Regression models

In the previous chapter we considered situations where the data may be summarized into one or a few counting processes registering the occurrences of an event of interest. Such situations occur when the population in question is grouped into a few subpopulations according to the value of one or two categorical covariates. However, usually there are more than two covariates of interest in a study, and some of them may be numeric. Then, as in almost all parts of statistics, grouping is no longer a useful option, and regression models are called for. For regression models we have to consider one counting process for each individual under study. Specifically, if we have data from n individuals, we consider the counting processes N 1,N 2, … ,N n with N i (t) counting the number of occurrences of the event of interest for individual i in [0, t] (Section 1.5.2). For survival data N i (t) = 1 if by time t the event has been observed to occur for individual i, otherwise N i (t) = 0. More generally, we consider situations where the event in question may occur more than once for each individual. For such recurrent event data the process N i (t) may take integer values larger than 1.