Estimating high-dimensional additive Cox model with time-dependent covariate processes

Shaogao Lv, Jiakun Jiang, Fanyin Zhou, Jian Huang, Huazhen Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

This paper is concerned with the estimation in the additive Cox model with time-dependent covariates when the number of additive components p is greater than the sample size n. By combining spline representation and the group lasso penalty, a penalized partial likelihood approach to estimating the unknown component functions is proposed. Given the non-iid nature of the log partial likelihood function and the nonparametric complexities of the component function estimation, it is challenging to analyze the theoretical properties of the proposed estimation. Through concentration inequities developed for martingale differences in the context of the additive Cox model, we establish nonasymptotic oracle inequalities for the group lasso in the additive Cox model with p=e o(n) under the compatibility and cone invertibility factors conditions on the Hessian matrix. An interesting and surprising aspect of our result is that the complexity of the component functions affects not only the approximation error but also the stochastic error. This is quite different from the additive mean models and suggests that the additive Cox model is more difficult to estimate than the additive mean models in high-dimensional settings.

Original languageEnglish
Pages (from-to)900-922
Number of pages23
JournalScandinavian Journal of Statistics
Volume45
Issue number4
DOIs
Publication statusPublished - 1 Dec 2018
Externally publishedYes

Keywords

  • additive Cox model
  • group lasso
  • oracle inequality
  • spline approximation
  • survival data
  • variable selection

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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