Penalized Survival Models and Frailty
V. Shane Pankratz, (Mayo Clinic - Division of Biostatistics), firstname.lastname@example.org,
Patricia M. Grambsch, (University of Minnesota School of Public Health - Division of Biostatistics), email@example.com, and
Terry M. Therneau, (Mayo Clinic - Division of Biostatistics), firstname.lastname@example.org
Interest in the use of random effects in survival analysis settings has been increasing. However, the computational complexity of such frailty models has limited their general use. While fitting frailty models has traditionally been difficult, parameter estimation in penalized Cox semi-parametric and parametric regression models can be done using simple extensions of the standard algorithms for fitting non-penalized models. We demonstrate that solutions for gamma shared frailty models can be obtained exactly via penalized estimation. Gaussian frailty models are also closely linked to penalized models. Therefore, 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. In this presentation, we outline the links between frailty models and penalized likelihood methods, and illustrate use of the algorithms implemented within the coxph S-Plus function with several examples. Of particular interest, we have successfully used these methods on data from a large study of the genetic epidemiology of breast cancer.