Modeling and analysis of multiple-event survival data

Date of Completion

January 1996






Multivariate event time data arises frequently in both medical and industrial settings. In such data sets: event times are often associated with quite different occurrences, event times can not be considered as independent--the distribution of time to occurrence of one event may change after the occurrence of another, events can occur simultaneously, available covariate information may provide useful explanation. Censoring in some of the observations, both partial and complete, occurs.^ Several bivariate lifetime distributions have been developed over the last few decades. Few of them have been extended to higher dimensions (see Block, 1975). Most of these distributions arise as shock models which have been frequently used in reliability theory to describe certain processes that deteriorate over time. Considered in this way, we gain useful insight as well as variety of extensions. But as we incorporate more complex shock models, the likelihood of the models become quite complicated. We use a representation approach, as suggested by Proschan and Sullo (1974), to develop generalizations of the existing models utilizing more complex shock processes.^ Even the simplest bivariate models have enjoyed limited practical application, in both classical and Bayesian literature due to the intricate structure of the likelihood, which even makes the computation of MLE quite involved. However, a convenient data augmentation scheme eliminates the need for working with such intricate structure and hence as a byproduct, the generalizations to the above mentioned models can be fitted rather straightforwardly using simulation based methods. Here we take a Bayesian viewpoint to analyze a substantial data set involving event times for AIDS patients.^ Finally we address the problem of model choice. What is required is a model choice criterion which rewards both goodness-of-fit and parsimony, which penalizes inadequacy but also overfitting? We develop a generic criterion for handling multivariate data, possibly with partial or complete censoring of some of the survival times, which meets this requirement but, in addition, can be routinely computed from the output of the data augmentation fitting of the model. Hence an effective and convenient model screening criterion emerges. In summary, the scope of multiple event survival models is substantially advanced. ^