Person-Time Units

It is common in medicine and epidemiology to express the frequency of occurrence of some event in terms of the number of events per person-time unit; for instance, the number of complications per 100 patient-days or the [Page 798]number of deaths per 100,000 person-years. A good example is the incidence rate, also known as the incidence density or force of morbidity or mortality. The incidence rate is calculated as

The numerator is always the number of new cases of the disease in the time period studied, and the denominator is the sum of the time of observation for all the subjects in the study. This fraction is usually converted to a standard unit such as cases per 100 to facilitate comparisons.

Person-time units are used when the subjects in a study have been observed for different lengths of time and have, therefore, been at risk for the event in question for longer or shorter times. Using a persontime denominator allows each subject to contribute to the denominator in proportion to the length of time they were observed and allows comparison across units (e.g., complication rates in different hospitals or mortality rates in different countries).

Consider the following example. We want to compare the quality of care for a particular condition in a particular year at two hospitals using the mortality rate for that condition. Table 1 presents hypothetical data on eight patients treated for this condition at two hospitals and includes the days observed (i.e., the number of days they were in that hospital and thus eligible for the event of death to occur at that hospital). Assuming this is the total patient population treated at those hospitals for that condition in the year under study, we can see that in Hospital A, two patients died (because they have a ‘Y’ for ‘yes’ in the ‘Event’ column), whereas in Hospital B, only one patient died. We might interpret this as meaning that Hospital A was somehow less safe or had a lower quality of care for this condition because they had two deaths per year versus one death per year for Hospital B, but we would be ignoring the fact that Hospital A had more patients at risk of death from this condition during this time period.

A more sensible comparison would be made using the mortality rate per 100 patient-days. In this case, Hospital A had 2 deaths per 100 patient-days, while Hospital B had 1 event in 20 patient-days or a rate of 5 deaths per 100 patient-days. By the criterion of mortality rate, Hospital A seems to be doing a better job in treating this condition. Of course, this example is greatly simplified, and hospital-to-hospital comparisons are generally done after correcting for expected mortality and morbidity, considering factors such as patient mix, but it illustrates why person-time units are commonly used in epidemiology.