Models and Frameworks for Analysis of Recurrent Events

Abstract

From both a theoretical and a practical perspective, the counting process notation introduced in Section 1.3 provides a convenient framework for the treatment of recurrent events. For now we dispense with subscripts that denote individuals or units and let N(s, t) denote the number of occurrences of some type of event over the time interval (s, t], for a specific individual. Unless stated otherwise, for convenience we assume that the process starts at t = 0 with N(0) = 0 and define N(t) = N(0, t) for t {>} 0. The process {{N(t),0} ≤t} is then the counting process for the event occurrences. For this and the following three chapters it is assumed that one type of event is of interest; multiple event types are considered in Chapter 6. In this section we derive probability distributions for observed event occurrence patterns and for gap times. The results, which are used in developing statistical methods throughout the book, are contained in Theorems 2.1 and 2.2. Readers who wish to focus on applications can safely skip over the derivations of these results.