Estimation by polynomial splines with variable selection in additive Cox models

Abstract

In this article, we consider penalized variable selection in additive Cox models based on (group) smoothly clipped absolute deviation penalty and hence widen the scope of applicability of penalized variable selection to semiparametric models for censored data. We demonstrate the asymptotic consistency in model selection and convergence rate in estimation. Our simulation study emphasizes comparison of several different criteria for tuning parameter selection and also compares two appropriate definitions of the degrees of freedom in additive models.

Variable selection and structure identification for varying coefficient Cox models

“…Some authors considered the same problem by using SCAD. For example, see Lian et al [16] and Zhang et al [25]. They proved the existence of local optimizer satisfying the same convergence rate as ours.…”

Feature screening in ultrahigh-dimensional additive Cox model

“…Recently, Lian et al [9] considered shrinkage variable selection and estimation in proportional hazards models with additive structure under risk factors and high dimensionality settings. Zhang et al [10] studied penalized variable selection in the additive Cox models based on (group) smoothly clipped absolute deviation penalty and hence widen the scope of applicability of penalized variable selection to semiparametric models for censored data. Lin et al [11] proposed a global partial likelihood method to estimate the additive Cox model and show that the proposed estimator is consistent and asymptotically normal.…”