The relative risk and the odds ratio are measures of association between exposure status and disease outcome in a population.
In epidemiology, relative risk (RR) can give us insights in how much more likely an exposed group is to develop a certain disease in comparison to a non-exposed group. Once we know the exposure and disease status of a research population, we can fill in their corresponding numbers in the following table.
To calculate the relative risk, we then use the following formula:
Basically, we divide the proportion of sick people in the exposed group by the proportion of sick people in the non-exposed group. So the formula for relative risk can also be expressed as follows:
Example 1: We want to know the relative risk of suffering a heart attack amongst long-term users of anabolic steroids compared to a control group of people who do not use anabolic steroids. We follow a group of fanatic gym attendees for 5 years in a prospective cohort study. In our cohort study, 80 participants happen to be steroid users, while 240 participants are non-steroid users. The 2×2 table with the exposure status and disease status can be seen below.
Amongst the steroid users, 5 out of 80 people suffered a heart attack during the study. In comparison, amongst the non-steroid users, 3 out of 240 people suffered a heart attack. The probability of suffering a heart attack is therefore 5.00 times higher for steroid users than for non-steroid users: (5/80) / (3/240) = 5.00.
The odds ratio illustrates how strongly the presence or absence of a certain characteristic relates to the presence or absence of another characteristic. When applying it in public health, we can use the odds ratio to see if a certain outcome (e.g. developing ischemic heart disease) is associated with exposure to a hypothesized risk factor (e.g. smoking). With an odds ratio, the outcome can be the starting point with which we can determine the relative odds of someone having been exposed to a risk factor. Alternatively, we can also use it to describe the ratio of disease odds given the exposure status. Once we know the exposure and disease status of a research population, we can fill in their corresponding numbers in the following table.
To calculate the odds ratio, we use one of the following formulas (both give the same outcome):
Example 2: We compare smokers and non-smokers with regard to the presence of ischemic heart disease. The following table shows the results.
We can now calculate the odds ratio: (10/40) / (5/45) = 2.25