Penalized Cox models and Frailty

A very general mechanism for penalized regression has been added to the coxph function in S Plus A user written S Plus function can be supplied that gives addi tional term s to the partial likelihood along with the rst and second derivatives of those terms The variance and degrees of freedom for the extended model are then computed as outlined in Gray Several other arguments control optional aspects of the iteration This setup allows for general shrinkage methods including ridge regression the lasso smoothing splines and other techniques There is an interesting connection between penalized regression and random e ects or frailty models It happens that the gamma frailty model can be repre sented exactly as a penalized regression and a Gaussian frailty can be represented approximately Thus we can t these models as well using the generalized program