When should I use an odds ratio instead of a relative risk?

Use the odds ratio for case-control studies, where people are selected because they are ill (cases) or not (controls), so you cannot calculate the risk of illness. In a cohort study or an outbreak where you know everyone exposed, calculate the relative risk. When the illness is rare, the odds ratio is close to the relative risk.

What does an odds ratio of 1 mean?

An odds ratio of 1.0 means the odds of exposure are the same among cases and controls — no association. Above 1, the exposure is associated with illness; below 1, it is associated with less illness (a possible protective factor).

How is the 95% confidence interval calculated?

This calculator uses the Woolf (logit) method: exp(ln OR ± 1.96 × √(1/a + 1/b + 1/c + 1/d)). If the interval does not include 1, the association is statistically significant at the 5% level.

Free tool · CIC® exam topic

Odds ratio calculator

Enter the four cells of a case-control 2×2 table to get the odds ratio and its 95% confidence interval.

Case-control 2×2 table
	Cases (ill)	Controls (well)
Exposed	Exposed, Cases (ill) (a)	Exposed, Controls (well) (b)
Not exposed	Not exposed, Cases (ill) (c)	Not exposed, Controls (well) (d)

Example: 20 of 30 cases and 15 of 60 controls ate the suspected food.

Result

Odds ratio: 6.00
95% confidence interval: 2.30 – 15.64

Cases had 6.00 times the odds of exposure compared with controls. The 95% confidence interval does not include 1, so the association is statistically significant at the 5% level.

What is an odds ratio?

The odds ratio compares the odds of exposure among people who are ill (cases) with the odds of exposure among people who are well (controls). It is the measure of association for case-control studies, which are common in outbreak investigations when you cannot identify everyone who was exposed.

Odds ratio formula

With the 2×2 table laid out as CDC does — exposure in rows, illness in columns:

	Cases	Controls
Exposed	a	b
Not exposed	c	d

Odds ratio = (a × d) ÷ (b × c)

Worked example

In the example above, 20 cases and 15 controls were exposed; 10 cases and 45 controls were not. The odds ratio is (20 × 45) ÷ (15 × 10) = 900 ÷ 150 = 6.00, with a 95% confidence interval of 2.30 – 15.64. Cases had 6.00 times the odds of exposure compared with controls. The 95% confidence interval does not include 1, so the association is statistically significant at the 5% level.

How to interpret it

OR = 1: no association between exposure and illness.
OR > 1: the exposure is associated with illness — the larger, the stronger.
OR < 1: the exposure is associated with less illness (possibly protective).
If the 95% confidence interval includes 1, the association is not statistically significant at the 5% level.

Test yourself: a CIC-style question

A case-control study investigating a healthcare-associated Legionella outbreak finds an odds ratio of 6.3 for patients who used the hospital shower. What does this suggest?

Patients who used the shower were 6.3 times less likely to develop Legionella
Shower use is a risk factor: patients who used it had 6.3 times the odds of disease
An odds ratio of 6.3 has no meaning without a p-value
The shower is the confirmed source and the investigation is complete

Show answer

B. Shower use is a risk factor: patients who used it had 6.3 times the odds of disease

An odds ratio of 6.3 means cases had 6.3 times the odds of shower exposure compared with controls — a strong association that justifies environmental sampling and remediation. Significance depends on the confidence interval, and an association alone does not prove the source.

Questions like this come up in the Surveillance and Epidemiologic Investigation domain of the CIC® exam. The 654 questions in the app each come with a written explanation.

FAQ

When should I use an odds ratio instead of a relative risk?: Use the odds ratio for case-control studies, where people are selected because they are ill (cases) or not (controls), so you cannot calculate the risk of illness. In a cohort study or an outbreak where you know everyone exposed, calculate the relative risk. When the illness is rare, the odds ratio is close to the relative risk.
What does an odds ratio of 1 mean?: An odds ratio of 1.0 means the odds of exposure are the same among cases and controls — no association. Above 1, the exposure is associated with illness; below 1, it is associated with less illness (a possible protective factor).
How is the 95% confidence interval calculated?: This calculator uses the Woolf (logit) method: exp(ln OR ± 1.96 × √(1/a + 1/b + 1/c + 1/d)). If the interval does not include 1, the association is statistically significant at the 5% level.

Sources

Checked against these sources on October 21, 2026. For education and CIC® exam preparation only — not a substitute for your facility’s policies, NHSN’s official reports, or clinical judgment. Calculations run in your browser; nothing you enter is sent anywhere.