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Research Articles

Variable selection and nonlinear effect discovery in partially linear mixture cure rate models

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Pages 156-177 | Received 13 Feb 2017, Accepted 23 Jul 2018, Published online: 08 Oct 2019

References

  • Boag JW. Maximum likelihood estimates of the proportion of patients cured by cancer therapy. J R Stat Soc. 1979;11:15–53.
  • Farewell VT. The use of mixture models for the analysis of survival data with long-term survivors. Biometrics. 1982;38:1041–1046. doi: 10.2307/2529885
  • Sy JP, Taylor JM. Estimation in a Cox proportional hazards cure model. Biometrics. 2000;56:227–236. doi: 10.1111/j.0006-341X.2000.00227.x
  • Cox DR. Regression models and life tables. J R Stat Soc Ser B. 1972;34:187–220.
  • Shao F, Li J, Ma S, et al. Semiparametric varying-coefficient model for interval censored data with a cured proportion. Stat Med. 2014;33(10):1700–1712. doi: 10.1002/sim.6054
  • Li J, Ma S. Interval-censored data with repeated measurements and a cured subgroup. J R Stat Soc Ser C. 2010;59(4):693–705.
  • Corbiére F, Commenges D, Taylor J, et al. A penalized likelihood approach in mixture cure models. Stat in Med. 2009;28:510–524. doi: 10.1002/sim.3481
  • Wang L, Du P, Liang H. Two-component mixture cure rate model with spline estimated nonparametric components. Biometrics. 2012;68(3):726–735. doi: 10.1111/j.1541-0420.2011.01715.x
  • Hastie T, Tibshirani R. Exploring the nature of covariate effects in the proportional hazards model. Biometrics. 1990;46:1005–1016. doi: 10.2307/2532444
  • Hastie T, Tibshirani R, Friedman J. The elements of statistical learning. New York: Springer-Verlag; 2001.
  • Tibshirani R. Regression shrinkage and selection via the LASSO. J R Stat Soc Ser B. 1996;56:267–288.
  • Tibshirani R. The LASSO method for variable selection in the Cox model. Stat Med. 1997;16:385–395. doi: 10.1002/(SICI)1097-0258(19970228)16:4<385::AID-SIM380>3.0.CO;2-3
  • Fan J, Li R. Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Stat Assoc. 2001;96:1348–1360. doi: 10.1198/016214501753382273
  • Zou H. The adaptive LASSO and its oracle properties. J Am Stat Assoc. 2006;101:1418–1429. doi: 10.1198/016214506000000735
  • Zhang HH, Lu W. Adaptive LASSO for Cox's proportional hazard model. Biometrika. 2007;94:691–703. doi: 10.1093/biomet/asm037
  • He Z, Tu W, Wang S, et al. Simultaneous variable selection for joint models of longitudinal and survival outcomes. Biometrics. 2015;71:178–187. doi: 10.1111/biom.12221
  • Eilers P, Marx B. Flexible smoothing with B-splines and penalties. Stat Sci. 1996;11(2):89–121. doi: 10.1214/ss/1038425655
  • Zhang HH, Cheng G, Liu Y. Linear or nonlinear? Automatic structure discovery for partially linear models. J Am Stat Assoc. 2011;10:1099–1012. doi: 10.1198/jasa.2011.tm10281
  • Liu X, Peng Y, Tu D, et al. Variable selection in semiparametric cure models based on penalized likelihood, with application to breast cancer clinical trials. Stat Med. 2012;31:2882–2891. doi: 10.1002/sim.5378
  • Wand MP, Ormerod J. On semiparametric regression with O'Sullivan penalised splines. Aus NZ J Stat. 2008;50:179–198. doi: 10.1111/j.1467-842X.2008.00507.x
  • O'Sullivan F. A statistical perspective on ill posed inverse problems. Stat Sci. 1986;1:505–527.
  • Schwarz G. Estimating the dimension of a model. Ann Stat. 1978;19:461–464. doi: 10.1214/aos/1176344136
  • Nishii R. Asymptotic properties of criteria for selection of variables in multiple regression. Ann Stat. 1984;12:758–765. doi: 10.1214/aos/1176346522
  • Zou H, Li R. One-step sparse estimates in nonconcave penalized likelihood models. Ann Stat. 2008;36:1509–1533. doi: 10.1214/009053607000000802
  • Zhang Y, Li R, Tsai CL. Regularization parameters selection via generalized information criterion. J Am Stat Assoc. 2010;105:312–323. doi: 10.1198/jasa.2009.tm08013
  • Moore D, McCabe GP. Introduction to the practice of statistics. Freeman and Company: New York; 2009.
  • Berk R, Brown L, Buja A, et al. Valid post-selection inference. Ann Stat. 2013;41(2):802–837. doi: 10.1214/12-AOS1077
  • Tu W, Eckert G, DiMeglio L, et al. Intesnsified effects of adiposity on blood pressure in overweight and obese children. Hypertension. 2011;58:818–824. doi: 10.1161/HYPERTENSIONAHA.111.175695
  • National High Blood Pressure Education Program Working Group on High Blood Pressure in Children and Adolescents. The fourth report on the diagnosis, evaluation, and treatment of high blood pressure in children and adolescents. Pediatrics. 2004;114:555–576. doi: 10.1542/peds.114.2.S2.555
  • Li Z, Liu H, Tu W. A sexually transmitted infection screening algorithm based on semiparametric regression models. Stat in Med. 2015;34(20):2844–2857. doi: 10.1002/sim.6515
  • Yan J, Huang J. Model selection for Cox models with time-varying coefficients. Biometrics. 2012;68(2):419–428. doi: 10.1111/j.1541-0420.2011.01692.x

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