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When can odds ratios mislead?

BMJ 1998; 316 doi: (Published 28 March 1998) Cite this as: BMJ 1998;316:989

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On the use, misuse and interpretation of odds ratios.

Dear Sir,

In a recent article, Davies et al. (1) commented on a potential problem when interpreting odds ratios (OR) as relative risks (RR) in epidemiological studies. However, their vague concept of effect measures as applied to different study designs in epidemiology may lead to misuse and false interpretation of OR.

Davies et al. (1) state that the odds ratio is a common measure in case-control studies, cohort studies, or clinical trails. Unfortunately, this first sentence of their article is not correct. For different study designs, OR should only be used as a measure of effect size when RR can not be estimated directly. In cohort studies as well as in clinical trials, RR (the cumulative incidence ratio or the incidence density ratio) can be estimated directly. Therefore, there is no need to use OR to represent the effect size. In contrast in case-control studies, incidence data is usually not available. Therefore, the ratio of the odds of exposure among cases to the odds of exposure among non-cases is calculated. In theory, all case-control studies can be viewed as nested case-control studies, in which both cases and controls are drawn from a well defined source population. If the controls are selected by incidence density sampling, then the OR derived from the case-control study is, apart from random error, the same as RR in the source population. No rare disease assumption is needed (2). In fact, only when cumulative sampling in case-control studies is used, the rare disease assumption is needed. Usually this assumption should not represent a problem, because case-control designs typically are preferred when the outcome of interest is rare (say less than 5%).

The situation, however, is different in cross-sectional studies (usually applied to investigate more common outcomes) when the prevalence odds ratio (POR) is used as an estimate of the prevalence ratio (PR). Since in cross-sectional studies only prevalent cases are drawn, there is no direct way of estimating RR. In the general population, the prevalence odds is equal to the product of the incidence times disease duration (3). If we assume that the exposure of interest has no influence on the disease duration, then the POR is, theoretically, equal to the RR. However, the assumption of equal duration of disease among the exposed and unexposed population is often questionable. Therefore, some authors propose the use of PR as a conservative estimator of the RR (4).

1 Davies HTO, Crombie IK, Tavakoli M. When can odds ratio mislead? BMJ 1998;316:989-91.
2 Greenland S, Thomas DC. On the need for the rare disease assumption in case-control studies. Am J Epidemiol 1982;116:547-53.
3 Rothman KJ, Greenland S. Modern Epidemiology. 2nd ed. Philadelphia: Lippincott-Raven, 1998.
4 Thompson ML, Myers JE, Kriebel D. Prevalence odds ratio or prevalence ratio in the analysis of cross sectional data: what is to be done? Occup Environ Med 1998;55:272-77.

Competing interests: No competing interests

10 August 1998
Dirk Taeger
Statistician (Dirk Taeger), Epidemiologist (Yi Sun, Kurt Straif)
Yi Sun, Kurt Straif
Institute of Epidemiology and Social Medicine, University of Muenster, 48129 Muenster, Germany