Skip to main content Accessibility help
×
Home

Mortality Projections using Generalized Additive Models with applications to annuity values for the Irish population

  • M. Hall and N. Friel
  • Please note a correction has been issued for this article.

Abstract

Generalized Additive Models (GAMs) with age, period and cohort as possible covariates are used to predict future mortality improvements for the Irish population. The GAMs considered are the 1-dimensional age + period and age + cohort models and the 2-dimensional age-period and age-cohort models. In each case thin plate regression splines are used as the smoothing functions. The generalized additive models are compared with the P-Spline (Currie et al., 2004) and Lee-Carter (Lee & Carter, 1992) models included in version 1.0 of the Continuous Mortality Investigation (CMI) library of mortality projections. Using the Root Mean Square Error to assess the accuracy of future predictions, the GAMs outperform the P-Spline and Lee-Carter models over intervals of 25 and 35 years in the age range 60 to 90. The GAMs allow intuitively simple models of mortality to be specified whilst also providing the flexibility to model complex relationships between the covariates. The majority of morality improvements derived from the projections of future Irish mortality yield annuity values at ages 60, 65, 70 and 80 in 2007 in the range of annuity values calculated, assuming a 2 to 4 percent annual compound improvement in mortality rates for both males and females.

Copyright

Corresponding author

Contact address Mary Hall, School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland. E-mail: mary.hall@ucd.ie

References

Hide All
Bashir, S.A., Esteve, J. (2001). Projecting cancer incidence and mortality using Bayesian age-period cohort models. Journal of Epidemiology and Biostatistics, 6, 287296.
Bray, I. (2002). Application of Markov Chain Monte Carlo Methods to Projecting Cancer Incidence and Mortality. Applied Statistics, 51, 151164.
Clements, M.S., Armstrong, B.K., Moolgavkar, S.H. (2005). Lung cancer rate predictions using generalized additive models. Biostatistics, 6, 576589.
Cleries, R., Ribes, J., Esteban, L., Martinez, J.M., Borras, J.M. (2006). Time trends of breast cancer mortality in Spain during the period 1977–2001 and Bayesian approach for projections during 2002-2016. Annals of Oncology, 17(12), 17831791.
CMI (2002). Continuous Mortality Investigation Working Paper No 1. Institute and Faculty of Actuaries, U.K.
CMI (2006a). Continuous Mortality Investigation Working Paper No 20. Institute and Faculty of Actuaries, U.K.
CMI (2006b). Continuous Mortality Investigation Working Paper No 22. Institute and Faculty of Actuaries, U.K.
CMI (2007a). Continuous Mortality Investigation Working Paper No 25. Institute and Faculty of Actuaries, U.K.
CMI (2007c). Continuous Mortality Investigation User Guide to Version 1.0 of the CMI Library of Mortality Projections. Institute and Faculty of Actuaries, U.K.
Currie, I.D., Durban, M., Eilers, P.H.C. (2004). Smoothing and forecasting mortality rates. Statistical Modeling, 4, 279298.
Dominici, F., McDermott, A., Zeger, S.L., Samet, J.M. (2002). On the Use of Generalized Additive Models in Time-Series Studies of Air Pollution and Health. American Journal of Epidemiology, 15, 193203.
Fewster, R.M., Buckland, S.T., Siriwardena, G.M., Baillie, S.R., Wilson, J.D. (2000). Analysis of Population Trends for Farmland Birds using Generalized Additive Models. Ecology, 81(7), 19701984.
Gallop, A. (2008). Mortality Projections in the United Kingdom. 2008 Living to 100 and Beyond Symposium, Society of Actuaries, US.
Holford, T.R. (1983). The Estimation of Age, Period and Cohort Effects for Vital Rates. Biometrics, 39, 311324.
Lee, R.D., Carter, L. (1992). Modeling and forecasting the time series of U.S. mortality. Journal of the American Statistical Association, 87, 659671.
Nelder, J.A., Wedderburn, R.W.N. (1972). Generalized Linear Models. Journal of the Royal Statistical Society, A, 135, 370384.
R Development Core Team (2009). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org.
Sithole, T., Haberman, S., Verrall, R. (2000). An investigation into parametric models for mortality projections, with applications to immediate annuitants’ and life office pensioners’ data. Insurance: Mathematics and Economics, 27, 285312.
Whelan, S. (2008). Recent Trends in Mortality and Morbidity in Ireland. Journal of the Statistical and Social Inquiry Society of Ireland.
Wong-Fupuy, C., Haberman, S. (2004). Projecting Mortality Trends: Recent Developments in the United Kingdom and the United States. North American Actuarial Journal, 8, 5683.
Wood, S.N. (2001). mgcv: GAMs and Generalized Ridge Regression for R. R News, 1, 2025.
Wood, S.N. (2003). Thin plate regression splines. Journal of the Royal Statistical Society B, 65(Part 1), 95114.
Wood, S.N. (2006). Generalized Additive Models, An Introduction with R. Chapman & Hall.

Keywords

Related content

Powered by UNSILO

Mortality Projections using Generalized Additive Models with applications to annuity values for the Irish population

  • M. Hall and N. Friel
  • Please note a correction has been issued for this article.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.

A correction has been issued for this article: