Penalized Survival Models and Frailty

Interest in the use of random effects in the survival analysis setting has been increasing. However, the computational complexity of such frailty models has limited their general use. Although fitting frailty models has traditionally been difficult, standard algorithms for fitting Cox semiparametric and parametric regression models can be readily extended to include penalized regression. We demonstrate that solutions for gamma shared frailty models can be obtained exactly via penalized estimation. Similarly, Gaussian frailty models are closely linked to penalized models. Fitting frailty models with penalized likelihoods can be made quite efficient by taking advantage of computational methods available for penalized models. We have implemented penalized regression for the coxph function of S-Plus and illustrate the algorithms with examples using the Cox model.