Abstract

The accelerated failure time model has garnered attention due to its intuitive linear

regression interpretation and has been successfully applied in fields such as biostatistics, clinical

medicine, economics, and social sciences. This paper considers a weighted least squares estimation

method with an ℓ0-penalty based on right-censored data in a high-dimensional setting. For practical implementation, we adopt an efficient primal dual active set algorithm and utilize a continuous

strategy to select the appropriate regularization parameter. By employing the mutual incoherence

property and restricted isometry property of the covariate matrix, we perform an error analysis

for the estimated variables in the active set during the iteration process. Furthermore, we identify

a distinctive monotonicity in the active set and show that the algorithm terminates at the oracle

solution in a finite number of steps. Finally, we perform extensive numerical experiments using

both simulated data and real breast cancer datasets to assess the performance benefits of our

method in comparison to other existing approaches.

Key words and phrases: High-dimensional accelerated failure time model, ℓ0-penalty, oracle solu- tion, primal dual active set with continuation algorithm, weighted least squares method

Information

Preprint No.SS-2025-0283
Manuscript IDSS-2025-0283
Complete AuthorsPeili Li, Ruoying Hu, Yanyun Ding, Yunhai Xiao
Corresponding AuthorsYunhai Xiao
Emailsyhxiao@henu.edu.cn

References

  1. Buckley, J. and I. James (1979). Linear regression with censored data. Biometrika 66(3), 429–436.
  2. Ying, Z. (1993). A large sample study of rank estimation for censored regression data. The Annals of Statistics 21(1), 76–99.
  3. Stute, W. (1996). Distributional convergence under random censorship when covariables are present. Scandinavian Journal of Statistics 23(4), 461–471.
  4. Stute, W. and J.-L. Wang (1993). The strong law under random censorship. The Annals of Statistics 21(3), 1591–1607.
  5. Johnson, B. A. (2008). Variable selection in semiparametric linear regression with censored data. Journal of the Royal Statistical Society Series B: Statistical Methodology 70(2), 351–370.
  6. Johnson, B. A., D. Y. Lin and D. Zeng (2008). Penalized estimating functions and variable selection in semiparametric regression models. Journal of the American Statistical Association 103(482), 672–680.
  7. Fan, J. and R. Li (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 96(456), 1348–1360.
  8. Cai, T., J. Huang and L. Tian (2009). Regularized estimation for the accelerated failure time model. Biometrics 65(2), 394–404.
  9. Zou, H. (2006). The adaptive lasso and its oracle properties. Journal of the American Statistical Association 101(476), 1418–1429.
  10. Hu, J. and H. Chai (2013). Adjusted regularized estimation in the accelerated failure time model with high dimensional covariates. Journal of Multivariate Analysis 122, 96–114.
  11. Huang, J. and S. Ma (2010). Variable selection in the accelerated failure time model via the bridge method. dimensional covariates. Biometrics 62(3), 813–820.
  12. Khan, M. H. R. and J. E. H. Shaw (2016). Variable selection for survival data with a class of adaptive elastic net techniques. Statistics and Computing 26(3), 725–741.
  13. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society Series B: Statistical Methodology 58(1), 267–288.
  14. Hong, D. and F. Zhang (2010). Weighted elastic net model for mass spectrometry imaging processing. Mathematical Modelling of Natural Phenomena 5(3), 115–133.
  15. Zou, H. and H. H. Zhang (2009). On the adaptive elastic-net with a diverging number of parameters. The Annals of Statistics 37(4), 1733–1751.
  16. Frank, L. E. and J. H. Friedman (1993). A statistical view of some chemometrics regression tools. Technometrics 35(2), 109–135.
  17. Zhang, C.-H. (2010). Nearly unbiased variable selection under minimax concave penalty. The Annals of Statistics 38(2), 894–942.
  18. Cheng, C., X. Feng, J. Huang, Y. Jiao and S. Zhang (2022). ℓ0-regularized high-dimensional accelerated failure time model. Computational Statistics & Data Analysis 170, 107430.
  19. Huang, J., Y. Jiao, Y. Liu and X. Lu (2018). A constructive approach to ℓ0 penalized regression. Journal of Machine Learning Research 19(10), 1–37.
  20. Jiao, Y., B. Jin and X. Lu (2015). A primal dual active set with continuation algorithm for the ℓ0-regularized optimization problem. Applied and Computational Harmonic Analysis 39(3), 400–426.
  21. Huang, J., Y. Jiao, B. Jin, J. Liu, X. Lu and C. Yang (2021). A unified primal dual active set algorithm for nonconvex sparse recovery. Statistical Science 36(2), 215–238.
  22. Li, P., Y. Jiao, X. Lu and L. Kang (2022). A data-driven line search rule for support recovery in high-dimensional data analysis. Computational Statistics & Data Analysis 174, 107524. method. SIAM Journal on Optimization 13(3), 865–888.
  23. Dai, W. and O. Milenkovic (2009). Subspace pursuit for compressive sensing signal reconstruction. IEEE Transactions on Information Theory 55(5), 2230–2249.
  24. Needell, D. and J. A. Tropp (2009). CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. Applied and Computational Harmonic Analysis 26(3), 301–321.
  25. Pati, Y. C., R. Rezaiifar and P. S. Krishnaprasad (1993). Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition. In: Proceedings of 27th Asilomar Conference on
  26. Signals, Systems and Computers, 40–44.
  27. Blumensath, T. and M. E. Davies (2008). Gradient pursuits. IEEE Transactions on Signal Processing 56(6), 2370–2382.
  28. Blumensath, T. (2012). Accelerated iterative hard thresholding. Signal Processing 92(3), 752–756.
  29. Foucart, S. (2011). Hard thresholding pursuit: an algorithm for compressive sensing. SIAM Journal on Numerical Analysis 49(6), 2543–2563. Henan University

Acknowledgments

We would like to thank professor Xiliang Lu from Wuhan university for his guidance and

significant assistance in the theoretical analysis of this paper.

Declarations

The authors report there are no competing interests to declare. All authors contributed

to the study conception and design. All authors read and approved the final manuscript.