Abstract: Regularization methods for the Cox proportional hazards regression with high-dimensional survival data have been extensively studied in recent literature. However, the specified models that these methods work on could be readily misspecified in practice, which would result in misleading statistical interpretation and prediction. To enhance the prediction accuracy for the relative risk and the survival probability of clinical interest we propose three model averaging approaches for high-dimensional Cox proportional hazards regression. Based on the martingale residual process, we define the delete-one cross-validation process. As its functionals, we novelly propose the end-time cross-validation, the integrated cross-validation, and the supremum cross-validation to achieve more accurate predictions for the risk quantities. The optimal weights for candidate models, without the constraint of summation being one, can be obtained by minimizing these functionals, respectively.The proposed model averaging approaches are shown to attain the lowest possible prediction losses asymptotically. Furthermore, we develop and analyze a greedy model averaging algorithm to overcome the computational obstacle in practice when dimension is very high. The performance of the proposed model averaging procedures is evaluated via extensive simulation studies, showing that our methods have favorable prediction accuracy over the existing typical regularization methods. As an illustration, we apply the proposed methods to the mantle cell lymphoma study.

个人简介: 吴远山，武汉大学数学与统计学院副教授、博士生导师。主要从事生存分析、分位数回归、高维数据分析等方面的研究工作，主持多项国家级和省部级科研项目，在统计学主流学术刊物发表20多篇研究论文。