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Abstract
Failure-time data with cured patients are common in clinical studies. Data from these studies are typically analyzed with cure rate models. Variable selection methods have not been well developed for cure rate models. In this research, we propose two least absolute shrinkage and selection operators based methods, for variable selection in mixture and promotion time cure models with parametric or nonparametric baseline hazards. We conduct an extensive simulation study to assess the operating characteristics of the proposed methods. We illustrate the use of the methods using data from a study of childhood wheezing.
References
| 1. | Cox, DR . Regression models and life-tables. J R Stat Soc Ser B 1972; 34: 187–220. Google Scholar |
| 2. | Sy, JP, Taylor, JMG. Estimation in a Cox proportional hazards cure model. Biometrics 2000; 56: 227–236. Google Scholar | Medline | ISI |
| 3. | Tepper, RS, Llapur, CJ, Jones, MH Expired nitric oxide and airway reactivity in infants at risk for asthma. Am Acad Allergy Asthma Immunol 2008; 122: 760–765. Google Scholar | Medline |
| 4. | Chen, T . Statistical issues and challenges in immuno-oncology. J Immunother Cancer 2013; 11: 1–18. Google Scholar |
| 5. | Boag, JW . Maximum likelihood estimates of the proportion of patients cured by cancer therapy. J R Stat Soc 1949; 11: 15–53. Google Scholar |
| 6. | Farewell, VT . The use of mixture models for the analysis of survival data with long-term survivors. Biometrics 1982; 38: 1041–1046. Google Scholar | Medline | ISI |
| 7. | Taylor, JMG . Semi-parametric estimation in failure time mixture models. Biometrics 1995; 51: 899–907. Google Scholar | Medline | ISI |
| 8. | Peng, Y, Dear, KBG. A nonparametric mixture model for cure rate estimation. Biometrics 2000; 56: 237–243. Google Scholar | Medline | ISI |
| 9. | Yakovlev, AY, Asselain, B, Bardou, VJ A nonparametric mixture model for cure rate estimation. Biometr Anal Dormees Spatio-Temporelles 1993; 12: 66–82. Google Scholar |
| 10. | Chen, MH, Ibrahim, JG, Sinha, D. A Bayesian approach to survival data with a cure fraction. J Am Stat Assoc 1999; 94: 909–919. Google Scholar | ISI |
| 11. | Ibrahim, JG, Chen, MH, Sinha, D. Bayesian survival analysis, New York, NY: Springer, 2002. Google Scholar |
| 12. | Chen, MH, Ibrahim, JG, Lipsitz, SR. Bayesian methods for missing covariates in cure rate models. Lifetime Data Anal 2002; 8: 117–146. Google Scholar | Medline | ISI |
| 13. | Chen, MH, Ibrahim, JG. Maximum likelihood methods for cure rate models with missing covariates. Biometrics 2001; 57: 43–52. Google Scholar | Medline | ISI |
| 14. | Tsodikov, AD, Ibrahim, JG, Yakovlev, AY. Estimating cure rates from survival data: an alternative to two-component mixture models. Lifetime Data Anal 2003; 98: 1063–1078. Google Scholar |
| 15. | Broët, P, De Rycke, Y, Tubert-Bitter, P A semiparametric approach for the two-sample comparison of survival times with long-term survivors. Biometrics 2001; 57: 844–852. Google Scholar | Medline | ISI |
| 16. | Yin, G, Ibrahim, JG. Cure rate models: a unified approach. Can J Stat 2005; 57: 559–570. Google Scholar |
| 17. | Breiman, L . Heuristics of instability and stabilization in model selection. Ann Stat 1996; 24: 2350–2383. Google Scholar | ISI |
| 18. | Tibshirani, R . Regression shrinkage and selection via the LASSO. J R Stat Soc Ser B 1996; 56: 267–288. Google Scholar |
| 19. | Tibshirani, R . The lasso method for variable selection in the Cox model. Stat Med 1997; 16: 385–395. Google Scholar | Medline | ISI |
| 20. | Fan, J, Li, R. Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Stat Assoc 2001; 96: 1348–1360. Google Scholar | ISI |
| 21. | Zhang, HH, Lu, W. Adaptive lasso for Cox’s proportional hazard model. Biometrika 2007; 94: 691–703. Google Scholar | ISI |
| 22. | He, Z, Tu, W, Wang, S Simultaneous variable selection for joint models of longitudinal and survival outcomes. Biometrics 2015; 71: 178–187. Google Scholar | Medline |
| 23. | Liu, X, Peng, Y, Tu, D Variable selection in semiparametric cure models based on penalized likelihood, with application to breast cancer clinical trails. Stat Med 2012; 31: 2882–2891. Google Scholar | Medline |
| 24. | Zou, H . The adaptive LASSO and its oracle properties. J Am Stat Assoc 2006; 101: 1418–1429. Google Scholar | ISI |
| 25. | Klein, JP . Semiparametric estimation of random effects using the Cox model based on the EM algorithm. Biometrics 1982; 48: 795–806. Google Scholar |
| 26. | Nishii, R . Asymptotic properties of criteria for selection of variables in multiple regression. Ann Stat 1984; 12: 758–765. Google Scholar |
| 27. | Schwarz, G . Estimating the dimension of a model. Ann Stat 1978; 19: 461–464. Google Scholar |
| 28. | Zou, H, Li, R. One step sparse estimates in nonconcave penalized likelihood models. Ann Stat 2008; 36: 1509–1533. Google Scholar | Medline | ISI |
| 29. | Zhang, Y, Li, R, Tsai, CL. Regularization parameters selection via generalized information criterion. J Am Stat Assoc 2010; 105: 312–323. Google Scholar | Medline | ISI |
| 30. | Moore, D, McCabe, GP. Introduction to the practice of statistics, New York, NY: Freeman and Company, 2009. Google Scholar |
| 31. | Berk, R, Brown, L, Buja, A A penalized likelihood approach in mixture cure models. Ann Stat 2013; 41: 802–837. Google Scholar |
| 32. | Tsodikov, D . A proportional hazards model taking account of long term survivors. Biometrics 1998; 54: 1508–1516. Google Scholar | Medline | ISI |
| 33. | Corbiere, F, Commenges, D, Taylor, JMC. A penalized likelihood approach in mixture cure models. Stat Med 2009; 28: 510–524. Google Scholar | Medline |
