Applied Bayesian Modelling - Free

Applied Bayesian Modelling. Peter CongdonCopyright © 2003 John Wiley & Sons, Ltd.ISBN: 0-471-48695-7CHAPTER 9Survival and Event HistoryModels9.1 INTRODUCTIONProcesses in the lifecycle of individuals including marriage and family formation,changes in health status, changes in job or residence may be represented as eventhistories. These record the timing of changes of state, and associated durations ofstay, in series of events such as marriage and divorce, job quits and promotions.Many applications of event history models are to non-repeatable events such as mortality,and this type of application is often called survival analysis. Survival and eventhistory models have grown in importance in clinical applications (e.g. in clinical trials),in terms of survival after alternative treatments, and in studies of times to diseaserecurrence and remission, or response times to stimuli.For non-renewable events the stochastic variable is the time from entry into observationuntil the event in question. So for human survival, observation commences at birthand the survival duration is defined by age at death. For renewable events, the dependentvariable is the duration between the previous event and the following event. We maybe interested in differences either in the rate at which the event occurs (the hazard rate),or in average inter-event times. Such heterogeneity in outcome rate or inter-eventdurations may be between population sub-groups, between individuals as defined bycombinations of covariates, or as in medical intervention studies, by different therapies.Thus, in a clinical trial we might be interested in differences in patient survival or relapsetimes according to treatment.Whereas parametric representations of duration of stay effects predominated in earlyapplications, the current emphasis includes semiparametric models, where the shape ofthe hazard function is essentially left unspecified. These include the Cox proportionalhazards model (Cox, 1972) and recent extensions within a Bayesian perspective such asgamma process priors either on the integrated hazard or hazard itself (Kalbflesich,1978; Clayton, 1991; Chen et al., 2000). While the shape of the hazard function in time isoften of secondary interest, characteristics of this shape may have substantive implications(Gordon and Molho, 1995).Among the major problems that occur in survival and inter-event time modelling is aform of data missingness known as `censoring'. A duration is censored if a respondentwithdraws from a study for reasons other than the terminating event, or if a subject does