國立東華大學應用數學系

專    題    演    講

主講人：Takeshi Emura

               Graduate Institute of Statistics, National Central University

講  題：An extension of the compound covariate prediction under the Cox proportional hazard models

時  間：102 年 05 月 17 日 (星期五)  15:20-16:50

地  點：理工一館 A324 會議室

摘   要

 Censored survival data often contains high-dimensional covariates. In such a case, the Cox’s partial likelihood function has infinitely many maxima. Ridge regression (Hoerl & Kennard 1970) can effectively solve this problem by penalizing the partial likelihood with penalty, which leads to the unique maxima. The resultant linear prediction based on the ridge estimator has superior performance among many other available methods with high-dimensional covariates, including Lasso and partial least square (e.g., Bovelstad et al., 2007).

In this talk, we propose an alternative method that aims to improve the ridge regression. We first introduce the compound covariate prediction (Tukey 1993; Radmacher et al. 2002; Matsui 2006), which has been used in survival data with microarrays. We derive some asymptotic results for the compound covariate predictors based on the theory of misspecified Cox regression analysis. In light of the asymptotic results and some geometric idea, we modify the compound covariate method to derive a new method. The proposed method is compared with ridge regression and Lasso via simulations and data analysis. This is joint work with Dr. Yi-Hau Chen and Hsuan-Yu Chen from Institute of Statistical Science, Academia Sinica.

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