A Monte Carlo method for Bayesian inference in frailty models

Many analyses in epidemiological and prognostic studies and in studies of event history data require methods that allow for unobserved covariates or "frailties." Clayton and Cuzick (1985, Journal of the Royal Statistical Society, Series A 148, 82-117) proposed a generalization of the proportional hazards model that implemented such random effects, but the proof of the asymptotic properties of the method remains elusive, and practical experience suggests that the likelihoods may be markedly nonquadratic. This paper sets out a Bayesian representation of the model in the spirit of Kalbfleisch (1978, Journal of the Royal Statistical Society, Series B 40, 214-221) and discusses inference using Monte Carlo methods.