Sparse regression techniques in low-dimensional survival data settings

This work investigates classical shrinkage techniques such as the lasso, new techniques that address this problem, such as elastic net and SCAD, and boosting technique CoxBoost and extensions of it, which allow to incorporate additional structure in high-dimensional data settings.

Abstract

In high-dimensional data settings, sparse model fits are desired, which can be obtained through shrinkage or boosting techniques. We investigate classical shrinkage techniques such as the lasso, which is theoretically known to be biased, new techniques that address this problem, such as elastic net and SCAD, and boosting technique CoxBoost and extensions of it, which allow to incorporate additional structure. To examine, whether these methods, that are designed for or frequently used in high-dimensional survival data analysis, provide sensible results in low-dimensional data settings as well, we consider the well known GBSG breast cancer data. In detail, we study the bias, stability and sparseness of these model fitting techniques via comparison to the maximum likelihood estimate and resampling, and their prediction performance via prediction error curve estimates.