A marginal likelihood approach to estimation in frailty models

A marginal likelihood approach is proposed for estimating the parameters in a frailty model using clustered survival data. To overcome the analytic intractability of the marginal likelihood function, we propose a Monte Carlo approximation using the technique of importance sampling. Implementation is by means of simulations from the uniform distribution. The suggested method can cope with censoring and unequal cluster sizes and can be applied to any frailty distribution with explicit Laplace transform. We concentrate on a two-parameter family that includes the gamma, inverse Gaussian, and positive stable distributions as special cases. The method is illustrated using data from an animal carcinogenesis experiment and validated in a simulation study.