A Newton-Type Method for ℓ0-Regularized Accelerated Failure Time Model Under the Case–Cohort Design

The case–cohort design has been widely used to reduce the cost of covariate measurements in large cohort studies. In this paper, we study the high-dimensional accelerated failure time (AFT) model under the case–cohort design. Based on ℓ 0 -regularization and a newly defined weight function, we propo...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series Vol. 41; no. 9; pp. 2275 - 2300
Main Authors: Liu, Yanyan, Tian, Ke, Wang, Danlu, Zhang, Jing
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2025
Springer Nature B.V
Subjects:
Algorithms
Failure times
Gene expression
Least squares method
Mathematics
Mathematics and Statistics
Newton methods
Parameter estimation
Regularization
Weighting functions
62N01
62P10
62N02
newton-type method
regularization
case–cohort design
62D99
Accelerated failure time model
support detection and root finding algorithm
ISSN:1439-8516, 1439-7617
Online Access:Get full text
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Summary:The case–cohort design has been widely used to reduce the cost of covariate measurements in large cohort studies. In this paper, we study the high-dimensional accelerated failure time (AFT) model under the case–cohort design. Based on ℓ 0 -regularization and a newly defined weight function, we propose a weighted least squares procedure for variable selection and parameter estimation. Computationally, we develop a support detection and root finding (SDAR) algorithm, where the support is first determined based on the primal and dual information, then the estimator is obtained by solving the weighted least squares problem restricted to the estimated support. We show the proposed algorithm is essentially one Newton-type algorithm, thus it is more efficient and stable compared with other regularized methods. Theoretically, we establish a sharp error bound for the solution sequences generated from the proposed method. Furthermore, we propose an adaptive version of the proposed SDAR algorithm, which determines the support size of the estimated coefficient in a data-driven manner. Extensive simulation studies demonstrate the superior performance of the proposed procedures, especially for the computational efficiency. As an illustration, we apply the proposed method to a malignant breast tumor gene expression data.
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-025-3226-2