A new mixture cure model under competing risks to score online consumer loans

References

• An, M. and Qi, Z., Competing risks models using mortgage duration data under the proportional hazards assumption. J. Real Estate Res., 2012, 34(1), 1–26.
   Web of Science ®Google Scholar
• Baesens, B., Van Gestel, T., Stepanova, M., Van den Poel, D. and Vanthienen, J., Neural network survival analysis for personal loan data. J. Oper. Res. Soc., 2005, 56(9), 1089–1098. doi: 10.1057/palgrave.jors.2601990
   Web of Science ®Google Scholar
• Banasik, J., Crook, J. and Thomas, L.C., Not if but when will borrowers default. J. Oper. Res. Soc., 1999, 50(12), 1185–1190. doi: 10.1057/palgrave.jors.2600851
   Web of Science ®Google Scholar
• Bellotti, T. and Crook, J., Credit scoring with macroeconomic variables using survival analysis. J. Oper. Res. Soc., 2009, 60(12), 1699–1707. doi: 10.1057/jors.2008.130
   Web of Science ®Google Scholar
• Bender, R., Augustin, T. and Blettner, M., Generating survival times to simulate Cox proportional hazards models. Stat. Med., 2005, 24(11), 1713–1723. doi: 10.1002/sim.2059
   PubMed Web of Science ®Google Scholar
• Bilmes, J.A., A gentle tutorial of the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models. Tech. rep., 1998.
   Google Scholar
• Casella, G. and Berger, R.L., Statistical Inference, 2002 (Duxbury: Pacific Grove, CA).
   Google Scholar
• Cox, D.R., Regression models and life-tables. J. R. Stat. Soc. Ser. B, 1972, 34(2), 187–220.
   Web of Science ®Google Scholar
• Crowder, M.J., Classical Competing Risks, 2001 (Chapman and Hall/CRC: London).
   Google Scholar
• Dirick, L., Claeskens, G. and Baesens, B., Time to default in credit scoring using survival analysis: A benchmark study. J. Oper. Res. Soc., 2017, 68(6), 652–665. doi: 10.1057/s41274-016-0128-9
   Web of Science ®Google Scholar
• Farewell, V.T., The use of mixture models for the analysis of survival data with long-term survivors. Biometrics, 1982, 38(4), 1041–1046. doi: 10.2307/2529885
   PubMed Web of Science ®Google Scholar
• Fine, J.P. and Gray, R.J., A proportional hazards model for the subdistribution of a competing risk. J. Am. Stat. Assoc., 1999, 94(446), 496–509. doi: 10.1080/01621459.1999.10474144
   Web of Science ®Google Scholar
• Friedman, J., Hastie, T. and Tibshirani, R., The Elements of Statistical Learning, 2001 (Springer: Berlin). Springer Series in Statistics.
   Google Scholar
• Green, J.R. and Shoven, J.B., The effects of interest rates on mortgage prepayments. NBER Working Paper No. w1246, December 1983. Available online at SSRN: https://ssrn.com/abstract=321301.
   Google Scholar
• Hernández-Orallo, J., Flach, P. and Ferri, C., A unified view of performance metrics: Translating threshold choice into expected classification loss. J. Mach. Learn. Res., 2012, 13(Oct), 2813–2869.
   Google Scholar
• Lam, K. and Wong, K.-Y., Semiparametric analysis of clustered interval-censored survival data with a cure fraction. Comput. Stat. Data. Anal., 2014, 79(Supplement C), 165–174. doi: 10.1016/j.csda.2014.05.019
   Google Scholar
• Lambrecht, B., Perraudin, W. and Satchell, S., Time to default in the UK mortgage market. Econ. Model., 1997, 14(4), 485–499. doi: 10.1016/S0264-9993(97)00003-5
   Web of Science ®Google Scholar
• Lending Club, 2017. Available online at: https://www.lendingclub.com/info/statistics.action (accessed 12 April 2017).
   Google Scholar
• Leow, M. and Crook, J., A new mixture model for the estimation of credit card exposure at default. Eur. J. Oper. Res., 2016, 249(2), 487–497. doi: 10.1016/j.ejor.2015.10.001
   Web of Science ®Google Scholar
• Lin, D.Y., On the Breslow estimator. Lifetime Data. Anal., 2007, 13(4), 471–480. doi: 10.1007/s10985-007-9048-y
   PubMed Web of Science ®Google Scholar
• Louzada, F., Cancho, V.G., De Oliveira Jr., M.R. and Bao, Y., Modeling time to default on a personal loan portfolio in presence of disproportionate hazard rates. J. Stat. Appl. Probab., 2014, 3, 1–11. doi: 10.18576/jsap/030101
   Google Scholar
• Narain, B., Survival analysis and the credit granting decision. In Credit Scoring and Credit Control, pp. 109–121, 1992. (Oxford University Press: Oxford).
   Google Scholar
• Peng, Y. and Dear, K.B., A nonparametric mixture model for cure rate estimation. Biometrics, 2000, 56(1), 237–243. doi: 10.1111/j.0006-341X.2000.00237.x
   PubMed Web of Science ®Google Scholar
• Schönbucher, P.J., Credit Derivatives Pricing Models: Models, Pricing and Implementation, 2003 (John Wiley & Sons: Hoboken, NJ).
   Google Scholar
• Serrano-Cinca, C., Gutierrez-Nieto, B. and López-Palacios, L., Determinants of default in P2P lending. PloS One, 2015, 10(10), e0139427. doi: 10.1371/journal.pone.0139427
   PubMed Web of Science ®Google Scholar
• Stepanova, M. and Thomas, L., Survival analysis methods for personal loan data. Oper. Res., 2002, 50(2), 277–289. doi: 10.1287/opre.50.2.277.426
   Web of Science ®Google Scholar
• Sy, J.P. and Taylor, J.M., Estimation in a Cox proportional hazards cure model. Biometrics, 2000, 56(1), 227–236. doi: 10.1111/j.0006-341X.2000.00227.x
   PubMed Web of Science ®Google Scholar
• Tong, E.N., Mues, C. and Thomas, L.C., Mixture cure models in credit scoring: If and when borrowers default. Eur. J. Oper. Res., 2012, 218(1), 132–139. doi: 10.1016/j.ejor.2011.10.007
   Web of Science ®Google Scholar
• West, D., Neural network credit scoring models. Comput. Oper. Res., 2000, 27(11), 1131–1152. doi: 10.1016/S0305-0548(99)00149-5
   Web of Science ®Google Scholar
• Wolter, M. and Rösch, D., Cure events in default prediction. Eur. J. Oper. Res., 2014, 238(3), 846–857. doi: 10.1016/j.ejor.2014.04.046
   Web of Science ®Google Scholar
• Wu, Y., Lin, Y., Lu, S.-E., Li, C.-S. and Shih, W.J., Extension of a Cox proportional hazards cure model when cure information is partially known. Biostatistics, 2014, 15(3), 540–554. doi: 10.1093/biostatistics/kxu002
   PubMed Web of Science ®Google Scholar
• Yu, B. and Peng, Y., Mixture cure models for multivariate survival data. Comput. Stat. Data Anal., 2008, 52(3), 1524–1532. doi: 10.1016/j.csda.2007.04.018
   Web of Science ®Google Scholar
• Zheng, M. and Klein, J.P., Estimates of marginal survival for dependent competing risks based on an assumed copula. Biometrika, 1995, 82(1), 127–138. doi: 10.1093/biomet/82.1.127
   Web of Science ®Google Scholar
• Zhu, C., Byrd, R.H., Lu, P. and Nocedal, J., Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization. ACM Trans. Math. Softw., 1997, 23(4), 550–560. doi: 10.1145/279232.279236
   Web of Science ®Google Scholar
• Zucchini, W., An introduction to model selection. J. Math. Psychol., 2000, 44(1), 41–61. doi: 10.1006/jmps.1999.1276
   PubMed Web of Science ®Google Scholar