A Simple Method for Deriving the Confidence Regions for the Penalized Cox's Model via the Minimand Perturbation.

Published

Journal Article

We propose a minimand perturbation method to derive the confidence regions for the regularized estimators for the Cox's proportional hazards model. Although the regularized estimation procedure produces a more stable point estimate, it remains challenging to provide an interval estimator or an analytic variance estimator for the associated point estimate. Based on the sandwich formula, the current variance estimator provides a simple approximation, but its finite sample performance is not entirely satisfactory. Besides, the sandwich formula can only provide variance estimates for the non-zero coefficients. In this article, we present a generic description for the perturbation method and then introduce a computation algorithm using the adaptive least absolute shrinkage and selection operator (LASSO) penalty. Through simulation studies, we demonstrate that our method can better approximate the limiting distribution of the adaptive LASSO estimator and produces more accurate inference compared with the sandwich formula. The simulation results also indicate the possibility of extending the applications to the adaptive elastic-net penalty. We further demonstrate our method using data from a phase III clinical trial in prostate cancer.

Full Text

Duke Authors

Cited Authors

  • Lin, C-Y; Halabi, S

Published Date

  • 2017

Published In

Volume / Issue

  • 46 / 10

Start / End Page

  • 4791 - 4808

PubMed ID

  • 29326496

Pubmed Central ID

  • 29326496

International Standard Serial Number (ISSN)

  • 0361-0926

Digital Object Identifier (DOI)

  • 10.1080/03610926.2015.1085568

Language

  • eng

Conference Location

  • United States