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Unified multivariate survival model with a surviving fraction: an application to a Brazilian customer churn data

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  • Vicente G. Cancho
  • Dipak K. Dey
  • Francisco Louzada

Abstract

In this paper we propose a new lifetime model for multivariate survival data in presence of surviving fractions and examine some of its properties. Its genesis is based on situations in which there are m types of unobservable competing causes, where each cause is related to a time of occurrence of an event of interest. Our model is a multivariate extension of the univariate survival cure rate model proposed by Rodrigues et al. [37]. The inferential approach exploits the maximum likelihood tools. We perform a simulation study in order to verify the asymptotic properties of the maximum likelihood estimators. The simulation study also focus on size and power of the likelihood ratio test. The methodology is illustrated on a real data set on customer churn data.

Suggested Citation

  • Vicente G. Cancho & Dipak K. Dey & Francisco Louzada, 2016. "Unified multivariate survival model with a surviving fraction: an application to a Brazilian customer churn data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(3), pages 572-584, March.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:3:p:572-584
    DOI: 10.1080/02664763.2015.1071341
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    References listed on IDEAS

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    1. Dimitris Karlis, 2003. "An EM algorithm for multivariate Poisson distribution and related models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(1), pages 63-77.
    2. Chen, Ming-Hui & Ibrahim, Joseph G. & Sinha, Debajyoti, 2002. "Bayesian Inference for Multivariate Survival Data with a Cure Fraction," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 101-126, January.
    3. Mazucheli, Josmar & Louzada-Neto, Francisco & Achcar, Jorge A., 2001. "Bayesian inference for polyhazard models in the presence of covariates," Computational Statistics & Data Analysis, Elsevier, vol. 38(1), pages 1-14, November.
    4. Barriga, Gladys D.C. & Louzada-Neto, Franscisco & Cancho, Vicente G., 2011. "The complementary exponential power lifetime model," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1250-1259, March.
    5. Buckinx, Wouter & Van den Poel, Dirk, 2005. "Customer base analysis: partial defection of behaviourally loyal clients in a non-contractual FMCG retail setting," European Journal of Operational Research, Elsevier, vol. 164(1), pages 252-268, July.
    6. Francisco Louzada-Neto, 1999. "Polyhazard Models for Lifetime Data," Biometrics, The International Biometric Society, vol. 55(4), pages 1281-1285, December.
    7. Nilanjan Chatterjee & Joanna Shih, 2001. "A Bivariate Cure-Mixture Approach for Modeling Familial Association in Diseases," Biometrics, The International Biometric Society, vol. 57(3), pages 779-786, September.
    8. Tong, Edward N.C. & Mues, Christophe & Thomas, Lyn C., 2012. "Mixture cure models in credit scoring: If and when borrowers default," European Journal of Operational Research, Elsevier, vol. 218(1), pages 132-139.
    9. Rodrigues, Josemar & Cancho, Vicente G. & de Castro, Mrio & Louzada-Neto, Francisco, 2009. "On the unification of long-term survival models," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 753-759, March.
    10. Vicente Cancho & Heleno Bolfarine, 2001. "Modeling the presence of immunes by using the exponentiated-Weibull model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(6), pages 659-671.
    11. Cooner, Freda & Banerjee, Sudipto & Carlin, Bradley P. & Sinha, Debajyoti, 2007. "Flexible Cure Rate Modeling Under Latent Activation Schemes," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 560-572, June.
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