Applied Bayesian Modelling, 2nd Edition

Chapter 10Survival and event history models

10.1 Introduction

Processes (economic, demographic) in the life cycle of individuals may be represented as event histories. These record the timing of changes of state, and associated durations of stay, in series of events such as marriage and divorce, job quits and promotions. Event histories may also describe mechanical operating times (Hamada et al., 2008), and changes in political regimes (Box-Steffensmeier and Jones, 1997). Many applications of event history models are to non-renewable events such as mortality, and this type of application is often called survival analysis, with the stochastic variable being the time from entry into observation until the event in question. For renewable events the dependent variable is the duration between the previous event and the following event. Interest may focus on the instantaneous rate at which the event occurs (the hazard rate), or on average inter-event times. Heterogeneity in event rates or inter-event durations may be between population sub-groups, or between individuals defined by combinations of risk factors or therapies. A Bayesian inferential overview of survival models is provided by Ibrahim et al. (2001a), with computing options including BUGS (Mostafa, 2012), R-INLA (Martino et al., 2011), R2BayesX, BMA (http://cran.r-project.org/web/packages/BMA/index.html), and ddpsurvival (De Iorio et al., 2009).

Parametric representations of duration of stay and survival times are important ...