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Erschienen in: Soft Computing 1/2014

01.01.2014 | Methodologies and Application

A novel L1/2 regularization shooting method for Cox’s proportional hazards model

verfasst von: Xin-Ze Luan, Yong Liang, Cheng Liu, Kwong-Sak Leung, Tak-Ming Chan, Zong-Ben Xu, Hai Zhang

Erschienen in: Soft Computing | Ausgabe 1/2014

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Abstract

Nowadays, a series of methods are based on a L 1 penalty to solve the variable selection problem for a Cox’s proportional hazards model. In 2010, Xu et al. have proposed a L 1/2 regularization and proved that the L 1/2 penalty is sparser than the L 1 penalty in linear regression models. In this paper, we propose a novel shooting method for the L 1/2 regularization and apply it on the Cox model for variable selection. The experimental results based on comprehensive simulation studies, real Primary Biliary Cirrhosis and diffuse large B cell lymphoma datasets show that the L 1/2 regularization shooting method performs competitively.

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Literatur
Zurück zum Zitat Akaike H (1973) Information theory and an extension of the maximum likelihood principle. In: Petrov BN, Caki F (eds) Second International Symposium on Information Theory. Akademiai Kiado, Budapest, pp 267–281 Akaike H (1973) Information theory and an extension of the maximum likelihood principle. In: Petrov BN, Caki F (eds) Second International Symposium on Information Theory. Akademiai Kiado, Budapest, pp 267–281
Zurück zum Zitat Brier GW (1950) Verification of forecasts expressed in terms of probability. Mon Weather Rev 78:1–3CrossRef Brier GW (1950) Verification of forecasts expressed in terms of probability. Mon Weather Rev 78:1–3CrossRef
Zurück zum Zitat Cox DR (1972) Regression models and life-tables. J R Statist Soc B 34:187–220MATH Cox DR (1972) Regression models and life-tables. J R Statist Soc B 34:187–220MATH
Zurück zum Zitat Dickson E, Grambsch P, Fleming T, Fisher L, Langworthy A (1989) Prognosis in primary biliary cirrhosis: model for decision making. Hepatology 10:1–7CrossRef Dickson E, Grambsch P, Fleming T, Fisher L, Langworthy A (1989) Prognosis in primary biliary cirrhosis: model for decision making. Hepatology 10:1–7CrossRef
Zurück zum Zitat Fan J, Heng P (2004) Nonconcave penalty likelihood with a diverging number of parameters. Ann Stat 32(2):928–961MATH Fan J, Heng P (2004) Nonconcave penalty likelihood with a diverging number of parameters. Ann Stat 32(2):928–961MATH
Zurück zum Zitat Fan J, LI R (2001) Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Stat Assoc 96:1348–1360CrossRefMATHMathSciNet Fan J, LI R (2001) Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Stat Assoc 96:1348–1360CrossRefMATHMathSciNet
Zurück zum Zitat Fu W (1998) Penalized regression: the bridge versus the lasso. J Comp Graph Stat 7:397–416 Fu W (1998) Penalized regression: the bridge versus the lasso. J Comp Graph Stat 7:397–416
Zurück zum Zitat Graf E, Schmoor C, Sauerbrei W, Schumacher M (1999) Assessment and comparison of prognostic classification schemes for survival data. Stat Med 18:2529–2545CrossRef Graf E, Schmoor C, Sauerbrei W, Schumacher M (1999) Assessment and comparison of prognostic classification schemes for survival data. Stat Med 18:2529–2545CrossRef
Zurück zum Zitat Gui J, Li H (2005) Penalized Cox regression analysis in the high-dimensional and low-sample size settings, with applications to microarray gene expression data. Bioinformatics 21:3001–3008CrossRef Gui J, Li H (2005) Penalized Cox regression analysis in the high-dimensional and low-sample size settings, with applications to microarray gene expression data. Bioinformatics 21:3001–3008CrossRef
Zurück zum Zitat Heagerty PJ et al (2000) Time dependent ROC curves for censored survival data and a diagnostic marker. Biometrics 56:337–344CrossRefMATHMathSciNet Heagerty PJ et al (2000) Time dependent ROC curves for censored survival data and a diagnostic marker. Biometrics 56:337–344CrossRefMATHMathSciNet
Zurück zum Zitat Huang J, Harrington D (2002) Penalized partial likelihood regression for right censored data with bootstrap selection of the penalty parameter. Biometrics 58:781–791CrossRefMATHMathSciNet Huang J, Harrington D (2002) Penalized partial likelihood regression for right censored data with bootstrap selection of the penalty parameter. Biometrics 58:781–791CrossRefMATHMathSciNet
Zurück zum Zitat Ibrahim JG, Chen M-H, Maceachern SN (1999) Bayesian variable selection for proportional hazards models. Can J Stat 27:701–717CrossRefMATHMathSciNet Ibrahim JG, Chen M-H, Maceachern SN (1999) Bayesian variable selection for proportional hazards models. Can J Stat 27:701–717CrossRefMATHMathSciNet
Zurück zum Zitat Qian J, Li B, Chen PY (2010) Generating survival data in the simulation studies of cox model. Inf Comput (ICIC) 4:93–96 Qian J, Li B, Chen PY (2010) Generating survival data in the simulation studies of cox model. Inf Comput (ICIC) 4:93–96
Zurück zum Zitat Rosenwald A et al (2002) The use of molecular profiling to predict survival after chemotherapy for diffuse large B-cell lymphoma. New Engl J Med 346:1937–1946CrossRef Rosenwald A et al (2002) The use of molecular profiling to predict survival after chemotherapy for diffuse large B-cell lymphoma. New Engl J Med 346:1937–1946CrossRef
Zurück zum Zitat Sauerbrei W, Schumacher M (1992) A bootstrap resampling procedure for model building: application to the cox regression model. Stat Med 11:2093–2109CrossRef Sauerbrei W, Schumacher M (1992) A bootstrap resampling procedure for model building: application to the cox regression model. Stat Med 11:2093–2109CrossRef
Zurück zum Zitat Smyth P (2001) Model selection of probabilistic clustering using cross-validated likelihood. Stat and Comput 10:63–72CrossRef Smyth P (2001) Model selection of probabilistic clustering using cross-validated likelihood. Stat and Comput 10:63–72CrossRef
Zurück zum Zitat Therneau TM, Grambsch PM (2000) Modeling survival data: Extending the Cox model. Springer-Verlag Inc., NewYorkCrossRef Therneau TM, Grambsch PM (2000) Modeling survival data: Extending the Cox model. Springer-Verlag Inc., NewYorkCrossRef
Zurück zum Zitat Tibshirani R (1996) Regression shrinkage and selection via the lasso. J R Stat Soc B 58:267–288MATHMathSciNet Tibshirani R (1996) Regression shrinkage and selection via the lasso. J R Stat Soc B 58:267–288MATHMathSciNet
Zurück zum Zitat Tibshirani R (1997) The lasso method for variable selection in the Cox model. Stat Med 16:385–395CrossRef Tibshirani R (1997) The lasso method for variable selection in the Cox model. Stat Med 16:385–395CrossRef
Zurück zum Zitat Van Der Laan MJ, Dudoit S, Keles S (2003) Asymptotic Optimality of likelihood based Cross Validation, Technical Report, Division of Biostatistics, University of California, Berkeley Van Der Laan MJ, Dudoit S, Keles S (2003) Asymptotic Optimality of likelihood based Cross Validation, Technical Report, Division of Biostatistics, University of California, Berkeley
Zurück zum Zitat Verwij PJM, Van Houwelingen JC (1993) Cross validation in survival analysis. Stat Med 12:2305–2314CrossRef Verwij PJM, Van Houwelingen JC (1993) Cross validation in survival analysis. Stat Med 12:2305–2314CrossRef
Zurück zum Zitat Xu ZB, Zhang H, Wang Y, Chang XY (2010) L 1/2 regularization. Sci China, ser F 40(3):1–11 Xu ZB, Zhang H, Wang Y, Chang XY (2010) L 1/2 regularization. Sci China, ser F 40(3):1–11
Zurück zum Zitat Zou H (2006) The adaptive Lasso and its oracle properties. J Am Stat Assoc 101(476):1418–1429CrossRefMATH Zou H (2006) The adaptive Lasso and its oracle properties. J Am Stat Assoc 101(476):1418–1429CrossRefMATH
Metadaten
Titel
A novel L1/2 regularization shooting method for Cox’s proportional hazards model
verfasst von
Xin-Ze Luan
Yong Liang
Cheng Liu
Kwong-Sak Leung
Tak-Ming Chan
Zong-Ben Xu
Hai Zhang
Publikationsdatum
01.01.2014
Verlag
Springer Berlin Heidelberg
Erschienen in
Soft Computing / Ausgabe 1/2014
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-013-1042-6

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