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Penalized partial likelihood regression for right-censored data with bootstrap selection of the penalty parameter. (English) Zbl 1210.62042

Summary: The Cox proportional hazards model is often used for estimating the association between covariates and a potentially censored failure time, and the corresponding partial likelihood estimators are used for the estimation and prediction of relative risk of failure. However, partial likelihood estimators are unstable and have large variance when collinearity exists among the explanatory variables or when the number of failures is not much greater than the number of covariates of interest. A penalized (\(\log\)) partial likelihood is proposed to give more accurate relative risk estimators. We show that asymptotically there always exists a penalty parameter for the penalized partial likelihood that reduces mean squared estimation error for log relative risk, and we propose a resampling method to choose the penalty parameter. Simulations and an example show that the bootstrap-selected penalized partial likelihood estimators can, in some instances, have smaller bias than the partial likelihood estimators and have smaller mean squared estimation and prediction errors of log relative risk. These methods are illustrated with a data set in multiple myeloma from the Eastern Cooperative Oncology Group.

MSC:

62G08 Nonparametric regression and quantile regression
62N02 Estimation in survival analysis and censored data
62N01 Censored data models
62G05 Nonparametric estimation
65C60 Computational problems in statistics (MSC2010)
62P10 Applications of statistics to biology and medical sciences; meta analysis
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