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Modelling Income Protection Claim Termination Rates by Cause of Sickness I: Recoveries

Published online by Cambridge University Press:  10 May 2011

S. Y. Ling ,
H. R. Waters  and
A. D. Wilkie
H. R. Waters
Affiliation:
Department of Actuarial Mathematics and Statistics, and the Maxwell Institute for the Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, U.K. :, Email: H.R.Waters@hw.ac.uk
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Abstract

In this paper we present methods and results for the estimation and modelling of the recovery intensity for Income Protection (IP) insurance claims, allowing for different causes of claim. We use UK data supplied by the Continuous Mortality Investigation relating to claims paid in the years 1975 to 2002, inclusive. Each claim is classified by one of 70 possible causes according to ICD8.

We group causes where appropriate, and then use the Cox model and generalised linear models to model the recovery intensity.

In two subsequent papers we complete our modelling of IP claim termination rates by discussing the modelling of the mortality of IP claimants.

There are two main reasons why it is useful to incorporate cause of sickness in the modelling of IP claim terminations:

(i) The cause of sickness will be known to the insurer for a claim in the course of payment. A reserve can be set more accurately for such a claim if a model of the termination rates appropriate for this cause is available.

(ii) Different causes of claim will become more or less significant over time. For example, tuberculosis may have been an important cause of sickness in the past, but is likely to be far less significant now; the swine flu pandemic starting in 2009 is likely to have a significant effect on observed aggregate claim termination rates, skewing them towards higher rates at shorter durations. Information about trends in morbidity, together with a model of termination rates by cause of claim, allows future aggregate claim termination rates to be predicted more accurately, reserves to be set at more appropriate levels and policies to be priced more accurately.

One of the covariates included in our models for recovery intensities is Calendar Year. Aggregate recovery intensities have been decreasing over the period considered, 1975 to 2002, and this is generally reflected in the models for recovery intensities by cause of sickness. However, when these intensities are projected for years beyond 2002, the results are not always plausible.

Keywords

Income Protection InsuranceRecoveriesCause of ClaimProportional HazardsCox ModelGeneralised Linear Models
Type
Papers
Information
Annals of Actuarial Science , Volume 4 , Issue 2 , September 2009 , pp. 199 - 239
Copyright
Copyright © Institute and Faculty of Actuaries 2009

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References

References for Papers I, II and III

Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716–723.CrossRefGoogle Scholar
CMIR2 (1976). Continuous Mortality Investigation Reports: Number 2. The Institute of Actuaries and the Faculty of Actuaries.Google Scholar
CMIR6 (1983). Continuous Mortality Investigation Reports: Number 6. The Institute of Actuaries and the Faculty of Actuaries.Google Scholar
CMIR8 (1986). Continuous Mortality Investigation Reports: Number 8. The Institute of Actuaries and the Faculty of Actuaries.Google Scholar
CMIR12 (1991). Continuous Mortality Investigation Reports: Number 12. The Institute of Actuaries and the Faculty of Actuaries.Google Scholar
CMIR15 (1996). Continuous Mortality Investigation Reports: Number 15. The Institute of Actuaries and the Faculty of Actuaries.Google Scholar
CMIR17 (1999). Continuous Mortality Investigation Reports: Number 17. The Institute of Actuaries and the Faculty of Actuaries.Google Scholar
CMIR18 (2000). Continuous Mortality Investigation Reports: Number 18. The Institute of Actuaries and the Faculty of Actuaries.Google Scholar
CMIR22 (2005). Continuous Mortality Investigation Reports: Number 22. The Institute of Actuaries and the Faculty of Actuaries.Google Scholar
CMIWP5 (2004). Continuous Mortality Investigation Working Paper: Number 5. The Institute of Actuaries and the Faculty of Actuaries.Google Scholar
CMIWP23 (2006). Continuous Mortality Investigation Working Paper: Number 23. The Institute of Actuaries and the Faculty of Actuaries.Google Scholar
Cordeiro, I.M.F. (1998). A stochastic model for the analysis of permanent health insurance claims by cause of disability. Ph.D. Thesis, Heriot-Watt University, Edinburgh.Google Scholar
Cordeiro, I.M.F. (2002). A multiple state model for the analysis of permanent health insurance claims by cause of disability. Insurance: Mathematics and Economics, 30, 167–186.Google Scholar
Cox, D.R. (1972). Regression Models and Life Tables (with Discussion). Journal of the Royal Statistical Society. Series B (Methodological), 34(2), 187–220.Google Scholar
Devlin, T.F. & Weeks, B.J. (1986). Spline functions for logistic regression modeling. Proc. 11th Annual SAS Users Group Intnl Conf. Cary NC: SAS Institute, Inc., 646–651.Google Scholar
Dickman, P.W., Sloggett, A., Hills, M. & Hakulinen, T. (2004). Regression models for relative survival. Statistics in Medicine, 23, 51–64.CrossRefGoogle ScholarPubMed
Forfar, D.O., McCutcheon, J.J. & Wilkie, A.D. (1988). On graduation by mathematical formula. Journal of The Institute of Actuaries, 115(1), 1–149.CrossRefGoogle Scholar
ICD8 (1967). Manual of the International Statistical Classification of Diseases, Injuries and Causes of Death, 8th Edition. World Health Organisation.Google Scholar
Kluwer (2001). Income protection insurance 2001. Croner Publications and Kluwer Publishing, United Kingdom.Google Scholar
Lee, R.D. & Carter, L. (1992). Modeling and forecasting the time series of U.S. mortality. Journal of the American Statistical Association, 87, 659–671.Google Scholar
Ling, S.Y. (2008). Supporting document for Ph.D thesis at http://www.ma.hw.ac.uk/~singyee/.Google Scholar
Ling, S.Y. (2009). Models for income protection insurance incorporating cause of sickness. Ph.D. Thesis, Heriot-Watt University, Edinburgh.Google Scholar
Ling, S.Y., Waters, H.R. & Wilkie, A.D. (2009a). Modelling income protection claim termination rates by cause of sickness I: recoveries. Annals of Actuarial Science, 4, 199–239.CrossRefGoogle Scholar
Ling, S.Y., Waters, H.R. & Wilkie, A.D. (2009b). Modelling income protection claim termination rates by cause of sickness II: mortality of UK assured lives. Annals of Actuarial Science, 4, 241–259.CrossRefGoogle Scholar
Ling, S.Y., Waters, H.R. & Wilkie, A.D. (2009c). Modelling income protection claim termination rates by cause of sickness III: mortality. Annals of Actuarial Science, 4, 261–286.CrossRefGoogle Scholar
McCullagh, P. & Nelder, J. A. (1989). Generalized linear models. Chapman and Hall, United Kingdom.CrossRefGoogle Scholar
Pitt, D.G.W. (2007). Modelling the claim duration of income protection insurance policyholders using parametric mixture models. Annals of Actuarial Science, 2(1), 1–24.CrossRefGoogle Scholar
Renshaw, A.E. & Haberman, S. (1995). On the graduation associated with a multiple state model in permanent health insurance. Insurance: Mathematics and Economics, 17(1), 1–17.Google Scholar
Renshaw, A.E. & Haberman, S. (2000). Modelling the recent time trends in UK permanent health insurance recovery, mortality and claim inception transition intensities. Insurance: Mathematics and Economics, 27(3), 365–396.Google Scholar
Sanders, A.J. & Silby, N.F. (1988). Actuarial aspects of PHI in the UK. Journal of the Institute of Actuaries Students' Society, 31, 1–57.Google Scholar
Therneau, T. & Grambsch, P. (1994). Proportional hazards tests and diagnostics based on weighted residuals. Biometrika, 81(3), 515–526.Google Scholar
Willetts, R.C., Gallop, A.P., Leandro, P.A., Lu, J.L.C., Macdonald, A.S., Miller, K.A., Richards, S.J., Robjohns, N., Ryan, J.P. & Waters, H.R. (2004). Longevity in the 21st century. British Actuarial Journal, 10, 685–832.CrossRefGoogle Scholar