Variable selection in proportional hazards cure model with time-varying covariates, application to US bank failuresFootnote^*

* An oral presentation of this paper was given at the 10th International Conference of the ERCIM WG on Computational and Methodological Statistics, Senate House, University of London, UK, 16–18 December 2017

References

• H. Akaike, Information theory and an extension of the maximum likelihood principle, 2nd International Symposium on Information Theory, Academiai Kiado, 1973.
   Google Scholar
• J.W. Boag, Maximum likelihood estimates of the proportion of patients cured by cancer therapy, J. R. Stat. Soc. Ser. B. Stat. Methodol. 11 (1949), pp. 15–53.
   Web of Science ®Google Scholar
• L. Breiman, Heuristics of instability and stabilization in model selection, Ann. Statist. 24 (1996), pp. 2350–2383. doi: 10.1214/aos/1032181158
   Web of Science ®Google Scholar
• N.E. Breslow, Contribution to the discussion of the paper by D.R. Cox, J. R. Stat. Soc. Ser. B. Stat. Methodol. 34 (1972), pp. 216–217.
   Google Scholar
• A.B. Cantor and J.J. Shuster, Parametric versus non-parametric methods for estimating cure rates based on censored survival data, Stat. Med. 11 (1992), pp. 931–937. doi: 10.1002/sim.4780110710
   PubMed Web of Science ®Google Scholar
• R.A. Cole and J.W. Gunther, Separating the likelihood and timing of bank failure, J. Bank. Financ. 19 (1995), pp. 1073–1089. doi: 10.1016/0378-4266(95)98952-M
   Web of Science ®Google Scholar
• D.R. Cox, Regression models and life-tables, J. R. Stat. Soc. Ser. B. Stat. Methodol. 34 (1972), pp. 187–220.
   Web of Science ®Google Scholar
• D. De Leonardis and R. Rocci, Default risk analysis via a discrete-time cure rate model, Appl. Stoch. Models Bus. Ind. 30 (2014), pp. 529–543. doi: 10.1002/asmb.1998
   Web of Science ®Google Scholar
• A. Demirgüç-Kunt, Deposit-institution failures: A review of empirical literature, Fed. Res. Bank Cleve. Econ. Rev. 25 (1989), pp. 2–19.
   Google Scholar
• Y. Demyanyk and I. Hasan, Financial crises and bank failures: A review of prediction methods, Omega 38 (2010), pp. 315–324. doi: 10.1016/j.omega.2009.09.007
   Web of Science ®Google Scholar
• J.W. Denham, E. Denham, K.B. Dear, and G.V. Hudson, The follicular non-hodgkin's lymphomas – I. The possibility of cure, Eur. J. Cancer 32 (1996), pp. 470–479. doi: 10.1016/0959-8049(95)00607-9
   Web of Science ®Google Scholar
• L. Dirick, T. Bellotti, G. Claeskens, and B. Baesens, Macro-economic factors in credit risk calculations: Including time-varying covariates in mixture cure models, J. Bus. Econom. Statist. (2016), pp. 1–14. DOI:10.1080/07350015.2016.1260471.
   Web of Science ®Google Scholar
• L. Dirick, G. Claeskens, and B. Baesens, An akaike information criterion for multiple event mixture cure models, Eur. J. Oper. Res. 241 (2015), pp. 449–457. doi: 10.1016/j.ejor.2014.08.038
   Web of Science ®Google Scholar
• J. Fan and R. Li, Variable selection via nonconcave penalized likelihood and its oracle properties, J. Amer. Statist. Assoc. 96 (2001), pp. 1348–1360. doi: 10.1198/016214501753382273
   Web of Science ®Google Scholar
• J. Fan and R. Li, Variable selection for Cox's proportional hazards model and frailty model, Ann. Statist. 30 (2002), pp. 74–99. doi: 10.1214/aos/1015362185
   Web of Science ®Google Scholar
• J. Fan and R. Li, New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis, J. Amer. Statist. Assoc. 99 (2004), pp. 710–723. doi: 10.1198/016214504000001060
   Web of Science ®Google Scholar
• J. Fan and H. Peng, Nonconcave penalized likelihood with a diverging number of parameters, Ann. Statist. 32 (2004), pp. 928–961. doi: 10.1214/009053604000000256
   Web of Science ®Google Scholar
• V.T. Farewell, The use of mixture models for the analysis of survival data with long-term survivors, Biometrics 38 (1982), pp. 1041–1046. doi: 10.2307/2529885
   PubMed Web of Science ®Google Scholar
• V.T. Farewell, Mixture models in survival analysis: Are they worth the risk? Canad. J. Statist. 14 (1986), pp. 257–262. doi: 10.2307/3314804
   Web of Science ®Google Scholar
• M. Ghitany, R.A. Maller, and S. Zhou, Exponential mixture models with long-term survivors and covariates, J. Multivariate Anal. 49 (1994), pp. 218–241. doi: 10.1006/jmva.1994.1023
   Web of Science ®Google Scholar
• D.J. Hendry, Data generation for the Cox proportional hazards model with time-dependent covariates: A method for medical researchers, Stat. Med. 33 (2014), pp. 436–454. doi: 10.1002/sim.5945
   PubMed Web of Science ®Google Scholar
• A.E. Hoerl and R.W. Kennard, Ridge regression: Applications to nonorthogonal problems, Technometrics 12 (1970), pp. 69–82. doi: 10.1080/00401706.1970.10488635
   Web of Science ®Google Scholar
• D.R. Hunter and R. Li, Variable selection using MM algorithms, Ann. Statist. 33 (2005), pp. 1617–1642. doi: 10.1214/009053605000000200
   PubMed Web of Science ®Google Scholar
• D. Jones, R. Powles, D. Machin, and R. Sylvester, On estimating the proportion of cured patients in clinical studies, Biom. Praximetrie 21 (1981), pp. 1–11.
   Google Scholar
• J.D. Kalbfleisch and R.L. Prentice, The Statistical Analysis of Failure Time Data, John Wiley & Sons, Hoboken, NJ, 2002.
   Google Scholar
• A.Y. Kuk and C.H. Chen, A mixture model combining logistic regression with proportional hazards regression, Biometrika 79 (1992), pp. 531–541. doi: 10.1093/biomet/79.3.531
   Web of Science ®Google Scholar
• W.R. Lane, S.W. Looney, and J.W. Wansley, An application of the Cox proportional hazards model to bank failure, J. Bank. Financ. 10 (1986), pp. 511–531. doi: 10.1016/S0378-4266(86)80003-6
   Web of Science ®Google Scholar
• H. Leeb and B.M. Pötscher, On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding, J. Multivariate Anal. 100 (2009), pp. 2065–2082. doi: 10.1016/j.jmva.2009.06.010
   Web of Science ®Google Scholar
• F. Liu, Z. Hua, and A. Lim, Identifying future defaulters: A hierarchical Bayesian method, Eur. J. Oper. Res. 241 (2015), pp. 202–211. doi: 10.1016/j.ejor.2014.08.008
   Web of Science ®Google Scholar
• T.A. Louis, Finding the observed information matrix when using the EM algorithm, J. R. Stat. Soc. Ser. B. Stat. Methodol. 44 (1982), pp. 226–233.
   Web of Science ®Google Scholar
• C.L. Mallows, Some comments on Cp, Technometrics 15 (1973), pp. 661–675.
   Web of Science ®Google Scholar
• G. McLachlan and T. Krishnan, The EM Algorithm and Extensions, John Wiley & Sons, Hoboken, NJ, 2008.
   Google Scholar
• Y. Peng and K.B. Dear, A nonparametric mixture model for cure rate estimation, Biometrics 56 (2000), pp. 237–243. doi: 10.1111/j.0006-341X.2000.00237.x
   PubMed Web of Science ®Google Scholar
• R.M. Pfeiffer, A. Redd, and R.J. Carroll, On the impact of model selection on predictor identification and parameter inference, Comput. Stat. 32 (2017), pp. 667–690. doi: 10.1007/s00180-016-0690-2
   PubMed Web of Science ®Google Scholar
• C. Sanderson and R. Curtin, Armadillo: A template-based c++ library for linear algebra, J. Open Source Softw. 1 (2016), pp. 26–32. doi: 10.21105/joss.00026
   Google Scholar
• G. Schwarz, Estimating the dimension of a model, Ann. Statist. 6 (1978), pp. 461–464. doi: 10.1214/aos/1176344136
   Web of Science ®Google Scholar
• H. Shi and G. Yin, Landmark cure rate models with time-dependent covariates, Stat. Methods Med. Res. 26 (2017), pp. 2042–2054. doi: 10.1177/0962280217708681
   PubMed Web of Science ®Google Scholar
• J.P. Sy and J.M. Taylor, Estimation in a Cox proportional hazards cure model, Biometrics 56 (2000), pp. 227–236. doi: 10.1111/j.0006-341X.2000.00227.x
   PubMed Web of Science ®Google Scholar
• J.P. Sy and J.M. Taylor, Standard errors for the Cox proportional hazards cure model, Math. Comput. Model 33 (2001), pp. 1237–1251. doi: 10.1016/S0895-7177(00)00312-5
   Google Scholar
• J.B. Thomson, Predicting bank failures in the 1980s, Fed. Res. Bank Cleve. Econ. Rev. 27 (1991), pp. 9–20.
   Google Scholar
• R. Tibshirani, Regression shrinkage and selection via the lasso, J. R. Stat. Soc. Ser. B. Stat. Methodol. 58 (1996), pp. 267–288.
   Web of Science ®Google Scholar
• E.N. Tong, C. Mues, and L.C. Thomas, Mixture cure models in credit scoring: If and when borrowers default, Eur. J. Oper. Res. 218 (2012), pp. 132–139. doi: 10.1016/j.ejor.2011.10.007
   Web of Science ®Google Scholar
• G. Whalen, A proportional hazards model of bank failure: An examination of its usefulness as an early warning tool, Fed. Res. Bank Cleve. Econ. Rev. 27 (1991), pp. 21–30.
   Google Scholar
• D.C. Wheelock and P.W. Wilson, Why do banks disappear? The determinants of US bank failures and acquisitions, Rev. Econ. Stat. 82 (2000), pp. 127–138. doi: 10.1162/003465300558560
   Web of Science ®Google Scholar
• Y. Zhang, R. Li, and C.L. Tsai, Regularization parameter selections via generalized information criterion, J. Amer. Statist. Assoc. 105 (2010), pp. 312–323. doi: 10.1198/jasa.2009.tm08013
   PubMed Web of Science ®Google Scholar
• H. Zou, The adaptive lasso and its oracle properties, J. Amer. Statist. Assoc. 101 (2006), pp. 1418–1429. doi: 10.1198/016214506000000735
   Web of Science ®Google Scholar