Interest in random effects (frailties) for survival analysis had grown, but the computational complexity of frailty models limited their use. Therneau, Grambsch and Pankratz show that standard algorithms for fitting Cox semiparametric and parametric regression models extend readily to penalized regression, and that frailty models can be fit through this penalized machinery: gamma shared-frailty solutions are obtained exactly via penalized estimation, Gaussian frailty models are closely linked to penalized models, and other frailties follow through Laplace approximations. This makes frailty fitting fast, and the authors implement penalized regression in the coxph survival routines.
coxph (S-Plus/R survival package), illustrated on Cox-model examples."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."
The practical breakthrough that made frailty models routine: rather than build bespoke EM or numerical-integration machinery, recognize that a frailty is a penalty and reuse the Cox solver everyone already has. The exact gamma-frailty↔penalized-likelihood correspondence is the clean special case, and the Laplace route generalizes it — the same penalty-as-random-effect duality that runs through penalized splines, REML smoothing, and mixed models, here applied to the partial likelihood. Its lasting footprint is less the theory than the survival package's frailty()/coxph implementation, which put correlated-event and recurrent-event survival modelling within reach of ordinary users. The standard caveats remain: the frailty distribution is weakly identified, and choosing the penalty/variance component is its own inference problem.