Analysis of overfitting in the regularized Cox model

Mansoor Sheikh; ACC Coolen

doi:10.1088/1751-8121/ab375c

Analysis of overfitting in the regularized Cox model

Mansoor Sheikh, ACC Coolen

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

118 Downloads (Pure)

Abstract

The Cox proportional hazards model is ubiquitous in the analysis of
time-to-event data. However, when the data dimension p is comparable to the
sample size N, maximum likelihood estimates for its regression parameters are
known to be biased or break down entirely due to overfitting. This prompted
the introduction of the so-called regularized Cox model. In this paper we use the replica method from statistical physics to investigate the relationship between the true and inferred regression parameters in regularized multivariate Cox regression with L2 regularization, in the regime where both p and N are large but with ζ = p/N ∼ O(1). We thereby generalize a recent study from maximum likelihood to maximum a posteriori inference. We also establish a relationship between the optimal regularization parameter and ζ, allowing for straightforward overfitting corrections in time-to-event analysis.

Original language	English
Article number	384002
Number of pages	23
Journal	Journal Of Physics A-Mathematical And Theoretical
Volume	52
Issue number	38
Early online date	31 Jul 2019
DOIs	https://doi.org/10.1088/1751-8121/ab375c
Publication status	Published - 26 Aug 2019

Keywords

Cox proportional hazards model
overfitting, replica method
survival analysis

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10.1088/1751-8121/ab375c

Analysis of overfitting_SHEIKH_Accepted31July2019_GREEN AAMAccepted author manuscript, 491 KBLicence: Unspecified

https://arxiv.org/pdf/1904.06632.pdfLicence: Unspecified

Cite this

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KW - survival analysis

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Analysis of overfitting in the regularized Cox model

Abstract

Keywords

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