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).

You can find an earlier version of this page on my original website.