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Frailty modelling of time-to-lapse of single policies for customers holding multiple car contracts. (English) Zbl 1401.91146

Summary: Corporate customers often hold multiple contracts and this might give dependence between the lapsing times of the single policies. We present a shared gamma frailty model in order to study the time-to-lapse of single car policies for customers holding multiple car contracts with the same insurance company, accounting for measured and time-dependent covariates. Customers with the highest frailty value tend to leave the company earlier than the others and finding these is a central aspect within a company’s customer relationship management strategy. We estimate conditional survival curves which illustrate the decreased survival probability of a customer after a lapse in a single car insurance policy. The individual survival curves are overestimated if the underlying association for cars with the same customer is ignored. Fitting misspecified Cox’s proportional hazards model also results in an underestimation of the standard error of the parameter estimates.

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
62N05 Reliability and life testing

Software:

car; frailtypack; R
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References:

[1] Aalen, O. O. (1988). Heterogeneity in survival analysis. Statistics in Medicine7 (11), 1121-1137.
[2] Antonio, K., Frees, E. W. & Valdez, E. A. (2010). A multilevel analysis of intercompany claim counts. Astin Bulletin40 (1), 151-177.
[3] Brockett, P. L., Golden, L. L., Guillen, M., Nielsen, J. P., Parner, J. & Perez-Marin, A. M. (2008). Survival analysis of a household portfolio of insurance policies: How much time do you have to stop total customer defection?The Journal of Risk and Insurance75 (3), 713-737.
[4] Clayton, D. G. (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika65 (1), 141-151. · Zbl 0394.92021
[5] Cox, D. R. (1972). Regression models and life-tables (with discussion). Journal of the Royal Statistical Society: Series B Statistical Methodology34 (2), 187-220. · Zbl 0243.62041
[6] Desjardins, D., Dionne, G. & Pinquet, J. (2001). Experience rating schemes for fleets of vehicles. Astin Bulletin31 (1), 81-105. · Zbl 1087.91513
[7] Dimakos, X. K., Storvik, B. & Vårdal, J. F., (2009). Kundelojalitet i PVK/BIL NL. NR-Note, SAMBA/51/08, Norwegian Computing Center.
[8] Drzewiecki, K. T. & Andersen, P. K. (1982). Survival with malignant melanoma: a regression analysis of prognostic factors. Cancer49 (11), 2414-2419.
[9] Fox, J. (2002). Cox Proportional-Hazards Regression for Survival Data: Appendix to An R and S-PLUS Companion to Applied Regression. Available online at: http://cran.r-project.org/doc/contrib/Fox-Companion/appendix-cox-regression.pdf.
[10] Günther, C.-C., Tvete, I. F., Aas, K., Sandnes, G. I. & Borgan, Ø. (2014). Modelling and predicting customer churn from an insurance company. Scandinavian Actuarial Journal2014 (1), 58-71. · Zbl 1401.91144
[11] Henderson, R. & Oman, P. (1999). Effect of frailty on marginal regression estimates in survival analysis. Journal of the Royal Statistical Society: Series B Statistical Methodology61 (2), 367-379. · Zbl 0913.62097
[12] Hirsch, K. & Wienke, A. (2012). Software for semiparametric shared gamma and log-normal frailty models: An overview. Computer Methods and Programs in Biomedicine107 (3), 582-597.
[13] Hougaard, P. (1995). Frailty models for survival data. Lifetime Data Analysis1 (3), 255-273.
[14] Hougaard, P. (2000). Analysis of multivariate survival data. New York: Springer. · Zbl 0962.62096
[15] Jepsen, P., Vilstrup, H., Andersen, P. K., Lash, T. L. & Sørensen, H. T. (2008). Comorbidity and survival of Danish cirrhosis patients: A nationwide population-based cohort study. Hepatology48 (1), 214-220.
[16] Keiding, N., Andersen, C. & Fledelius, P. (1998). The Cox regression model for claims data in non-life insurance. Astin Bulletin28 (1), 95-118. · Zbl 1168.62390
[17] Maruza, M., Albuquerque, M. F. P. M., Braga, M. C., Barbosa, M. T. S., Byington, R., Coimbra, I., Moura, L. V., Batista, J. D. L., Diniz, G. T. N., Miranda-Filho, D. B., Lacerda, H. R., Rodrigues, L. C. & Ximenes, R. A. A. (2012). Survival of HIV-infected patients after starting tuberculosis treatment: a prospective cohort study. The International Journal of Tuberculosis and Lung Disease16 (5), 618-624.
[18] Moger, T. A. & Aalen, O. O. (2008). Regression models for infant mortality data in Norwegian siblings, using a compound Poisson frailty distribution with random scale. Biostatistics9 (3), 577-591. · Zbl 1143.62063
[19] R Development Core Team, (2012). R: A language and environment for statistical computing. R Foundation for Statistical ComputingVienna, Austria. Available online at: http://www.r-project.org/.
[20] Rondeau, V., Mazroui, Y. & Gonzalez, J. R. (2012). frailtypack: An R package for the analysis of correlated survival data with frailty models using penalized likelihood estimation or parametrical estimation. Journal of Statistical Software47 (4), 1-28.
[21] Therneau, T. M. & Grambsch, P. M. (2000). Modeling survival data: Extending the Cox model. New York: Springer. · Zbl 0958.62094
[22] Therneau, T. M., Grambsch, P. M. & Pankratz, V. S. (2003). Penalized survival models and frailty. Journal of Computational and Graphical Statistics12 (1), 156-175.
[23] Van den Poel, D. & Lariviére, B. (2004). Customer attrition analysis for financial services using proportional hazard models. European Journal of Operational Research157 (1), 196-217. · Zbl 1106.91318
[24] Wong, J.-T. & Tsai, S.-C. (2012). A survival model for flight delay propagation. Journal of Air Transport Management23, 5-11.
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