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# Measure of Association - Rate Ratio

## Definition of Rate

In a cohort study:

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

We have limited the use of the word rate to measures of incidence based on person-time rates,

## Definition of Rate Ratio

Rate ratio = ratio of 2 incidence rates = relative rate

If we have limited the use of the word rate to measures of incidence based on person-time rates,

• so a ratio of two such measures is called a rate ratio.

## Example: Comparing of Two Person-time Rates with a Ratio

Ratio of two person-time rates

• (NOTE: denominators of two person-time rates must be in the same units)
In the Ray paper, the following data were given:
• Rate NSAID use = 12.02 per 1000 person-years
• Rate for non use = 11.86 per 1000 person-years
• Rate ratio = 1.01
This is the example of forming incidence rates in a cohort with a time varying exposure, in this case use of non-steroidal anti-inflammatory medications (NSAIDS).

The basic measure of association reported was the rate ratio,

• The event rate during the person-time of NSAID use divided by the rate during the person-time of no use.
A rate ratio is simply the ratio of two rates
• Is the analogue of the risk ratio for person-time measures of incidence.
It should be clear that an incidence rate should not be compared to cumulative incidence:
• A ratio using one of each type of incidence measure would not be interpretable.
In comparing two incidence rates, the important thing to remember is that the time units of the two measures forming the ratio must be the same.
• In the example above, if the first rate were per 100 person-years and the second remained per 1,000 person-years, the rate ratio would jump up to 10.1, and it would appear there was a strong association when there was no association.
The authors correctly reported their measure of association as a rate ratio.

## Example: Rate Ratio Described as Relative Risk

Cancer mortality rate ratio by BMI group Calle 2003:

1. 6 per 100,000 person-years ( BMI 40+)
2. 3 per 100,000 person-years ( BMI < 40)

• Rate ratio = 1.46
Described as relative risk in the article (very common practice)

Although we think everyone should use the rate ratio (relative rate is a defensible alternative since the term relative implies a ratio),

• rate ratios are probably reported as relative risks
• about as often as they are called rate ratios or relative rates

## References

E. E., Rodriguez, C., Walker-Thurmond, K., & Thun, M. J. (2003). Overweight, obesity, and mortality from cancer in a prospectively studied cohort of U.S. adults. N Engl J Med, 348 (17), 1625-1638

W. A., Stein, C. M., Daugherty, J. R., Hall, K., Arbogast, P. G., & Griffin, M. R. (2002). COX-2 selective non-steroidal anti-inflammatory drugs and risk of serious coronary heart disease. Lancet, 360 (9339), 1071-1073.

Jeff Martin, MD

-- MaryB? - 10 Mar 2009

Topic revision: r9 - 04 May 2009 - 18:16:20 - MaryB?
CTSpedia.RateRatio moved from CTSpedia.StudyAssocRate on 29 Apr 2009 - 23:05 by MaryB? - put it back

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