Calculating rates (April 6, 2007) Category: Poisson regression
Someone on the MedStats discussion group asked how to calculate a rate of needlestick incidents. The answer is quite simple, but there are a variety of possible responses.
The formula for a rate is x/y, or simple division. The Wikipedia definition of a rate is helpful.
A rate is a special kind of ratio, indicating a relationship between two measurements with different units, such as miles to gallons or cents to pounds. For example, suppose one spends 9 dollars on 2 pounds of candy. The rate $9 / 2 pounds compares the money spent to the number of pounds of candy. en.wikipedia.org/wiki/Rate
In this particular case, the numerator is the number of needlestick incidents and the denominator is some other type of measurement. Typically the denominator is a measure of workload, area, volume or time. So one possible denominator is simply time itself. Divide the 6 needlesticks by the 30 days in a month to produce a rate of 0.2 needlesticks per day.
Another possibility is the number of needles used in that month. Divide the 6 needlesticks by the 6,000 needles used in the month to produce a rate of 0.001 sticks per needle used. This particular rate is perhaps more accurately called a probability.
A third possibility is the number of employees. Divide the 6 needlesticks by the 120 employees who regularly use needles to produce a rate of 0.05 needlesticks per employee.
Other possibilities, such as dividing by the number of patient days, may also make sense.
I've been very interested in rates, especially rates of safety events. I believe that you can get a more meaningful perspective on safety events by looking at the inverse of the rate. For example, if you experience 6 needlesticks in a 30 day month, that means that you have to wait an average of 30/6=5 days between needlesticks on average. If you experience 6 needlesticks out of every 6,000 needles distributed, then you have a problem with every thousandth needle on average. If you have 120 employees and 6 experience needlesticks, every 20th employee on average has been injured.
In some contexts, the inverse of the rate can be interpreted as the number needed to harm. See
and related links on that page for an interesting example and further elaboration about this. I'm also starting to pull together some of the formulas needed for confidence intervals for count data.
This webpage was written by Steve Simon and was last modified on 07/08/2008.~~~