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Analysis of overfitting in the regularized Cox model

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Original languageEnglish
Article number384002
Number of pages23
JournalJournal Of Physics A-Mathematical And Theoretical
Volume52
Issue number38
Early online date31 Jul 2019
DOIs
Publication statusPublished - 26 Aug 2019

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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.

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