Aspects of the analysis of multivariate failure time data

Multivariate failure time data arise in various forms including recurrent event data when individuals are followed to observe the sequence of occurrences of a certain type of event; correlated failure time when an individual is followed for the occurrence of two or more types of events for which the individual is simultaneously at risk, or when distinct individuals have dependent event times; or more complicated multistate processes when individuals may move among a number of discrete states over the course of a follow-up study and the states and associated sojourn times are recorded. Here we provide a critical review of statistical models and data analysis methods for the analysis of recurrent event data and correlated failure time data. This review suggests a valuable role for partially marginalized intensity models for the analysis of recurrent event data, and points to the usefulness of marginal hazard rate models and nonparametric estimates of pairwise dependencies for the analysis of correlated failure times. Areas in need of further methodology development are indicated. MSC: 62N01, 62N02, 62N03,62H10, 92B15