaccurate confidence intervals (CIs). The authors explore the use of binomial regression as an alternative technique to directly estimate RRs and associated CIs in cohort studies of common outcomes.

METHODS: Using actual study data, the authors describe how to perform binomial regression using the SAS System for Windows, a statistical analysis program widely used by US health researchers.

RESULTS: In a sample data set, the OR for the exposure of interest overestimated the RR more than twofold. The 95% CIs for the OR and converted RR were wider than for the directly estimated RR.

CONCLUSIONS: The authors argue that for cohort studies, the use of logistic regression should be sharply curtailed, and that instead, binomial regression be used to directly estimate RRs and associated CIs.

Section snippets

Selected Abbreviations and Acronyms

ORs = odds ratios

RRs = risk ratios

BMI = body mass index

RD = risk difference

Methods

Recent releases of the SAS System for Windows have included a generalized linear modeling procedure known as PROC GENMOD (10). In PROC GENMOD, the user can specify a number of features of the regression model, such as the distribution of the dependent variable, the link function, and whether an offset term is to be used. To perform the popular logistic regression procedure, users would specify a binomial distribution and a logit link. (If we denote a probability as p, the logit of p refers to

Results

Table 1 shows results from analysis of data from a cohort of 16,778 men on active duty in the US Air Force. These men were given a test that had a binary (pass/fail) outcome, and the values of several predictor variables were measured prior to testing. Only results relating to the effect of obesity, defined as a body mass index (BMI, equal to weight in kg divided by height squared in m²) ≥ 30.0 kg/m², are shown. The referent group was composed of persons with normal weight, i.e., 18.5 kg/m² ≤

Discussion

In order to avoid the recurring problems associated with ORs, we advocate that whenever possible, investigators directly estimate and report RRs. Of course, if an outcome is truly uncommon in a study population (< 5%), ORs will give unbiased estimates of RRs. In such cases, the difference between the OR and RR may be so small that some investigators may prefer the more convenient OR. Moreover, in cohort studies, the OR may be used as an index of association on its own, i.e., not as an estimator

Acknowledgements

This work was performed as part of the authors' duties as employees of the US Federal Government, and no other sources of support were involved. The views expressed in this paper are those of the authors only, and should not be interpreted as the official position of the US Air Force or the Department of Defense.

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Original reportWhat's the Relative Risk? A Method to Directly Estimate Risk Ratios in Cohort Studies of Common Outcomes

Abstract

Section snippets

Selected Abbreviations and Acronyms

Methods

Results

Discussion

Acknowledgements

Methods in Observational Epidemiology

What's the relative risk? A method of correcting the odds ratio in cohort studies of common outcomes

JAMA.

Correcting the odds ratio in cohort studies of common outcomes

JAMA.

The effect of race and sex on physicians' recommendations for cardiac catheterization

N Engl J Med.

Misunderstandings about the effects of race and sex on physicians' referrals for cardiac catheterization

N Engl J Med.

Binomial regression in GLIMEstimating risk ratios and risk differences

Am J Epidemiol.

Original report
What's the Relative Risk? A Method to Directly Estimate Risk Ratios in Cohort Studies of Common Outcomes