Distributions determined by non-negative Lévy processes, which include the power variance function (PVF) distributions among others, are commonly used as frailty distributions to model dependent survival times in family data. We present a hierarchical frailty model constructed by randomizing scale parameters, corresponding to time parameters of Lévy processes, in the Lévy frailty distributions. In its simplest form, this yields a two-model with heterogeneity the individual and family level. The family level frailty is shared within families, creating dependence. In the more complex models, it is extended to allow for several levels of dependence. This yields models with nested dependence structures (all individuals in a family are dependent, but some more than others), or genetic models for two-generation families (parents-children, where the parents are independent). The model allows for several different options on where to include covariates, and each alternative gives different interpretations of the regression coefficients. An application to dependent data on post-perinatal (7-364 days) infant mortality in siblings from the Medical Birth Registry of Norway is included. We compare the results for some of the different covariate modeling options from a case-cohort analysis of the data by using a two-level Lévy model.
Moger, Tron Anders and Aalen, Odd O., "Hierarchical Lévy Frailty Models and a Frailty Analysis of Data on Infant Mortality in Norwegian Siblings" (June 2006). UW Biostatistics Working Paper Series. Working Paper 290.