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Relative risk is a statistical term used to describe the risk that a particular event will occur in one group but not another. It is often used within epidemiology and evidence-based medicine, where the relative risk helps to identify the risk of developing a particular disease after an exposure (i.e. after medication / treatment or an environmental exposure) relative to the risk of developing a disease in the absence of the exposure. This article demonstrates how the relative risk calculation works.

To step

1. Draw a table of 2x2 cells. A 2x2 table is the basis for many epidemiological calculations.
   • Before you can draw such a table, you need to understand the variables:
     • A = the number of people who have both been exposed and developed the disease
     • B = the number of people who were exposed but did not develop the disease
     • C = the number of people who have not been exposed but who have developed the disease
     • D = the number of people who have neither been exposed nor developed the disease
   • Let's work out an example of a 2x2 table.
     • A study looks at 100 smokers and 100 non-smokers, and tracks the development of lung cancer within these groups.
     • We can immediately fill in part of the table. The disease is lung cancer, the exposure is smoking, the total numbers for each group are 100, and the total of all people in the study is 200.
     • At the end of the study, it was found that 30 of the smokers and 10 of the non-smokers had developed lung cancer. Now we can fill in the rest of the table.
     • Because A = the number of exposed people who got the disease (i.e. smokers who got lung cancer), and we know it's 30. We can calculate B simply by subtracting A from the total: 100 - 30 = 70. Likewise, C is the number of non-smokers who have developed lung cancer (and we know this is 10), and D = 100 - 10 = 90.
2. Calculate the relative risk using the 2x2 table.
   • The general formula for the relative risk, using a 2x2 table, is:
     • ${ displaystyle RR = { frac {A / (A + B)} {C (/ C + D)}}}$Interpret the results of relative risk.
       • If the relative risk is 1, then there is no difference in risk between the two groups.
       • If the relative risk is less than 1, then there is less risk in the exposed group compared to the unexposed group.
       • If the relative risk is greater than 1 (as in the example), then there is more risk in the exposed group compared to the unexposed group.

Tips

• Studies that are designs such as cohort studies and clinical studies allow the investigator to calculate incidence, as opposed to case-control studies. The relative risk can thus be calculated for cohort studies and clinical studies, but not for case-control studies. Probability ratio can be used to estimate the relative risk for a case-control study.