During the process of reviewing several articles published in Cancer Epidemiology Biomarkers & Prevention, it has come to our attention that the interpretation of relative risk (RR) and odds ratio (OR) as an estimated measure of hypothetical protective effects is wrong in some of them (1–3). We are worried that readers may be mislead by such misinterpretations.
Effect measures such as RR and OR have a range of values from 0 to ∝, with a value of 1 meaning no effect. This implies that the range from 0 to 1 is somehow equivalent to the range from 1 to ∝. Therefore, it is incorrect to interpret a RR = 0.7 as a 30% protective effect or an OR = 0.2 as an 80% protective effect.
The correct interpretation of the effect is obtained by calculating the inverse of the effect measure 1/RR or 1/OR. Therefore, an estimated value of RR = 0.7 should be interpreted as offering a protection of 1/RR = 1/0.7 = 1.43 (i.e., 43%). Similarly, an estimated RR = 0.5 gives a protection of 1/0.5 = 2 (i.e., a 100% protecting effect). The same method can be used with the confidence intervals to estimate the range of effects.
Wrong interpretations as these have appeared in several articles recently published in your journal that may lead to wrong conclusions (1–3).
For instance, the article by SatiaAbouta et al. (3) attributes to the higher intake of vitamin E in AfroAmericans a significant protective effect of 70% (OR = 0.3), when, in fact, the protective effect according to their data would be 1/0.3 = 3.33 or 233%. This is three times greater than the authors' estimate. The same misinterpretation is repeated for other micronutrients.
This happens again in the article by Neuhouser et al. (2). They report a significant protective effect of 31% (OR = 0.69) for the highest quintile of βcryptoxanthin intake (in the placebo group), when, in fact, the effect is 45%.
The study by Yuan et al. 1) reports a 35–40% protective effect among smokers due to the intake of carotenoids, βcryptoxanthin, and retinol. A correct interpretation yields an effect size of 54–66%, an important difference.
We consider that more care should be taken to interpret this type of measures. The protective effect is underestimated if we do not apply the right calculation. This should be addressed by both authors and referees.
Although it is often not possible, it would be even more useful from a public health stand if these measures could be combined with prevalence estimates for the populations of interest.
Alberto RuanoRavina ^{1}
Juan Miguel BarrosDios
Adolfo Figueiras
Department of Preventive Medicine and Public Health
University of Santiago de Compostela
Santiago de Compostela, Spain
Pedro BrañasTato
Medical Inspection
Galician Health Service
Santiago, Spain
Footnotes

↵1 To whom requests for reprints should be addressed.
 Accepted December 16, 2003.
 Received December 12, 2003.
References
Reply
Dr. RuanoRavina et al. refer in their letter to our publication “Fruits and vegetables are associated with lower lung cancer risk only in the placebo arm of the βcarotene and retinol efficacy trial (CARET)” [Cancer Epidemiol Biomarkers & Prev 2003;12:350–8].
The relative risk (RR) estimates the likelihood of developing the disease of interest in the exposed group compared with the unexposed (or least exposed) as the referent. These estimates take on the values of 0 to ∝ where the value of 1.0 implies “no association” or no difference in disease risk between the exposed and the unexposed. For example, a RR for lung cancer of 1.3 represents a 30% increased risk for disease among the exposed relative to the unexposed after the null value of 1.0 is subtracted from 1.3 [(1.3 − 1.0)/1.0]. Likewise, a RR of <1.0 represents an inverse association such that a RR of 0.7 represents a 30% reduced risk of disease after the null value of 1.0 is subtracted [(0.7 − 1.0)/1.0], as is standard in epidemiological textbooks (1, 2).
Dr. RuanoRivera et al. appear to be arguing that because the point of no association (i.e., RR = 1.0) is not in the center of the range of possible RRs, RRs on one side of 1.0 are somehow misleading, and further decide that the misleading RRs are the ones less than 1.0. If group 1 has half the risk of group 2, we should instead describe group 2 as having twice the risk of group 1. This argument ignores the importance of the proper selection of the referent. Our reference group is composed of those study participants in the lowest quintile of dietary intake of each nutrient or food group being examined, as is common in nutrition epidemiology. This reference group takes on the null value of 1.0.
We disagree with Dr. RuanoRivera et al. that the correct interpretation of the RR measure is the inverse of the estimate when the RR is <1.0. We know of no statistical methods suggesting that RRs or odds ratios should be interpreted as the inverse of the calculated measure of association (1/RR). The letter contains no references to support their proposition.
Marian L. Neuhouser
Mark D. Thornquist
Division of Public Health Sciences
Fred Hutchinson Cancer Research Center
Seattle, WA
Gilbert S. Omenn
Gary E. Goodman
Departments of Internal Medicine and Human Genetics
University of Michigan
Ann Arbor, MI