In previous chapters the basic unit of observation has been the individual patient. Sometimes, however, it makes more sense to analyze events per person–year of observation. This may be either because the data come to us in this form or because survival methods using suitable models are too complex and numerically intensive. For example, analyzing large cohorts with hazard regression models that have many time-dependent covariates can require substantial computation time. In this situation, converting the data to events per person–year of observation can greatly simplify the analysis. If the event rate per unit of time is low, then an excellent approach to consider is Poisson regression. We will introduce this technique in the next two chapters.

Elementary statistics involving rates

The incidenceI of an event is the expected number of events during 100 000 person–years of follow-up. Suppose that we observe d independent events during n person–years of observation, where d is small compared with n. Then the observed incidence of the event is Î = 100 000 × d/n, which is the observed number of events per 100 000 patient–years of follow-up. For example, Table 8.1 is derived from the 4699 patients in the didactic data set from the Framingham Heart Study (Levy, 1999). This data set contains a total of 104 461 person–years of follow-up. Let di be the number of CHD events observed in ni person–years of follow-up among men (i = 1) and women (i = 0), respectively.