Lesson 5: Understanding 2×2 tables

Visualising possible relationships between disease and exposure

By the end of this step, you should be able to describe the 2×2 table and discuss its uses in epidemiology.

What is a 2×2 table?

This is a table with 2 rows and 2 columns. For example, if there were 10 girls and 6 boys in a school class, and 7 girls and 3 boys wore spectacles, the 2×2 table would look like this (it is helpful to put in the row and column totals).

In epidemiology, we use 2×2 tables a lot, particularly when trying to understand the relationship between a disease and hypothesised exposure. The presence and absence of disease in the study population is indicated at the top and exposed and unexposed participants on the y-axis.

Why do we use 2×2 tables?

2×2 tables are very useful when calculating odds ratios and relative risk. You will often see the table written as shown below, with the letters used in formulae for calculating risk.

However, rather than remembering the letters, it is important to know what goes in each box if you have some data.

• In ‘a’, you put the number of people with the disease who have been exposed.
• In ‘b’, you put the number of people without the disease who have been exposed.
• In ‘c’, you put the number of people with the disease who have not been exposed
• In ‘d’, you put the number of people without the disease who have not been exposed.

Using a 2×2 table to calculate the odds ratio

We’ll use the results of a case-control study of age-related macular degeneration (AMD) and the effect of smoking to show how 2×2 tables can be used to calculate the odds ratio. The disease is AMD and the exposure is having ever being a smoker (shown as exposure+) versus having never being a smoker (exposure-). There are 80 cases who have been smokers, and 20 cases who have not been smokers. There are 40 controls who have been smokers, and 60 controls who have not been smokers.

Here is the 2×2 table showing this information.

Using a 2×2 table to calculate relative risk

A 2×2 table can also be used to calculate the relative risk or risk ratio, but just be aware that the calculation is slightly different. Here we calculate the risk of having the disease if exposed and the risk of having the disease if unexposed.

Remember that the type of measure used depends on the type of study design. Using the same 2×2 table, the calculations are as follows:

In conclusion
A 2×2 table is a very useful way to set out the relationship between disease and exposure. We can then use this information to further calculate the odds ratios and risk ratios.