Odd Ratio and Relative Risk

Odd Ratio and Relative Risk Difference

Odds Ratio and Relative Risk are two types of measures for comparing the risk of an event in two groups. These measures are used to assess the strength of an association between two variables. The Odds Ratio and Relative Risk are usually used in epidemiological studies.

Relative risk is a measure of risk difference between two groups that have been divided into categories based on their exposure or lack thereof to an independent variable (e.g., smoking status). It is calculated by:

Relative risk = incidence rate for group A /incidence rate for incidence B

Ø  For example, if there were 100 people with cancer and 100 people without cancer, and ten people with cancer died from their disease, we would say that ten deaths occurred among those with cancer compared to 0 deaths among those without cancer.

Ø  Relative risk compares the risk of exposed people versus non-exposed people:

For example, if 200 out of 1000 unexposed people develop flu, and 300 out of 1000 exposed people develop flu, then the relative risk would be 2:1 or 2;

that means you have twice as much chance of developing flu if you are exposed to something as if you are not exposed.

This would mean that there was a 10:0 relative risk ratio between those with and without cancer when it came to death from their disease.

The odds ratio is a measure of association between two binary variables. So when we are talking about the odds of something happening, we are talking about its probability.

It can be calculated as:

Odds ratio =odds outcome/measure of association between two binaries

Ø  For example, if there are 100 people with cancer and 500 people without cancer; the exposed group will have 50 with cancer and 350 without cancer; this would give you a ratio of (50/350) = 1:2

Ø  If there were 1000 people with cancer, then there would be 500 exposed and 500 unexposed, giving us an odds ratio of (500/500) = 1:1

In other words, the odds are the number of times something will happen divided by the total number of possible outcomes.

For example, if a woman has two children and three miscarriages, there is an odd ratio of 1:3. 

References

Cummings, P. (2009). The relative merits of risk ratios and odds ratios. Archives of pediatrics & adolescent medicine, 163(5), 438-445.

Schmidt, C. O., & Kohlmann, T. (2008). When to use the odds ratio or the relative risk?. International journal of public health, 53(3), 165.

Szumilas, M. (2010). Explaining odds ratios. Journal of the Canadian academy of child and adolescent psychiatry, 19(3), 227.

Tenny, S., & Hoffman, M. R. (2017). Relative risk.