Simultaneous Estimation and Variable Selection for Interval-Censored Data With Broken Adaptive Ridge Regression

Abstract

The simultaneous estimation and variable selection for Cox model has been discussed by several authors when one observes right-censored failure time data. However, there does not seem to exist an established procedure for interval-censored data, a more general and complex type of failure time data, except two parametric procedures. To address this, we propose a broken adaptive ridge (BAR) regression procedure that combines the strengths of the quadratic regularization and the adaptive weighted bridge shrinkage. In particular, the method allows for the number of covariates to be diverging with the sample size. Under some weak regularity conditions, unlike most of the existing variable selection methods, we establish both the oracle property and the grouping effect of the proposed BAR procedure. An extensive simulation study is conducted and indicates that the proposed approach works well in practical situations and deals with the collinearity problem better than the other oracle-like methods. An application is also provided.

Keywords:

• Broken adaptive ridge regression
• Cox’s proportional hazards model
• Grouping effect
• Interval-censored data
• Variable selection

Acknowledgments

The authors wish to thank the Editor, Dr. Hongyu Zhao, the Associate Editor and two reviewers for their many critical and constructive comments and suggestions that greatly improved the article.

Funding

Additional information

Funding

The research of Zhao was partially supported by the National Natural Science Foundation of China grants 11471135 and 11861030.