**StATS: ****Incidence density ratio (April 19, 2005)**

Someone asked me about a technical term, incidence density ratio, that was used in an article:

**Comprehensive discharge planning and home follow-up of hospitalized elders: a randomized clinical trial.**Naylor MD, Brooten D, Campbell R, Jacobsen BS, Mezey MD, Pauly MV, Schwartz JS. Jama 1999: 281(7); 613-20. [Medline]

Looking at the article, they only mention the term once and in context with another term, rate ratio, that you are probably familiar with. A rate represents a number of events over time (or sometimes over area), and that makes sense here. You have a number of readmissions per week/month, or whatever. A rate ratio compares the rates of two different groups. Again that makes sense.

There's something a bit tricky about this data in that they used a proportional hazards regression, and the output is actually a hazard ratio. That is actually just a technical distinction, though, because a hazard ratio can again be thought of as a rate ratio. I need to write a web page about this, because it is not immediately obvious. The term incidence is often contrasted with prevalence, and you can find a discussion of this distinction in most Epidemiology text books.

All of this, quite honestly, is a distinction without a difference. The actual statistics they cite in the results section are:

Control group patients were more likely than intervention group patients to be readmitted at least once ((Table 2); 37.1% vs 20.3%; P<.001; relative risk, 1.8; 95% CI, 1.3-2.6).

That seems pretty easy to interpret to me, and knowing whether the numbers represent rate ratios, incidence ratios, or hazard ratios is only of academic importance.

I have a few web pages that discuss some of the technical issues if you are curious. The December 15, 2004 weblog entry on Neyman bias draws a careful distinction between incidence and prevalence. I also have September 15, 2004 weblog entry on rates versus proportions. Certain statistical models, such as a Poisson regression model will also produce incidence density ratios. I have to write up a web page about this model when I have time. It is on my list of unfinished business (Coming Soon! March 22, 2005 weblog entry).

This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Measuring benefit/risk.