ABSTRACT
Multivariate failure time data arise when a sampling unit contains a cluster of multiple, possibly correlated failure times. The sampling unit may be an individual at risk of multiple failures or a cluster of multiple individuals such as twin and household. For example, in a diabetic study, treatment regimens were randomly assigned to right eye and left eye of an individual. In this case, the sampling unit is patient and times to blindness of the right and left eye from the same patient were matched and may be correlated because they share common patient characteristics. The purpose of the matched design was to improve efficiency of the treatment comparison (Ederer et al., 1984). In family studies such as twin studies with survival endpoint (Anderson et al., 1992; Hougaard et al., 1992), age at onset can be used to
aggregation of the disease of interest. The sampling unit here is family, and ages at onset of a certain disease of family members are correlated because they share some common genetic and environmental risk factors. In cancer studies patients may experience multiple tumor recurrences during the course of follow-up, whereas patients after receiving bone marrow transplantation may be at risk of a range of treatment-related complications such as acute graft-versus-host disease and cytomegalovirus. Recurrent event times in the former are of the repeated events of the same type and times to different complications in the latter belong to different failure types. Competing risks result in another type of correlated failure times. They occur when a subject is at risk of multiple distinct failure types and only the first failure type is observed. Since other failure types are censored by the first observed failure type, dependency of failure times of the multiple failure types is not directly observable, and will not be considered in this chapter.
