High-dimensional variable selection for Cox's proportional hazards model

Variable selection in high dimensional space has challenged many contemporary statistical problems from many frontiers of scientific disciplines. Recent technological advances have made it possible to collect a huge amount of covariate information such as microarray, proteomic and SNP data via bioimaging technology while observing survival information on patients in clin- ical studies. Thus, the same challenge applies in survival analysis in order to understand the association between genomics information and clinical infor- mation about the survival time. In this work, we extend the sure screening procedure (6) to Cox's proportional hazards model with an iterative version available. Numerical simulation studies have shown encouraging performance of the proposed method in comparison with other techniques such as LASSO. This demonstrates the utility and versatility of the iterative sure independence screening scheme.

[1]  H. Zou,et al.  Regularization and variable selection via the elastic net , 2005 .

[2]  Yang Feng,et al.  Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models , 2009, Journal of the American Statistical Association.

[3]  R. Tibshirani.  The lasso method for variable selection in the Cox model. , 1997, Statistics in medicine.

[4]  H. Zou,et al.  One-step Sparse Estimates in Nonconcave Penalized Likelihood Models. , 2008, Annals of statistics.

[5]  Jianqing Fan,et al.  Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties , 2001 .

[6]  Jianqing Fan,et al.  Sure independence screening in generalized linear models with NP-dimensionality , 2009, The Annals of Statistics.

[7]  Jianqing Fan,et al.  Variable Selection for Cox's proportional Hazards Model and Frailty Model , 2002 .

[8]  Jianqing Fan,et al.  Sure independence screening for ultrahigh dimensional feature space , 2006, math/0612857.

[9]  D Faraggi,et al.  Bayesian variable selection method for censored survival data. , 1998, Biometrics.

[10]  Patrick Warnat,et al.  Customized oligonucleotide microarray gene expression-based classification of neuroblastoma patients outperforms current clinical risk stratification. , 2006, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

[11]  Rupert G. Miller,et al.  Survival Analysis , 2022, The SAGE Encyclopedia of Research Design.

[12]  M Schumacher,et al.  A bootstrap resampling procedure for model building: application to the Cox regression model. , 1992, Statistics in medicine.

[13]  Cun-Hui Zhang.  PENALIZED LINEAR UNBIASED SELECTION , 2007 .

[14]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[15]  H. Zou.  The Adaptive Lasso and Its Oracle Properties , 2006 .

[16]  Jianqing Fan,et al.  Ultrahigh Dimensional Variable Selection: beyond the linear model , 2008, 0812.3201.

[17]  M. Pagano,et al.  Survival analysis. , 1996, Nutrition.

[18]  Hao Helen Zhang,et al.  Adaptive Lasso for Cox's proportional hazards model , 2007 .

[19]  S. MacEachern,et al.  Bayesian variable selection for proportional hazards models , 1999 .

[20]  H. Zou,et al.  One-step Sparse Estimates in Nonconcave Penalized Likelihood Models. , 2008, Annals of statistics.

[21]  Jeffrey S. Morris,et al.  Sure independence screening for ultrahigh dimensional feature space Discussion , 2008 .

[22]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[23]  Yufeng Liu,et al.  VARIABLE SELECTION IN QUANTILE REGRESSION , 2009 .