Regularization methods for the Cox proportional hazards regression with high-dimensional survival data have been studied extensively in the literature. However, if the models are misspecified, this would result in misleading statistical inference 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 the high-dimensional Cox proportional hazards regression. Based on the martingale residual process, we define the delete-one cross validation process. Further, we propose three novel cross-validation functionals, including the end-time cross-validation, integrated cross-validation, and supremum cross-validation, to achieve more accurate prediction for the risk quantities. The optimal weights for candidate models, without the constraint of summing up to one, can be obtained by minimizing these functionals, respectively. The proposed model averaging approaches can attain the lowest possible prediction loss asymptotically. Furthermore, we develop a greedy model averaging algorithm to overcome the computational obstacle when the dimension is high. The performance of the proposed model averaging procedures is evaluated via extensive simulation studies, showing that our methods have superior prediction accuracy over the existing regularization methods. As an illustration, we apply the proposed methods to the mantle cell lymphoma study.
嘉宾简介 About the Speaker
刘妍岩，武汉大学数学与统计学院教授，博士生导师。2001年获武汉大学理学博士学位。主要研究方向为生存分析、半参数统计推断、大数据统计分析等。主持完成国家自然科学基金以及教育部基金项目6项，目前主持国家自然科学基金面上项目一项，参加完成的成果“风险模型中的统计方法及相关理论与应用” 2013年湖北省自然科学奖三等奖（排名第一）。在统计学期刊 Journal of Machine Learning Research, Biometrics, Biostatistics, Genetics，Lifetime Data Analysis等期刊发表SCI研究论文五十余篇。目前担任中国现场统计学会第十届理事会常务理事、中国工业统计学会常务理事、中国数学会女专家工作委员会委员。