Comparing One-Part Models and Two-Parts Models for the Prediction of Total Claim Amount in Health Insurance

Abstract

Linear regression and lognormal models are the one-part models that are traditionally used to analyse health care expenditures. The method of two-part models is frequently used as an alternative to one-part models. Probability of health care utilization is modeled in the first part and the health care expenditures are modeled in the second part of two-part models. Considering the aggregate losses as the only observed responses of health insurance claims in an accounting period, we focus on the prediction of total claim amount of individuals using one-part models and two-part models. Accordingly, by using a private health insurance data set from a Turkish insurance company, predictive performance of candidate models are compared in terms of root mean square error (RMSE) and mean absolute error (MAE) criteria and the results are discussed.

Keywords

• One-part model,two-part model,generalized linear model,health insurance.

Sağlık Sigortasında Toplam Hasar Tutarının Kestirimi için Tek-kısım ve İki-kısım Modellerin Karşılaştırılması

Abstract

Doğrusal regresyon ve lognormal modelleri sağlık harcamalarının analizinde geleneksel olarak kullanılan tek-kısım modellerdir. İki-kısım modeller, tek-kısım modellere alternatif olarak sıklıkla tercih edilmektedir. İki-kısım modellerin ilk kısmında bireyin sağlık hizmetinden yararlanma olasılığı; ikinci kısmında sağlık harcamaları modellenmektedir. Bu çalışmada, bir hesap döneminde sağlık sigortası hasarlarında gözlenen yanıtların yalnızca toplam hasar tutarları olduğu durum göz önüne alınarak bireylerin toplam hasar tutarının tek-kısım modeller ve iki-kısım modeller ile kestirimine odaklanılmıştır. Bu amaçla, Türkiye’de faaliyet gösteren özel bir sigorta şirketinden alınan sağlık sigortası verisi kullanılarak, hata kareler ortalamasının karekökü ve ortalama mutlak hata kriterlerine göre aday modellerin kestirim performansı karşılaştırılmış, sonuçlar tartışılmıştır.

Keywords

• Tek-kısım model,iki-kısım model,genelleştirilmiş doğrusal model,sağlık sigortası.

References

1. A. Şentürk Acar, 2016, Heterojenliğin sağlık sigortalarında toplam hasar modellerine etkisi, Doktora tezi, Hacettepe Üniversitesi, Türkiye.
2. J. Aitchison, 1955, On the distribution of a positive random variable having a discrete probability mass at the origin, Journal of the American Statistical Association, 50(271): 901–8.
3. D. K. Blough, C. W. Madden, M. C. Hornbrook, 1999, Modeling risk using generalized linear models, Journal of Health Economics, 18(2):153–71.
4. M. J. Brockman, T. S. Wright, 1992, Statistical motor rating: Making effective use of your data, Journal of the Institute of Actuaries, 119(03):457–543.
5. M. B. Buntin, A. M. Zaslavsky, 2004, Too much ado about two-part models and transformation? Comparing methods of modeling medicare expenditures, Journal of Health Economics 23(3):525–42.
6. N. Duan, 1983, A nonparametric smearing estimate : Method retransformation, Journal of the American Statistical Association, 78(383):605–10.
7. N. Duan, W. G. Manning, C. N. Morris, J. P. Newhouse, 1983, A comparison of alternative models for the demand for medical care, Journal of Business & Economic Statistics, 1(2):115–26.
8. E. W. Frees, J. Gao, M.A. Rosenberg, 2011, Predicting the frequency and amount of health care expenditures, North American Actuarial Journal, 15(3):377–92.

9. E. W. Frees, R. A. Derrig, G. Meyers, 2014, Predictive modeling applications in actuarial science, 1st ed., Cambridge University Press.
10. M. Griswold, G. Parmigiani, A. Potosky, J. Lipscomb, 2004, Analyzing health care costs: A comparison of statistical methods motivated by medicare colorectal cancer charges, Biostatistics, 1(1):1–23.
11. S. Gschlößl, C. Czado, 2007, Spatial modelling of claim frequency and claim size in non-life insurance, Scandinavian Actuarial Journa,l 2007(3):202–25.
12. A. M. Jones, 2010, Models for health care, HEDG Working Papers, 10/01, Department of Economics, University of York.
13. P. Jong, Z. G. Heller, 2008, Generalized linear models for insurance data, London: Cambridge University Press.
14. R. Kaas, M. Goovaerts, J. Dhaene, M. Denuit, 2008, Modern actuarial risk theory using R, Verlag Berlin Heidelberg: Springer.
15. W. G. Manning, 1998, The logged dependent variable, heteroscedasticity and the retransformation problem, Journal of Health Economics, 17(3):283–95.
16. P. McCullagh, J. A. Nelder, 1989, Generalized linear models, Second Edi, London: Chapman and Hall.
17. J. Mullahy, 1998, Much ado about two: Reconsidering retransformation and the two-part model in health econometrics, Journal of Health Economics, 17(3):247–81.
18. P. Shi, X. Feng, A. Ivantsova, 2015, Dependent frequency – severity modeling of insurance claims, Insurance: Mathematics and Economics, 64:417–28.