Relative risk

The relative risk is a term descriptive statistics. It expresses the factor by which a risk is different (for example, a disease) into two groups. The ratio of the probabilities for an event / feature, so it is displayed. The relative risk, the importance of a risk factor, calculated as the quotient of these two probabilities. The risk quotient thus provides information about the strength of the association between exposure and disease, and is therefore well suited for studies on the causes of disease.

In medical statistics often results in the following data situation:

The relative risk is calculated here as follows

Or formally expressed using the conditional probability:

The relative risk takes values ​​between 0 and infinity. A value of 1 means that the risk for both groups is the same. Accordingly, there is no evidence for an association between the studied disease and the risk factor. If the value is greater than 1, which is an indication of a possible positive association between a risk factor such as smoking and disease. Is the relative risk of less than 1, the exposure has a protective ( protective ) effects, as is the case for example in vaccines.

The extent to which a relative risk of about 1 is to critically evaluate the risk factors for carriers, depends on various factors and therefore must be considered in more detail. Heart attacks are in Germany a common disease and cause of death. " Smokers have an approximately 2.5 - times as high cardiac risk as Non smoking. " With the risk factor smoking is a frequent morbidity and mortality thus more frequent and more relevant. Another meaning has a high relative risk, in cases where the risk of non- exposed persons is very small. For example, trained runners 30 minutes after a marathon 15 times as a high risk of cardiac death as in everyday life. However, since the risk is generally very low, is a high relative risk can not be overstated. Compared with the relative risk pulling the attributable risk therefore also consider how often a disease at all.

An example with fictitious data

Suppose we want to investigate the association between the occurrence of heart attacks and smoking. We observed 10,000 patients and determines whether they smoke or not, and whether they have ever had a heart attack. It results in the following crosstab:

It results in the following relative risk

That is, the risk of suffering a heart attack, is 7.4 times as high as among non-smokers among smokers.

Connection with the odds ratio

The relative risk is related to the odds ratio. Unlike the odds ratio can be calculated the relative risk but only if the marginal probabilities of the frequency table are random. That the number of patients can not be fixed by the study design. If cancer, the probability is low, odds ratio and relative risk are approximately equal.

So with the above example, the comparison looks like this: