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

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 ۳۷\% 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 ۳۶\% in real data analysis.

کلیدواژه ها:

Adaptive active-set ، Coordinate descent ، LASSO ، Time-Dependent Cox Model ، Variable selection