Hierarchical forecasting of causes of death with trend breaks in mortality modeling: Kenyan case
-
DOIhttp://dx.doi.org/10.21511/ins.16(1).2025.02
-
Article InfoVolume 16 2025, Issue #1, pp. 15-32
- 7 Views
-
0 Downloads
This work is licensed under a
Creative Commons Attribution 4.0 International License
Trends offer direction and momentum. However, trends in mortality are affected by trend breaks, which are a consequence of mortality shocks. Additionally, insufficient historical data challenge the credibility of the forecasted trends, which are useful for actuaries in pricing, reserving, and valuing life insurance products. To address these challenges, the study aims to determine and incorporate trend breaks among individual causes of death and coherently forecast them by applying the bottom-up hierarchical forecasting approach for life insurance models. The models used are categorized as base (linear model), auto-statistical (Arima, Exponential-Smoothing, and Prophet), and auto-machine learning. The data from the World Health Organization consisted of annualized mortality quantities by cause, gender, age, and period for Kenya. Results based on the mean absolute percentage error criteria across the causes of death showed that all the models apart from the base model showed significant improvement after accounting for the trend breaks with the best being the auto machine learning approach leading with seven causes of death. Updating forecasts based on the computed trend breakpoints that varied between 2007 to 2011 generally improved forecast accuracy. These results suggest that forecasting errors may be reduced after accounting for trend breaks and model specifications. Furthermore, this implies that insufficient data do not necessarily produce deficient forecasts. The study’s contribution involved applying approaches that enhance the accuracy of forecasting models to prevent adverse effects of mortality shocks in actuarial modeling.
- Keywords
-
JEL Classification (Paper profile tab)J11, G22
-
References49
-
Tables3
-
Figures8
-
- Figure 1. Three-level hierarchical data structure
- Figure 2. Top nine causes of death for males over 60 years of age
- Figure 3. Top nine causes of death for males aged 20 to 60 years
- Figure 4. Top nine causes of death for females over 60 years of age
- Figure 5. Top nine causes of death for females aged 20 to 60 years
- Figure 6. Other causes of death for males and females by age group
- Figure 7. Distribution of MAPE against models over the years 2000–2019
- Figures A1. Plot of causes of death trend breaks based on 2000–2019 dataset
-
- Table 1. Forecast notations for lower-level 1
- Table 2. Implemented models
- Table 3. Model results based on MAPE grouped by the causes of death
-
- Abolghasemi, M., Hyndman, R. J., Tarr, G., & Bergmeir, C. (2019). Machine learning applications in time series hierarchical forecasting (arXiv:1912.00370).
- Arnold, S., & Glushko, V. (2021). Cause-specific mortality rates: Common trends and differences. Insurance: Mathematics and Economics, 99, 294-308.
- Arnold, S., & Sherris, M. (2015). Causes-of-death mortality: What do we know on their dependence? North American Actuarial Journal, 19(2), 116-128.
- Athanasopoulos, G., Ahmed, R. A., & Hyndman, R. J. (2009). Hierarchical forecasts for Australian domestic tourism. International Journal of Forecasting, 25(1), 146-166.
- Bai, J. (1994). Least Squares Estimation of a Shift in Linear Processes. Journal of Time Series Analysis, 15(5), 453-472.
- Bai, J., & Perron, P. (1998). Estimating and testing linear models with multiple structural changes. Econometrica, 66(1), 47-78.
- Bai, J., & Perron, P. (2003). Computation and analysis of multiple structural change models. Journal of Applied Econometrics, 18(1), 1-22.
- Bengtsson, T., & Keilman, N. (2019). Old and new perspectives on mortality forecasting. Springer Nature.
- Bett, N., Kasozi, J., & Ruturwa, D. (2022). Temporal Clustering of the Causes of Death for Mortality Modelling. Risks, 10(5), 99.
- Bett, N., Kasozi, J., & Ruturwa, D. (2023). Dependency Modeling Approach of Cause-Related Mortality and Longevity Risks: HIV/AIDS. Risks, 11(2), 38.
- Billah, B., King, M. L., Snyder, R. D., & Koehler, A. B. (2006). Exponential smoothing model selection for forecasting. International Journal of Forecasting, 22(2), 239-247.
- Breiman, L. (2001). Statistical modeling: The two cultures (with comments and a rejoinder by the author). Statistical Science, 16(3), 199-231.
- Cairns, A. J., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., Ong, A., & Balevich, I. (2009). A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North American Actuarial Journal, 13(1), 1-35.
- Caselli, G., Vallin, J., & Marsili, M. (2019). How useful are the causes of death when extrapolating mortality trends. An update. In Bengtsson, T., & Keilman, N. (Eds.), Old and New Perspectives on Mortality Forecasting (pp. 237-259). Demographic Research Monographs. Cham: Springer.
- Chen, X., & Moraga, P. (2024). Assessing dengue forecasting methods: A comparative study of statistical models and machine learning techniques in Rio de Janeiro, Brazil. medRxiv, 2024-06.
- Coelho, E., & Nunes, L. C. (2011). Forecasting mortality in the event of a structural change. Journal of the Royal Statistical Society Series A: Statistics in Society, 174(3), 713-736.
- Dayanik, S., Goulding, C., & Poor, H. V. (2008). Bayesian Sequential Change Diagnosis. Mathematics of Operations Research, 33(2), 475-496.
- Fearnhead, P. (2005). Exact Bayesian curve fitting and signal segmentation. IEEE Transactions on Signal Processing, 53(6), 2160-2166.
- Freedman, D. A. (2009). Statistical models: Theory and practice. Cambridge University Press.
- Giuseppi, A., & Pietrabissa, A. (2022). Bellman’s principle of optimality and deep reinforcement learning for time-varying tasks. International Journal of Control, 95(9), 2448-2459.
- Gross, C. W., & Sohl, J. E. (1990). Disaggregation methods to expedite product line forecasting. Journal of Forecasting, 9(3), 233-254.
- Hamilton, J. D. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica: Journal of the Econometric Society, 57(2), 357-384.
- Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: Principles and practice. OTexts.
- Hyndman, R. J., Ahmed, R. A., Athanasopoulos, G., & Shang, H. L. (2011). Optimal combination forecasts for hierarchical time series. Computational Statistics & Data Analysis, 55(9), 2579-2589.
- Killick, R., Eckley, I. A., Ewans, K., & Jonathan, P. (2010). Detection of changes in variance of oceanographic time-series using changepoint analysis. Ocean Engineering, 37(13), 1120-1126.
- LeDell, E., & Poirier, S. (2020). H2o autoML: Scalable automatic machine learning. Proceedings of the AutoML Workshop at ICML, 2020.
- Lee, R. D., & Carter, L. R. (1992). Modeling and Forecasting U.S. Mortality. Journal of the American Statistical Association, 87(419), 659-671.
- Li, H., & Lu, Y. (2018). Modeling cause-of-death mortality using hierarchical Archimedean copula. Scand. Actuarial Journal, 2019(3), 247-272.
- Mancuso, P., Piccialli, V., & Sudoso, A. M. (2021). A machine learning approach for forecasting hierarchical time series. Expert Systems with Applications, 182, 115102.
- Mélard, G., & Pasteels, J.-M. (2000). Automatic ARIMA modeling including interventions, using time series expert software. International Journal of Forecasting, 16(4), 497-508.
- Milidonis, A., Lin, Y., & Cox, S. H. (2011). Mortality Regimes and Pricing. North American Actuarial Journal, 15(2), 266-289.
- Mullainathan, S., & Spiess, J. (2017). Machine learning: An applied econometric approach. Journal of Economic Perspectives, 31(2), 87-106.
- Perron, P. (1989). The great crash, the oil price shock, and the unit root hypothesis. Econometrica: Journal of the Econometric Society, 57(6), 1361-1401.
- Petropoulos, F., Nikolopoulos, K., Spithourakis, G. P., & Assimakopoulos, V. (2013). Empirical heuristics for improving intermittent demand forecasting. Industrial Management & Data Systems, 113(5), 683-696.
- Pettitt, A. N. (1979). A Non-Parametric Approach to the Change-Point Problem. Applied Statistics, 28(2), 126-135.
- Richman, R. (2018). AI in actuarial science. Actuarial Science of South Africa.
- Robertson, T., Batty, G. D., Der, G., Fenton, C., Shiels, P. G., & Benzeval, M. (2013). Is socioeconomic status associated with biological aging as measured by telomere length? Epidemiologic Reviews, 35(1), 98-111.
- Smolensky, P., Mozer, M. C., & Rumelhart, D. E. (2013). Mathematical perspectives on neural networks. Psychology Press.
- Tang, S., Li, J., & Tickle, L. (2022). A New Fourier Approach under the Lee-Carter Model for Incorporating Time-Varying Age Patterns of Structural Changes. Risks, 10(8), 147.
- Taylor, S. J., & Letham, B. (2018). Forecasting at Scale. The American Statistician, 72(1), 37-45.
- Team, R. C. (2020). R: A language and environment for statistical computing, R Foundation for Statistical. Computing.
- United Nations (UN). (2017). World Population Prospects: The 2017 Revision Data Booklet (ST/ESA/SER. A/401).
- Van Berkum, F., Antonio, K., & Vellekoop, M. (2016). The impact of multiple structural changes on mortality predictions. Scandinavian Actuarial Journal, 2016(7), 581-603.
- Van Berkum, F., Antonio, K., Vellekoop, M., & Leuven, K. (2013). Structural changes in mortality rates with an application to Dutch and Belgian data.
- Waweru, M. N. (2014). Determinants of insolvency in selected insurance companies in Kenya (Ph.D. Thesis). University of Nairobi.
- Wickramasuriya, S. L., Athanasopoulos, G., & Hyndman, R. J. (2019). Optimal Forecast Reconciliation for Hierarchical and Grouped Time Series Through Trace Minimization. Journal of the American Statistical Association, 114(526), 804-819.
- World Health Organization (WHO). (2022). Global health estimates: Leading causes of death.
- Zeileis, A., Kleiber, C., Krämer, W., & Hornik, K. (2003). Testing and dating of structural changes in practice. Computational Statistics & Data Analysis, 44(1-2), 109-123.
- Zhang, B., Kang, Y., Panagiotelis, A., & Li, F. (2023). Optimal reconciliation with immutable forecasts. European Journal of Operational Research, 308(2), 650-660.