An Efficient LASSO Estimation for Time‑Dependent Cox Models via Adaptive Active‑Set Coordinate Descent

Document Type : Research article

Authors

1 Department of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran

2 Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran.

Abstract

The penalized Cox proportional hazard model is a popular analytical approach for survival data with a large set of covariates. Such problems are especially challenging when covariates vary over follow-up time (i.e., the covariates are time-dependent), leading to increased computational complexity and difficulties in efficient variable selection. In this paper, we propose an Adaptive Active-Set Coordinate Descent (AACD) algorithm for LASSO-penalized time-dependent Cox models. The proposed method combines coordinate descent with an adaptive active-set strategy and warm starts along the regularization path, allowing the algorithm to focus computation on relevant variables and better exploit sparsity. Simulation studies demonstrate that AACD consistently outperforms \texttt{glmnet}, achieving uniformly lower mean squared errors with relative efficiency greater than one across all settings, and reducing estimation error by up to 37\% in small samples. The method remains robust as dimensionality increases, improves variable selection by reducing false negatives, and produces more parsimonious models with comparable predictive performance while reducing runtime by approximately 36\% in real data analysis.

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Analytical and Numerical Solutions for Nonlinear Equations
Volume 11, Issue 2
September 2026
Pages 273-288

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History

  • Receive Date: 17 April 2026
  • Revise Date: 24 May 2026
  • Accept Date: 18 June 2026
  • Publish Date: 04 September 2026

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