Consider an intervention to reduce bloodstream infections. The intervention aims to reduce the time over which patients are exposed to bloodstream infections by prompting clinicians to remove intravenous central lines earlier rather than later. Intravenous exposure is indeed reduced. But bloodstream infection rates go up. How can this be?
Well it depends on the denominator. If this is days exposed to the device, then the denominator deflates as a result of the intervention, artificially inflating the rate. Population at risk might be a better denominator here, unless there is a difference in death rates after discharge by intervention. A way to proceed when there is a choice between incidence rate (denominator = units of time), and incidence proportion (denominator = population at risk), is a competing risk analysis. The CLAHRC WM Director strongly recommends an excellent article brought to his attention by News Blog reader Sam Watson. It not only explains the algebra of competing risk analysis, but also the history. The concept is not new and the method was used by Florence Nightingale and her statistical colleague William Farr. But even they were not the first; the idea harks back to the great Bernoulli who did not just discover that pressure drops when a fluid passes through a constriction, but also worked on a small pox vaccine in 1760.
— Richard Lilford, CLAHRC WM Director
- Beyersmann J, & Schrade C. Florence Nightingale, William Farr and competing risks. J R Statist Soc (A). 2016