Shared Frailty Graphical Survival Models

This work introduces graphical models for clustered survival data with unobserved heterogeneity at cluster level. Particularly shared frailty models [HOU00] are here defined as an intersection of multilevel graphical models [GR04] with duration graphical models [GOT99]. The proposed models are survival frailty models satisfying Markov properties with respect to a chain graph. The use of graphical models is helpful for an intuitive understanding of the complex association structure of clustered survival data. Moreover, it allows to study the joint distribution of involved variables with survival times. The graph suggests a convenient recursive factorization of the likelihood function, to pick out an efficient computational algorithms for its maximization. Shared frailty graphical models can be relevant in many fields. They can be useful whenever the interest is focused not only on the conditional distribution of survival times, but also on the dependence structure of a multivariate set involving point processes and random variables.