A Bayesian Correlated Frailty Model Applied to Swedish Breast Cancer Data

Isabella Locatelli, Università Bocconi
Paul Lichtenstein, Karolinska Institutet
Anatoli Yashin, Max Planck Institute for Demographic Research

Frailty was first introduced in survival analysis in order to assess for unobserved heterogeneity. Frailty models represent an extension of the proportional hazards model in which both the frailty term and the covariate effects are assumed to act multiplicatively on the baseline hazard. Multivariate frailty models were than created with the aim to introduce mutual dependence between the lifespans of related individuals. In our work a correlated log-normal frailty model is used in order to analyse breast cancer data from the Swedish Twin Register. An estimate of the narrow sense heritability for the individual susceptibility towards breast cancer is given via application of the ACE model. The inferential problem is solved in a Bayesian framework and the numerical work is carried out using MCMC methods. Estimates are compared with results of traditional maximum likelihood methods. Limitations and possible extensions of the model are discussed.