Multivariate frailty models

Data in survival analysis are usually assumed to be univariate, with one, possibly censored, lifetime for each individual. All the standard methodology, including Kaplan-Meier plots and Cox analysis, is geared toward handling this situation. However, multivariate survival data also arise naturally in many contexts. Such data pose a problem for ordinary multivariate methods, which will have difficulty handling censored data. There are two typical ways multivariate survival data can arise. One, which may be termed the recurrent events situation, is when several successive events of the same type are registered for each individual, for instance, repeated occurrences of ear infections. The other, which may be termed the clustered survival data situation, is when several units that may fail are collected in a cluster. Examples of the clustered survival data situation may be the possible failure of several dental fillings for an individual or the lifetimes of twins. The cluster structure may in fact be rather complex, including, for instance, related individuals in family groups. Sometimes one would assume common distributions for the individual units in a cluster; in other cases, like when considering the lifetimes of father and son, the distributions may be different.