William Farr and Florence Nightingale can no longer defend themselves against the misrepresentation of their work on hospital statistics by Dr. Iezzoni [1]. They calculated mortality per person-time of observation, which is one of the two correct ways to calculate incidences on hospital data [2].

Incidences on hospital data can be obtained by following each patient from admission until discharge (to calculate cumulative risks) or by dividing the number of events by the total person-time spent in the hospital. A third statistic divides the number of events by the number of admissions (or discharges); this technique was advocated by Farr's critics. That this third method yields a meaningless ratio was already discerned by Farr in 1885 and by Greenwood in 1948 [3]. The ratio depends on the turn-over of patients and does not consider observation time. It is still mistakenly used in the current literature because of its unfortunate resemblance to cumulative risk [2]. An example: An intensive care unit with 100 admissions per month and a mean length of stay of 4 days might record 20 nosocomial infections, yielding a ratio of 20%; a long-stay hospital with 100 admissions per month and a mean length of stay of 14 days might also register 20 nosocomial infections, again yielding a ratio of 20%. The problem is clear: The volume of observation time is different in both situations. The incidence rate-5 infections/100 patient-days in the intensive care unit and 1.4 infections/100 patient-days in the long-stay hospital-reflects the fact that nosocomial infections occur more frequently in intensive care units than in long-stay hospitals.

Farr calculated the amount of person-time spent in hospital in different ways [3]. As a shortcut approximation, he used the number of persons present on a single day and took this as the average number of persons present during the year. This approach is similar to the calculation of population death rates, in which the number of persons present in the middle of the year is taken to be the average number present during the whole year. In later publications, Nightingale presents two calculations: the right one, using person-time denominators, and the poor one, using number of admissions. Nightingale and Farr compromised to soothe political attacks. This compromise is not the hidden "methodologic shift" that Dr. Iezzoni makes of it.

It can be understood why this calculation upset Farr's contemporaries and still upsets Dr. Iezzoni. A peculiar feature of the incidence calculated with person-time denominators is that the incidence can become larger than unity. In contrast to proportions or risks that range between 0 and unity, incidence rates range between 0 and infinity [4]. For example, for a given hospital bed that has been constantly occupied (such as a bed in an intensive care unit), three of the patients occupying that bed might have died in a year; this yields a mortality rate of 3 deaths per patient-year or "300 per cent of numbers constantly sick," as Farr called it. Farr and Nightingale could have improved the understanding of the incidence rate by using patient-days rather than patient-years in the denominator: Three deaths per patient-year is about the same as 1 death per 100 patient-days. The use of person-years is not "intentionally skewing statistics to bolster political arguments" as Dr. Iezzoni calls it. It is simply good epidemiology.