报告题目： Variable and Frailty Selection for Cox Proportional Hazard Frailty Model
主讲人：潘建新教授（曼切斯特大学）
时间：2018年4月4日（周三）10:00 a.m. - 11:30 a.m.
地点：北院卓远楼305
主办单位：统计与数学学院

摘要： Extending the Cox Proportional Hazard (PH) model to Cox PH frailty model may increase the dimension of variable components and become a very challenging task in terms of the significance and estimation of regression coefficients and variance components. On the other hand, variable selection has always been one of the fundamental problems when it comes to statistical modelling with high-dimensional variables and has attracted a remarkable attention. Various techniques of variable selection have been proposed such as the best subset variable selection and stepwise elimination, but suffer from several drawbacks in contrast with penalty-based methods. However, the method proposed here, aims to produce a simultaneous variable selection on both fixed effects and frailty components through penalty functions such as LASSO and SCAD. A modified Cholesky decomposition is considered for the covariance matrix of frailty term to guarantee the positive definiteness of the covariance matrix estimate. The idea is to "double penalize" the log-partial likelihood function of the Cox PH frailty model; one penalty for fixed effects and another for frailty terms, optimized by a Newton-Raphson algorithm providing closed iterative forms for the estimation of fixed effects and prediction of frailty terms. Simulation studies showed that the proposed procedure works well in simultaneous selecting and estimating significant fixed and frailty terms. The proposed method is also applied to real data analysis for Kidney disease and Diabetes Type 2 practises.

潘建新教授现任英国曼彻斯特大学教授，是英国曼彻斯特大学医学院荣誉研究员，担任四川大学客座教授，并于2015年入选国家“海外高层次人才引进计划”。潘建新教授是英国皇家统计学会Fellow，目前担任世界著名统计学期刊Biometrics和Biometrical Journal的Associated Editor，同时也是International Statistical Institute和Institute of Mathematical Statistics等国际学术组织的会员。潘建新教授曾担任曼彻斯特大学数学学院概率统计系系主任，致力于统计学领域内复杂数据模型的理论研究及其在生物医学、金融及工业上的应用研究，取得了多项创新性研究成果。具体研究方向包括纵向数据分析、生存数据分析、广义估计方程、生长曲线模型、均值与方差的同时建模，缺失数据问题及统计诊断等等。在包括JRSSB等期刊在内的国际著名统计学期刊发表SCI收录论文数十篇，出版学术专著多部。