A Primal Dual Active Set with Continuation Algorithm for $\ell_0$-Penalized High-dimensional Accelerated Failure Time Model

TL;DR

This paper introduces an efficient primal dual active set algorithm with a continuation strategy for high-dimensional $\,\ell_0$-penalized accelerated failure time models, demonstrating its effectiveness through theoretical analysis and numerical experiments.

Contribution

It presents a novel primal dual active set algorithm with a continuation approach for $\,\ell_0$-penalized high-dimensional AFT models, including error analysis and finite-step convergence proof.

Findings

Algorithm terminates at the oracle solution in finite steps.

Error bounds are established under mutual incoherence and restricted isometry conditions.

Numerical experiments show superior performance over existing methods.

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 $\ell_0$-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.