## What is a Rate Ratio?

A rate ratio (sometimes called an incidence density ratio) is a measure of association that compares the incidence of events happening at different times. It is used extensively in epidemiology. The formula is the ratio of exposed groups to unexposed groups:

Rate ratio = IR_{e} / IR_{u}

where:

IR = incidence rate

e = exposed

u = unexposed

The rate ratio tells you how more (or less) common a particular event happened in an exposed group. For example, a ratio of 5 means that the event occurred at 5 times the rate in the exposed group than in the non-exposed group.

**Example 1:** A study is undertaken to find out whether depression risks are higher for people working minimum wage than other groups. The study finds that the frequency for severe depression in people who earn minimum wage is 27 out of 1,000 people. For higher-income earners, the frequency is 3 out of 1,000. What is the rate ratio?

Rate ratio = IR_{e} / IR_{u}

Rate ratio = 27/3 = 9.

This means that people who earned minimum wage had 9 times the rate of depression than people earning higher incomes.

Rate ratios are sometimes interpreted as *risk ratios*. In other words, the above ratio would be reported as “people earning minimum wage had 9 times the **risk **of being depressed compared to higher incomes. However, it’s more accurate to report it in terms of rate rather than risk.

**Example 2:** Two events were held at a church, one on Saturday, and one on Sunday. Both were catered by “XYZ Caterers.” Out of 70 guest who attended the reception on Saturday, 20 people developed signs of food poisoning. Out of 60 guest who attended the reception on Sunday, 5 developed signs of food poisoning. Which event was the likely cause of the food poisoning?

Illness rate (Saturday) = 20/75=27%

Illness rate (Sunday) = 5/60 = 8%

As more people were ill on Saturday, it looks like Saturday was the exposed group and Sunday was the unexposed group, so the rate ratio is: 27/8 = 3.4. People attending the event on Saturday had 3.4 times the rate of illness than people who attended the event on Sunday. This makes it the likely source of the food poisoning.

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*Statistical concepts explained visually* - Includes many concepts such as sample size, hypothesis tests, or logistic regression, explained by Stephanie Glen, founder of StatisticsHowTo.

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