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# Risk Ratio versus Rate Ratio

## RR

Relative risk or RR is very common in the literature, but may represent:

There can be substantial difference in the association of a risk factor with
In the general medical literature, rate is often incorrectly used for prevalence measures.

These inconsistencies are even greater and are compounded by the fact that an abbreviation for both a risk ratio and a rate ratio is RR.

• Often RR is used to mean relative risk, which is taken loosely to include several different ratio measures.

## Relative Risk

Risk is based on proportion of persons with disease = cumulative incidence
• Risk ratio = ratio of 2 cumulative incidence estimates = relative risk
Since all of the measures are ratios, either of probabilities or of odds, it is clearer and simpler to use the word ratio in describing each type.

Risk reflects the proportion of persons experiencing the event, so it follows that comparing two cumulative incidences is called a risk ratio.

## Relative Rate

Rate is based on events per person-time = incidence rate

• Rate ratio = ratio of 2 incidence rates = relative rate
Rate should be limited to measures of incidence based on person-time rates, so a ratio of two such measures is called a rate ratio.

## Comparison: Risk Ratio and Rate Ratio

Risk must be a proportion; therefore, it must be between 0 and 1
• Thus in comparing 2 groups high risk in unexposed group limits how large ratio can be
• For example, risk in unexposed group = 0.7 means
• maximum risk ratio = 1.0/0.7 = 1.42
Rates are not restricted between 0 and 1
• If exposed rate = 10/100 person-years and
• unexposed rate = 5/100 person-years, risk (cumulative incidence)
• in 2 groups after 20 years = 0.88 and 0.64.
• Risk ratio would be 0.88/0.64 = 1.38
• Rate ratio = 10/5 = 2.0.

## Rate Ratio vs Risk Ratio - What do you report?

Is the risk ratio or 1.38 telling you something different than the rate ratio of 2.0?

• It would be perfectly legitimate to report either risk ratio or rate ratio, or even both, but your choice would depend on your research question and what you were trying to emphasize.
• So they are telling you something different even though they use the same data.

### Risk Ratio: Long-Term Probability of the Disease

You might prefer the risk ratio if your emphasis is on how different the long-term probability of the disease is for an exposed and an unexposed population.

### Rate Ratio: Disease Causality

If your emphasis is on whether the exposure is causal for the disease, the rate ratio would be preferable because it preserves the larger relative force on disease occurrence of being exposed compared to being unexposed.

So this comparison illustrates why we refer to the rate as the more fundamental measure of disease occurrence. When we form ratio (relative) measures with it, it is not subject to the artifact of the ceiling effect that we see here with ratio measures of two proportions.

Topic revision: r6 - 01 Jun 2009 - 14:41:35 - MaryB?

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