Confidence intervals for high-dimensional Cox models

Yi Yu; Jelena Bradic; Richard J. Samworth

doi:10.5705/ss.202018.0247

Confidence intervals for high-dimensional Cox models

Yi Yu, Jelena Bradic, Richard J. Samworth

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Abstract

We provide theoretical justification for post-selection inference in highdimensional Cox models, based on the celebrated debiased Lasso procedure (e.g. Zhang and Zhang, 2014; van de Geer et al., 2014). Our generic model setup allows time-dependent covariates and an unbounded time interval, which is unique among post-selection inference studies on high-dimensional survival analysis. In addition, we adopt a novel proof technique to replace the use of Rebolledo’s central limit theorem as in the seminal work of Andersen and Gill (1982). Our theoretical results, which provide conditions under which our confidence intervals are asymptotically valid, are supported by extensive numerical experiments.

Original language	English
Pages (from-to)	243-267
Number of pages	25
Journal	Statistica Sinica
Volume	31
Issue number	1
DOIs	https://doi.org/10.5705/ss.202018.0247
Publication status	Published - 1 Jan 2021

Bibliographical note

Funding Information:
The third author is supported by Engineering and Physical Sciences Research Council fellowships EP/J017213/1 and EP/P031447/1, and grant RG81761 from the Leverhulme Trust. The first and third authors would like to thank the Isaac Newton Institute for Mathematical Sciences for its support and hospitality during the programme "Statistical Scalability" when work on this paper was undertaken. This work was supported by Engineering and Physical Sciences Research Council grant number EP/K032208/1. The second author is supported by the National Science Foundation grant number NSF-DMS/1712481.

Funding Information:
The third author is supported by Engineering and Physical Sciences Research Council fellowships EP/J017213/1 and EP/P031447/1, and grant RG81761 from the Leverhulme Trust. The first and third authors would like to thank the Isaac Newton Institute for Mathematical Sciences for its support and hospitality during the programme “Statistical Scalability” when work on this paper was undertaken. This work was supported by Engineering and Physical Sciences Research Council grant number EP/K032208/1. The second author is supported by the National Science Foundation grant number NSF-DMS/1712481.

Publisher Copyright:
© 2021 Institute of Statistical Science. All rights reserved.

Keywords

Survival analysis
High-dimension statistical inference
Debiased Lasso

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title = "Confidence intervals for high-dimensional Cox models",

abstract = "We provide theoretical justification for post-selection inference in highdimensional Cox models, based on the celebrated debiased Lasso procedure (e.g. Zhang and Zhang, 2014; van de Geer et al., 2014). Our generic model setup allows time-dependent covariates and an unbounded time interval, which is unique among post-selection inference studies on high-dimensional survival analysis. In addition, we adopt a novel proof technique to replace the use of Rebolledo{\textquoteright}s central limit theorem as in the seminal work of Andersen and Gill (1982). Our theoretical results, which provide conditions under which our confidence intervals are asymptotically valid, are supported by extensive numerical experiments.",

keywords = "Survival analysis, High-dimension statistical inference, Debiased Lasso",

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doi = "10.5705/ss.202018.0247",

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N2 - We provide theoretical justification for post-selection inference in highdimensional Cox models, based on the celebrated debiased Lasso procedure (e.g. Zhang and Zhang, 2014; van de Geer et al., 2014). Our generic model setup allows time-dependent covariates and an unbounded time interval, which is unique among post-selection inference studies on high-dimensional survival analysis. In addition, we adopt a novel proof technique to replace the use of Rebolledo’s central limit theorem as in the seminal work of Andersen and Gill (1982). Our theoretical results, which provide conditions under which our confidence intervals are asymptotically valid, are supported by extensive numerical experiments.

AB - We provide theoretical justification for post-selection inference in highdimensional Cox models, based on the celebrated debiased Lasso procedure (e.g. Zhang and Zhang, 2014; van de Geer et al., 2014). Our generic model setup allows time-dependent covariates and an unbounded time interval, which is unique among post-selection inference studies on high-dimensional survival analysis. In addition, we adopt a novel proof technique to replace the use of Rebolledo’s central limit theorem as in the seminal work of Andersen and Gill (1982). Our theoretical results, which provide conditions under which our confidence intervals are asymptotically valid, are supported by extensive numerical experiments.

KW - Survival analysis

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DO - 10.5705/ss.202018.0247

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EP - 267

JO - Statistica Sinica

JF - Statistica Sinica

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ER -

Confidence intervals for high-dimensional Cox models

Abstract

Bibliographical note

Keywords

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