Some recent developments for regression analysis of multivariate failure time data

Cox's seminal 1972 paper on regression methods for possibly censored failure time data popularized the use of time to an event as a primary response in prospective studies. But one key assumption of this and other regression methods is that observations are independent of one another. In many problems, failure times are clustered into small groups where outcomes within a group are correlated. Examples include failure times for two eyes from one person or for members of the same family. This paper presents a survey of models for multivariate failure time data. Two distinct classes of models are considered: frailty and marginal models. In a frailty model, the correlation is assumed to derive from latent variables ("frailties") common to observations from the same cluster. Regression models are formulated for the conditional failure time distribution given the frailties. Alternatively, marginal models describe the marginal failure time distribution of each response while separately modelling the association among responses from the same cluster. We focus on recent extensions of the proportional hazards model for multivariate failure time data. Model formulation, parameter interpretation and estimation procedures are considered.