Lee-Carter–ARIMA hybrid approach and machine learning for mortality rate forecasting in the United States: Implications for national defense and population risk assessment
DOI:
https://doi.org/10.58524/app.sci.def.v4i2.1146Keywords:
ANN, ARIMA, Forecasting, Lee-Carter, Random ForestAbstract
Background: The Accuracy of mortality rate forecasting plays an important role in various decision-making processes in the life insurance sector, including determining premium amounts. In addition, it also contributes to assessing the readiness of human resources to support national defense, as well as to conducting risk assessments aimed at maintaining demographic stability. The United States mortality data was selected as the study object due to the availability of comprehensive and high-quality.
Aims: This study explores five hybrid approaches that combine stochastic models and machine learning, along with one non-hybrid approach to assess their potential to improve forecasting accuracy.
Method: In this study, the Lee-Carter–ARIMA, Lee-Carter–Random Forest, Lee-Carter–ANN, Lee-Carter–ARIMA–Random Forest, Lee-Carter–ARIMA–ANN, and ANN models were evaluated. These models were applied to mortality rate data from nine divisions in the United States (US), stratified by gender, using training data from 1966 to 2005 and test data from 2006 to 2015. The best model is determined based on the smallest Mean Absolute Percentage Error (MAPE) value while also considering the interpretability of the model.
Result: The study's results show that, across the number of divisions, the Lee-Carter–ARIMA–Random Forest model produces the smallest MAPE values most often. However, in terms of average MAPE, the Lee-Carter–ARIMA–ANN model performs better, with MAPEs of 9.66% for females and 9.28% for males. Furthermore, neither of these models yields a substantial improvement in predictive accuracy compared with the Lee-Carter–ARIMA model.
Conclusion: Considering the relatively small decrease in MAPE and the difficulty of interpreting machine learning models due to their black box nature, the Lee-Carter–ARIMA model demonstrates the best overall performance relative to the other models. Nevertheless, the Lee-Carter–ARIMA–Random Forest and Lee-Carter–ARIMA–ANN models show potential as alternative approaches that merit further investigation and may contribute to national defense planning and support the maintenance of demographic stability.
References
Abdulkarim, S., & Garko, A. (2015). Forecasting maternal mortality rate using particle swarm optimization based artificial neural network. Dutse Journal of Pure and Applied Sciences, 1(1), 55–59.
Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723. https://doi.org/10.1109/TAC.1974.1100705
Atsalakis, G., Nezis, D., Matalliotakis, G., Ioana, C., & Skiadas, C. (2007). forecasting mortality rate using a neural network with fuzzy inference system. Working Papers 0806, University of Crete, Department of Economics. https://ideas.repec.org/p/crt/wpaper/0806.html
Ayoo, K., Mikhaeil, J. S., Huang, A., & Wąsowicz, M. (2020). The opioid crisis in North America: Facts and future lessons for Europe. Anaesthesiology Intensive Therapy, 52(2), 139–147. https://doi.org/10.5114/AIT.2020.94756
Bjerre, D. S. (2022). Tree-based machine learning methods for modeling and forecasting mortality. ASTIN Bulletin, 52(3), 765–787. https://doi.org/10.1017/asb.2022.11
Booth, H., & Tickle, L. (2008). Mortality modelling and forecasting: A review of methods. Annals of Actuarial Science, 3, 3–43. https://doi.org/10.1017/S1748499500000440
Box, G. E. P., Sons., J. W. &, Jenkins, G. M., & Reinsel, G. C. (2008). Time series analysis : Forecasting and control. John Wiley & Sons, Inc. http://www.123library.org/book_details/?id=30721
Breiman, L. (2001). Random forests. Machine Learning, 45(2001), 5-32. https://doi.org/10.1023/A:1010933404324
Camarda, C. G., & Basellini, U. (2021). Smoothing, decomposing and forecasting mortality rates. European Journal of Population, 37(3), 569–602. https://doi.org/10.1007/s10680-021-09582-4
Chen, Y., & Khaliq, A. Q. M. (2022). Comparative study of mortality rate prediction using data-driven recurrent neural networks and the lee–carter model. Big Data and Cognitive Computing, 6(4), 134. https://doi.org/10.3390/bdcc6040134
Cincotta, R. (2023). Population age structure and the vulnerability of states to coups d’État. Statistics, Politics and Policy, 14(3), 331–355. https://doi.org/10.1515/spp-2023-0029
Elder, G. H., Clipp, E. C., Brown, J. S., Martin, L. R., & Friedman, H. S. (2009). The lifelong mortality risks of World War II experiences. Research on Aging, 31(4), 391–412. https://doi.org/10.1177/0164027509333447
Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom Inflation. Econometrica, 50(4), 987–1007. https://doi.org/10.2307/1912773
Goswami, B. (2019). A brief introduction to nonlinear time series analysis and recurrence plots. Vibration, 2(4), 332–368. https://doi.org/10.3390/vibration2040021
Hinman, A. R., Orenstein, W. A., Bloch, A. B., Bart, K. J., Eddins, D. L., Amler, R. W., & Kirby, C. D. (1983). Impact of measles in the United States. Reviews of Infectious Diseases, 5(3), 439–444. http://www.jstor.org/stable/4453053
Hong, W. H., Yap, J. H., Selvachandran, G., Thong, P. H., & Son, L. H. (2021). Forecasting mortality rates using hybrid Lee–Carter model, artificial neural network and random forest. Complex and Intelligent Systems, 7(1), 163–189. https://doi.org/10.1007/s40747-020-00185-w
Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: Principles and practice. OTexts.org/fpp/.
Hyndman, R. J., & Koehler, A. B. (2006). Another look at measures of forecast accuracy. International Journal of Forecasting, 22(4), 679–688. https://doi.org/https://doi.org/10.1016/j.ijforecast.2006.03.001
Ibrahim, N., Md Lazam, N., & Shair, S. (2021). Forecasting Malaysian mortality rates using the Lee-Carter model with fitting period variants. Journal of Physics: Conference Series, 1988, 12103. https://doi.org/10.1088/1742-6596/1988/1/012103
Kaukuntla, P. R. (2021). Advancing life insurance pricing accuracy through mortality forecasting: A time-series and survival analysis approach. International Journal of Multidisciplinary Research and Growth Evaluation, 2(1), 729–734. https://doi.org/10.54660/.ijmrge.2021.2.1.729-734
Lee, R. D., & Carter, L. R. (1992). Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87(419), 659–671. https://doi.org/10.1080/01621459.1992.10475265
Lee, R., & Miller, T. (2001). Evaluating the performance of the lee-carter method for forecasting mortality. Demography, 38, 537-549. https://doi.org/10.1353/dem.2001.0036
Ljung, G., & Box, G. (1978). On a measure of lack of fit in time series models. Biometrika, 65(20), 297-303. https://doi.org/10.1093/biomet/65.2.297
Makridakis, S., Wheelwright, S., & Hyndman, R. (1984). Forecasting: Methods and applications. The Journal of the Operational Research Society, 35, 79. https://doi.org/10.2307/2581936
Murphy, S. L., Kochanek, K. D., Xu, J., & Arias, E. (2024). Mortality in the United States, 2023. NCHS Data Brief, 2024 Dec(521), CS356116. https://doi.org/10.15620/cdc/170564
Nuraini, V., & Fitriyati, N. (2025). Transformation of traditional models to AI: SLR on the application of machine learning in mortality prediction. CAUCHY: Jurnal Matematika Murni Dan Aplikasi, 10(2), 998–1014. https://doi.org/10.18860/cauchy.v10i2.35972
Ospina, R., Gondim, J. A. M., Leiva, V., & Castro, C. (2023). An overview of forecast analysis with arima models during the covid-19 pandemic: Methodology and case study in Brazil. Mathematics, 11(14), 3069. https://doi.org/10.3390/math11143069
Probst, P., & Boulesteix, A.-L. (2018). To Tune or Not to Tune the Number of Trees in Random Forest. Journal of Machine Learning Research, 18, 1-18. https://jmlr.org/papers/volume18/17-269/17-269.pdf
Qiao, Y., Wang, C.-W., & Zhu, W. (2023). Machine Learning in long-term mortality forecasting. The Geneva Papers on Risk and Insurance-Issues and Prectice, 49, 340-362. https://doi.org/10.1057/s41288-024-00320-5
Raftery, A. E., & Ševčíková, H. (2023). Probabilistic population forecasting: Short to very long-term. International Journal of Forecasting, 39(1), 73–97. https://doi.org/10.1016/j.ijforecast.2021.09.001
Razali, N. M., & Wah, Y. B. (2011). Power Comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors and Anderson-Darling Tests. Journal of Statistical Modeling and Analytics, 2(1), 21-33.
Robinson, R. L. M., Palczewska, A., Palczewski, J., & Kidley, N. (2017). Comparison of the predictive performance and interpretability of random forest and linear models on benchmark data sets. Journal of Chemical Information and Modeling, 57(8), 1773–1792. https://doi.org/10.1021/acs.jcim.6b00753
Sakr, S., Elshawi, R., Ahmed, A. M., Qureshi, W. T., Brawner, C. A., Keteyian, S. J., Blaha, M. J., & Al-Mallah, M. H. (2017). Comparison of machine learning techniques to predict all-cause mortality using fitness data: the Henry ford exercIse testing (FIT) project. BMC Medical Informatics and Decision Making, 17(1), 174. https://doi.org/10.1186/s12911-017-0566-6
Shrader, J. G., Bakkensen, L., & Lemoine, D. (2023). Fatal errors: the mortality value of accurate weather forecasts. (NBER Working Paper Series). National Bureau of Economic Research. http://www.nber.org/data-appendix/w31361
Spooner, F. & Dattani, S. (2025, April 7). Vaccination eliminated polio from the United States - Our World in Data. https://ourworldindata.org/data-insights/vaccination-eliminated-polio-from-the-united-states?
Trotter Y., Jr., Dunn, F. L., Drachman, R. H., Henderson, D. A., Pizzi, M., & Langmuir, A. D. (1959). Asian Influenza in the United States, 1957-1958. American Journal of Epidemiology, 70(1), 34–50. https://doi.org/10.1093/oxfordjournals.aje.a120063
Vollset, S. E., Goren, E., Yuan, C.-W., Cao, J., Smith, A. E., Hsiao, T., Bisignano, C., Azhar, G. S., Castro, E., Chalek, J., Dolgert, A. J., Frank, T., Fukutaki, K., Hay, S. I., Lozano, R., Mokdad, A. H., Nandakumar, V., Pierce, M., Pletcher, M., … Murray, C. J. L. (2020). Fertility, mortality, migration, and population scenarios for 195 countries and territories from 2017 to 2100: a forecasting analysis for the Global Burden of Disease Study. The Lancet, 396(10258), 1285–1306. https://doi.org/https://doi.org/10.1016/S0140-6736(20)30677-2
World Health Organization. (2020, April 27). Archived: WHO Timeline - COVID-19. https://www.who.int/news/item/27-04-2020-who-timeline---covid-19?
Wu, Y. T., Niubo, A. S., Daskalopoulou, C., Moreno-Agostino, D., Stefler, D., Bobak, M., Oram, S., Prince, M., & Prina, M. (2021). Sex differences in mortality: Results from a population-based study of 12 longitudinal cohorts. CMAJ, 193(11), E361–E370. https://doi.org/10.1503/cmaj.200484
Zhang, G., Eddy Patuwo, B., & Y. Hu, M. (1998). Forecasting with artificial neural networks:: The state of the art. International Journal of Forecasting, 14(1), 35–62. https://doi.org/10.1016/S0169-2070(97)00044-7
Zhang, G. P. (2003). Time series forecasting using a hybrid ARIMA and neural network model. In Neurocomputing, 50, 159-175. https://doi.org/10.1016/S0925-2312(01)00702-0
Zhang, Y., Zhang, X., Razbek, J., Li, D., Xia, W., Bao, L., Mao, H., Daken, M., & Cao, M. (2022). Opening the black box: interpretable machine learning for predictor finding of metabolic syndrome. BMC Endocrine Disorders, 22(1), 214. https://doi.org/10.1186/s12902-022-01121-4
Zuo, W., Damle, A., & Tuljapurkar, S. (2025). Sensitivity and uncertainty in the Lee–Carter mortality model. International Journal of Forecasting, 41(2), 781–797. https://doi.org/https://doi.org/10.1016/j.ijforecast.2024.06.010
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