Medical studies often compare how often an outcome happens in one group versus another. A 2 by 2 table organizes the data by exposure or treatment status and by whether the outcome occurred. From this table, students can calculate absolute risk, relative risk, and odds ratio.
These measures help researchers describe whether an exposure is linked to higher, lower, or unchanged chance of disease.
Key Facts
- For a 2 by 2 table with exposed disease = a, exposed no disease = b, unexposed disease = c, unexposed no disease = d.
- Risk in exposed group = a / (a + b).
- Risk in unexposed group = c / (c + d).
- Relative risk = [a / (a + b)] / [c / (c + d)].
- Odds in exposed group = a / b, and odds in unexposed group = c / d.
- Odds ratio = (a / b) / (c / d) = ad / bc.
Vocabulary
- Absolute risk
- Absolute risk is the probability that an outcome occurs in a specific group.
- Relative risk
- Relative risk is the ratio of the risk in an exposed or treated group to the risk in an unexposed or control group.
- Odds
- Odds compare the number of times an outcome occurs to the number of times it does not occur.
- Odds ratio
- An odds ratio compares the odds of an outcome in one group with the odds of the outcome in another group.
- 2 by 2 contingency table
- A 2 by 2 contingency table is a four-cell table that counts subjects by group status and outcome status.
Common Mistakes to Avoid
- Using odds when the problem asks for risk. Risk uses outcome cases divided by the total number in that group, while odds use outcome cases divided by non-cases in that group.
- Flipping the comparison groups. Relative risk and odds ratio depend on which group is in the numerator, so reversing the groups changes the value to its reciprocal.
- Interpreting a relative risk of 2 as a 2 percentage point increase. A relative risk of 2 means the risk is twice as large, not that the absolute risk increased by 2 percent.
- Treating odds ratio and relative risk as always identical. They are close when the outcome is rare, but they can differ greatly when the outcome is common.
Practice Questions
- 1 In a study, 30 of 200 exposed people develop a disease, while 10 of 200 unexposed people develop it. Find the risk in each group and the relative risk.
- 2 A 2 by 2 table has a = 24, b = 76, c = 12, and d = 88. Calculate the odds in each group and the odds ratio.
- 3 A treatment study reports a relative risk of 0.60 for a bad outcome. Explain in words what this means and whether it suggests the treatment is associated with higher or lower risk.