Relative Risk

The relative risk (RR) is the most common measure epidemiologists use to quantify the association between a disease and a risk factor. It may be most easily explained in the case where both the disease and the risk factor may be viewed as binary variables. Let p1 and p0 denote the probabilities that a person with the risk factor develops the disease and that an unexposed person develops the disease, respectively. Then the relative risk is given by RR = p1/p0. In the following discussion, we will take risk factors to be exposures. These could be toxic substances to which a subject is exposed, such as cigarette smoke or asbestos, or potentially beneficial foods, such as cruciferous vegetables. But risk factors can also refer to the expression of the disease in relatives or to genetic polymorphisms, to name a few examples. Regardless of the disease or risk factor, an RR greater than one indicates an association between the risk factor and development of the disease, whereas an RR less than one indicates that the risk factor has a protective effect. An important feature of the RR is its multiplicative interpretation—if the RR for a particular exposure is 5, then an individual with that exposure is five times more likely to develop the disease than an unexposed individual.

The most direct way to estimate the relative risk is through a prospective study. In such a study, exposed and unexposed individuals who are free of the disease are recruited into the study and then followed for disease information. After a period of time long enough for sufficient numbers of the patients to develop the disease, the relative risk may be calculated as the ratio of the proportion of exposed subjects who develop the disease to the proportion of unexposed subjects who develop it. A well-known example is a study of lung cancer and smoking among British doctors. The study, reported in the British Medical Journal by Doll and Peto in 1976, with a follow-up in 1994, involved recruiting 34,440 British doctors in 1951. The subjects filled out questionnaires on smoking habits and were followed for 40 years. The risks of death from lung cancer among smokers and lifelong nonsmokers were, respectively, 209 and 14 per 100,000. The relative risk is thus 14.9. As this example illustrates, prospective studies require large numbers of subjects who are followed for long periods of time, often decades. Such studies are often the most definitive in establishing a causal relationship, and they allow one to study the effects of the exposure on a variety of diseases. But the time and expense of conducting them can be prohibitive. Furthermore, for very rare diseases, it may not be possible to recruit enough healthy subjects to produce [Page 833]enough disease cases to calculate a reliable estimate of the RR.

Case control (or retrospective) studies are an alternative form of study that can be used to estimate the RR for an exposure and a rare disease. In a case control study, the sampling is the reverse of that in a prospective study. One starts by sampling a set of individuals who have already developed the disease and a set of control patients who have similar characteristics to the cases, but who haven't developed the disease. One then compares the proportion of cases exposed to the risk factor to the proportion of controls who were exposed.

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