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.

Keywords:

• Akaike information criterion
• Bayesian information criterion
• generalized cross-validation
• polynomial splines
• proportional hazards models

Acknowledgements

The authors sincerely thank the AE and a referee for their insightful comments and suggestions that have improved the original manuscript. The research of Heng Lian is supported by Singapore MOE Tier 1 Grant. Zhang's research is partially supported by the National Natural Science Foundation of China (61070236).