Estimation of copula-based models for lifetime medical costs

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Abstract

Medical cost data are recorded through medical care and the cost is always related to some sojourn in the health status of the patient. The total medical cost accumulated in the entire lifetime of a life is of great interest to the health insurance industry and government policy makers. In this paper, we develop a new method to assess the lifetime medical cost up to the death time by incorporating the dynamics of change in the health status of the patient based on incomplete data. A copula model is proposed to fit the cost lifetime medical data subject to a terminal event (death). A two-stage estimation procedure is applied to draw the statistical inference of the marginals and the copula parameters. The asymptotic properties of the estimators are established, and a simulation is performed to evaluate the proposed model and estimation methods.

Keywords

Dynamic change Medical cost Sojourn Copula model Two-stage estimation Pseudo-likelihood 
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Notes

Acknowledgments

We are truly grateful to the Associate Editor and the reviewers for their valuable and constructive comments and suggestions that helped to improve our paper substantially. This work was partially supported by the NSFC under Grant No. 11271317, Zhejiang Provincial Natural Science Foundation under Grant No. LY12A01017, Zhejiang Provincial Planning Projects of Philosophy and Social Science under Grant No. 12JCJJ17YB, and the Institute of Actuaries of Australia Research Grant. The authors are grateful to Miss Cuiliu Xiao for her support of the simulation in this paper.

References

  1. Andersen, P. K., Borgan, O., Gill, R. D., Keiding, N. (1993). Statistical Models Based on Counting Processes. New York: Springer.Google Scholar
  2. Carides, G. W. (2000). A regression-based method for estimating mean treatment cost in the presence of right-censoring. Biostatistics, 1, 299–313.Google Scholar
  3. Castelli, C., Combescure, C., Foucher, Y., Daures, J. P. (2007). Cost-effectiveness analysis in colorectal cancer using a semi-Markov model. Statistics in Medicine, 26, 5557–5571.Google Scholar
  4. Etzioni, R. D., Feuer, E. J., Sullivan, S. D., Lin, D. Y., Hu, C. C., Ramsey, S. D. (1999). On the use of survival analysis techniques to estimate medical care costs. Journal of Health Economics, 18, 365–380.Google Scholar
  5. Gardiner, J. C., Luo, Z. H., Bradley, C. J., Sirbu, C. U., Given, C. W. (2006). A dynamic model for estimating change in health status and costs. Statistics in Medicine, 25, 3648–3667.Google Scholar
  6. Hofert, M. (2008a). Sampling Archimedean copulas. Computational Statistics and Data Analysis, 52, 5163–5174.Google Scholar
  7. Hofert, M. (2008b). Efficiently sampling nested Archimedean copulas. Computational Statistics and Data Analysis, 55, 57–70.Google Scholar
  8. Hsieh, H. J., Chen, T. H. H., Chang, S. H. (2002). Assessing chronic disease progression using non-homogeneous exponential regression Markov models: an illustration using a selective breast cancer screening in Taiwan. Statistics in Medicine, 21, 3369–3382.Google Scholar
  9. Huang, J. (1996). Efficient estimation for the proportional hazards model with interval censoring. The Annals of Statistics, 24, 540–568.Google Scholar
  10. Hu, H. L. (1998). Pseudo Maximum Likelihood Estimation for Semiparametric Models. Ph.D. Thesis, University of Washington.Google Scholar
  11. Joe, H. (1997). Multivariate Models and Dependence Concepts. London: Chapman & Hall.Google Scholar
  12. Joe, H. (2005). Asymptotic efficiency of the two-stage estimation methods for copula-based models. Journal of Multivariate Analysis, 94, 401–419.Google Scholar
  13. Lin, D. Y., Feuer, E. J., Etzioni, R., Wax, Y. (1997). Estimating medical costs from incomplete follow-up data. Biometrics, 53, 419–434.Google Scholar
  14. Lin, D. Y. (2003). Regression analysis of incomplete medical cost data. Statistics in Medicine, 22, 1181–1200.Google Scholar
  15. McNeil, A. (2008). Sampling nested Archimedean copulas. Journal of Statistical Computation and Simulation, 78, 567–581.Google Scholar
  16. Nelsen, B. (2005). An Introduction to Copulas (2nd ed.). New York: Springer.Google Scholar
  17. Nixon, R. M., Thompson, S. G. (2004). Parametric modeling of cost data in medical studies. Statistics in Medicine, 23, 1311–1331.Google Scholar
  18. Polverejan, E., Gardiner, J. C., Bradley, C. J., Rovner, M. H., Rovner, D. (2003). Estimating mean hospital cost as a function of length of stay and patient characteristics. Health Economics, 12, 935–947.Google Scholar
  19. Shih, J. H., Louis, T. A. (1995). Inferences on the association parameter in copula models for bivariate survival data. Biometrics, 51, 1384–1399.Google Scholar
  20. Shorack, G. R., Wellner, J. A. (1986). Empirical Processes with Applications to Statistics. New York: John Wiley and Sons.Google Scholar
  21. Van Der Vaart, A. W., Weller, J. A. (1996). Weak Convergence and Empirical Processes (2nd ed.). New York: Springer.Google Scholar
  22. Zhou, X. H. (1998). Estimation of the log-normal mean. Statistics in Medicine, 17, 2251–2264.Google Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 2014

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsZhejiang University of Finance and EconomicsXia-Sha District, HangzhouChina
  2. 2.Department of Applied Finance and Actuarial StudiesMacquarie UniversityNorth RydeAustralia

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