Estimation and variable selection via frailty models with penalized likelihood.

The penalized likelihood methodology has been consistently demonstrated to be an attractive shrinkage and selection method. It does not only automatically and consistently select the important variables but also produces estimators that are as efficient as the oracle estimator. In this paper, we apply this approach to a general likelihood function for data organized in clusters, which corresponds to a class of frailty models, which includes the Cox model and the Gamma frailty model as special cases. Our aim was to provide practitioners in the medical or reliability field with options other than the Gamma frailty model, which has been extensively studied because of its mathematical convenience. We illustrate the penalized likelihood methodology for frailty models through simulations and real data.