Promoting structural effects of covariates in the cure rate model with penalization

Cure rate models have been widely adopted for characterizing survival data that have long-term survivors. Under a mixture cure rate model where the population is a mixture of cured and susceptible subjects, a primary goal is to study covariate effects on the cure probability and survival function of the susceptible subjects. In this article, we propose a penalization method for estimating the mixture cure rate model where we explicitly consider the structural effects of covariates. The proposed method is more informative than the standard estimations and more flexible than the existing works on structural effects. Depending on data characteristics, we develop different penalties and corresponding computational algorithms. Simulation shows that the proposed method outperforms the alternatives by more accurately estimating parameters and identifying relevant variables. Two breast cancer datasets, one with low-dimensional clinical variables and the other with high-dimensional genetic variables, are analyzed.