Survival models for censored point processes
In studies of recurrent events, there can be a lot of information about a cohort over a period of time, but it may not be possible to extract as much information from the data as would be liked. This thesis considers data on individuals experiencing recurrent events, before and after they are randomised to treatment. The prerandomisation outcome is a period count, while the post-randomisation outcome is a survival time. Standard survival analysis may treat the pre-randomisation period count as a covariate, but it is proposed that point process models will give a more precise estimate of the treatment effect. A joint model is presented, based on a Poisson process with individual frailty. The pre-randomisation seizure counts are distributed as Poisson variables with rate depending on explanatory variables as well as a random frailty. The model for the post-randomisation survival times is the exponential distribution with the same individual seizure rate, modified by a multiplicative treatment effect. A conjugate mixing distribution (frailty) is used, and alternative mixing distributions are also discussed. The model is motivated by and illustrated on individual patient data from five randomised trials of two treatments for epilepsy. The data are presented, and the standard analyses are contrasted with the results of the joint model. This thesis also considers the relative efficiency of the joint model compared to other survival models. Finally, some extensions to the model are considered, including a more general non-conjugate mixing distribution, and alternative ways of including explanatory variables in the joint model.