A Flexible Adaptive Lasso Cox Frailty Model Based on the Full Likelihood

Abstract

ABSTRACT In this work, a method to regularize Cox frailty models is proposed that accommodates time‐varying covariates and time‐varying coefficients and is based on the full likelihood instead of the partial likelihood. A particular advantage of this framework is that the baseline hazard can be explicitly modeled in a smooth, semiparametric way, for example, via P‐splines. Regularization for variable selection is performed via a lasso penalty and via group lasso for categorical variables while a second penalty regularizes wiggliness of smooth estimates of time‐varying coefficients and the baseline hazard. Additionally, adaptive weights are included to stabilize the estimation. The method is implemented in the R function coxlasso , which is now integrated into the package PenCoxFrail , and will be compared to other packages for regularized Cox regression.