Bias Reduction of Likelihood Estimators in Semiparametric Frailty Models

Frailty models with a non-parametric baseline hazard are widely used for the analysis of survival data. However, their maximum likelihood estimators can be substantially biased in finite samples, because the number of nuisance parameters associated with the baseline hazard increases with the sample size. The penalized partial likelihood based on a first-order Laplace approximation still has non-negligible bias. However, the second-order Laplace approximation to a modified marginal likelihood for a bias reduction is infeasible because of the presence of too many complicated terms. In this article, we find adequate modifications of these likelihood-based methods by using the hierarchical likelihood.