The Cox model is an exceedingly popular semiparametric hazard regression model for the analysis of time-to-event accompanied by explanatory variables. Within the ultrahigh-dimensional data setting, not like the marginal screening strategy, there is a joint feature screening method based on the partial likelihood of the Cox model but it leaves computational feasibility unsolved. In this paper, we develop an enhanced iterative hard-thresholding algorithm by adapting the non-monotone proximal gradient method under the Cox model. The proposed algorithm is efficient because it is computationally both effective and fast. Meanwhile, our proposed algorithm begins with a LASSO initial estimator rather than the naive zero initial and still enjoys sure screening in theory and further enhances the computational efficiency in practice. We also give a rigorous theory proof. The advantage of our proposed work is demonstrated by numerical studies and illustrated by the diffuse large B-cell lymphoma data example.

Cox模型是一种非常流行的半参数风险回归模型，用于分析事件发生时间并附带解释变量。在超高维数据设置中，不同于边缘筛选策略，存在一种基于Cox模型的部分似然性的联合特征筛选方法，但其计算可行性尚未解决。在本文中，我们通过在Cox模型下采用非单调近端梯度法，开发了一种增强的迭代硬阈值算法。所提出的算法是有效的，因为它在计算上既有效又快速。同时，我们提出的算法从LASSO初始估计量开始，而不是朴素的零初始值，并且在理论上仍然可以肯定地筛选，并且在实践中进一步提高了计算效率。我们还给出了严格的理论证明。我们的工作的优势通过数值研究得到证明，并通过弥漫性大B细胞淋巴瘤数据示例得到说明。