Odds ratio (OR)

Odds ratio (OR): , Θ cross-product ratio relative odds Quotient obtained by dividing one set of odds by another. The term “odds” or “odds ratio” is defined differently according to the situation under discussion.

Cross-product ratio

The odds ratio is sometimes called the cross-product ratio because the numerator is based on multiplying the value in cell “a” times the value in cell “d,” whereas the denominator is the product of cell “b” and cell “c.” A line from cell “a” to cell “d” (for the numerator) and another from cell “b” to cell “c” (for the denominator) creates an x or cross on the two-by-two table.

Exposure and Disease

Exposure and Disease in a Hypothetical Population of 10,000 Persons
	Disease	No Disease	Total	Risk
Exposed	a = 100	b = 1,900	2,000	5.0%
Not Exposed	c = 80	d = 7,920	8,000	1.0%
Total	180	9,820	10,000

Use the data in table above to calculate the risk and odds ratios.

Risk ratio

5.0 ⁄ 1.0 = 5.0

Odds ratio

(100 × 7,920) ⁄ (1,900 × 80) = 5.2

Notice that the odds ratio of 5.2 is close to the risk ratio of 5.0. That is one of the attractive features of the odds ratio — when the health outcome is uncommon, the odds ratio provides a reasonable approximation of the risk ratio. Another attractive feature is that the odds ratio can be calculated with data from a case-control study, whereas neither a risk ratio nor a rate ratio can be calculated.

Case control study

In a case-control study, investigators enroll a group of case-patients (distributed in cells a and c of the two-by-two table), and a group of non-cases or controls (distributed in cells b and d).

The odds ratio is the measure of choice in a case-control study. A case-control study is based on enrolling a group of persons with disease (“case-patients”) and a comparable group without disease (“controls”). The number of persons in the control group is usually decided by the investigator. Often, the size of the population from which the case-patients came is not known. As a result, risks, rates, risk ratios or rate ratios cannot be calculated from the typical case-control study. However, you can calculate an odds ratio and interpret it as an approximation of the risk ratio, particularly when the disease is uncommon in the population.

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