Forecasting Mortality Trends: Advanced Techniques and the Impact of COVID-19
Abstract
:1. Introduction
2. Data and Methods
2.1. Data
2.2. Methods
2.2.1. Lee–Carter (LC)
2.2.2. Age–Period–Cohort (APC)
2.2.3. Two-Step Approach with Gradient Boosting Machine (GBM)
2.2.4. Generalized Additive Model (GAM) in APC Framework
3. Results
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Data Preparation
Appendix B. Details on Gradient Boosting Machine
Appendix C. Details on Hyperparameter Optimization
Appendix D. Additional Results
Country | Female | Male | ||||||
---|---|---|---|---|---|---|---|---|
LC | APC | GBM | GAM | LC | APC | GBM | GAM | |
FIN | 0.0045 | 0.0015 | 0.0035 | 0.0011 | 0.0072 | 0.0027 | 0.0066 | 0.0013 |
DE | 0.0015 | 0.0022 | 0.0004 | 0.001 | 0.0021 | 0.0021 | 0.0007 | 0.001 |
ITA | 0.0025 | 0.0021 | 0.001 | 0.001 | 0.0012 | 0.0025 | 0.0008 | 0.001 |
NLD | 0.0019 | 0.0032 | 0.0014 | 0.001 | 0.0017 | 0.0015 | 0.0014 | 0.001 |
US | 0.0014 | 0.0033 | 0.0005 | 0.0013 | 0.0017 | 0.0028 | 0.0004 | 0.0011 |
References
- Lee, R.D.; Carter, L.R. Modeling and forecasting US mortality. J. Am. Stat. Assoc. 1992, 87, 659–671. [Google Scholar]
- Bjerre, D.S. Tree-based machine learning methods for modeling and forecasting mortality. ASTIN Bull. J. IAA 2022, 52, 765–787. [Google Scholar] [CrossRef]
- Levantesi, S.; Pizzorusso, V. Application of machine learning to mortality modeling and forecasting. Risks 2019, 7, 26. [Google Scholar] [CrossRef]
- Schnürch, S.; Kleinow, T.; Korn, R.; Wagner, A. The impact of mortality shocks on modelling and insurance valuation as exemplified by COVID-19. Ann. Actuar. Sci. 2022, 16, 498–526. [Google Scholar] [CrossRef]
- Richman, R.; Wüthrich, M.V. A neural network extension of the Lee–Carter model to multiple populations. Ann. Actuar. Sci. 2021, 15, 346–366. [Google Scholar] [CrossRef]
- Hastie, T.; Tibshirani, R. Generalized additive models: Some applications. J. Am. Stat. Assoc. 1987, 82, 371–386. [Google Scholar] [CrossRef]
- Bray, I. Application of Markov chain Monte Carlo methods to projecting cancer incidence and mortality. J. R. Stat. Soc. Ser. C Appl. Stat. 2002, 51, 151–164. [Google Scholar] [CrossRef]
- Clements, M.S.; Armstrong, B.K.; Moolgavkar, S.H. Lung cancer rate predictions using generalized additive models. Biostatistics 2005, 6, 576–589. [Google Scholar] [CrossRef]
- Bashir, S.A.; Estève, J. Projecting cancer incidence and mortality using Bayesian age-period-cohort models. J. Epidemiol. Biostat. 2001, 6, 287–296. [Google Scholar]
- Dodds, S.; Williams, L.J.; Roguski, A.; Vennelle, M.; Douglas, N.J.; Kotoulas, S.-C.; Riha, R.L. Mortality and morbidity in obstructive sleep apnoea–hypopnoea syndrome: Results from a 30-year prospective cohort study. ERJ Open Res. 2020, 6, 00057–2020. [Google Scholar] [CrossRef]
- Clèries, R.; Ribes, J.; Esteban, L.; Martinez, J.M.; Borras, J.M. Time trends of breast cancer mortality in Spain during the period 1977–2001 and Bayesian approach for projections during 2002–2016. Ann. Oncol. 2006, 17, 1783–1791. [Google Scholar] [CrossRef] [PubMed]
- Robben, J.; Antonio, K.; Devriendt, S. Assessing the impact of the COVID-19 shock on a stochastic multi-population mortality model. Risks 2022, 10, 26. [Google Scholar] [CrossRef]
- Barigou, K.; Loisel, S.; Salhi, Y. Parsimonious predictive mortality modeling by regularization and cross-validation with and without Covid-type effect. Risks 2020, 9, 5. [Google Scholar] [CrossRef]
- Clayton, D.; Schifflers, E. Models for temporal variation in cancer rates. II: Age–period–cohort models. Stat. Med. 1987, 6, 469–481. [Google Scholar] [CrossRef] [PubMed]
- Human Mortality Database; University of California, Berkeley, CA, USA; Max Planck Institute for Demographic Research, Max Planck Society for the Advancement of Science e.V., Munich, Germany. 2024. Available online: https://www.mortality.org/ (accessed on 1 March 2024).
- Short-term Mortality Fluctuations (STMF); University of California, Berkeley, CA, USA; Max Planck Institute for Demographic Research, Max Planck Society for the Advancement of Science e.V., Munich, Germany. 2024. Available online: https://www.mortality.org/ (accessed on 1 March 2024).
- Brouhns, N.; Denuit, M.; Vermunt, J.K. A Poisson log-bilinear regression approach to the construction of projected lifetables. Insur. Math. Econ. 2002, 31, 373–393. [Google Scholar] [CrossRef]
- Villegas Ramirez, A. Mortality: Modelling, Socio-Economic Differences and Basis Risk. Ph.D. Dissertation, City University London, London, UK, 2015. [Google Scholar]
- Hobcraft, J.; Menken, J.; Preston, S. Age, Period, and Cohort Effects in Demography: A Review; Springer: Berlin/Heidelberg, Germany, 1985. [Google Scholar]
- Currie, I.D.; Durban, M.; Eilers, P.H. Smoothing and forecasting mortality rates. Stat. Model. 2004, 4, 279–298. [Google Scholar] [CrossRef]
- Yan, J.; Guszcza, J.; Flynn, M.; Wu, C.S.P. Applications of the offset in property-casualty predictive modeling. Casualty Actuar. Soc.-Forum 2009, 1, 366–385. [Google Scholar]
- Weigert, M.; Bauer, A.; Gernert, J.; Karl, M.; Nalmpatian, A.; Küchenhoff, H.; Schmude, J. Semiparametric APC analysis of destination choice patterns: Using generalized additive models to quantify the impact of age, period, and cohort on travel distances. Tour. Econ. 2022, 28, 1377–1400. [Google Scholar] [CrossRef]
- Bauer, A.; Weigert, M.; Jalal, H. APCtools: Descriptive and Model-based Age-Period-Cohort Analysis. J. Open Source Softw. 2022, 7, 4056. [Google Scholar] [CrossRef]
- Wood, S.N. Generalized Additive Models: An Introduction with R; CRC Press: Boca Raton, FL, USA, 2017. [Google Scholar]
- Hyndman, R.J.; Khandakar, Y. Automatic time series forecasting: The forecast package for R. J. Stat. Softw. 2008, 27, 1–22. [Google Scholar] [CrossRef]
- Bai, J.; Perron, P. Estimating and testing linear models with multiple structural changes. Econometrica 1998, 66, 47–78. [Google Scholar] [CrossRef]
- Zeileis, A.; Kleiber, C.; Kramer, W.; Hornik, K. Testing and Dating of Structural Changes in Practice, Computational Statistics and Data Analysis. Comput. Stat. Data Anal. 2003, 44, 109–123. [Google Scholar] [CrossRef]
- Ramirez Villegas, M.A.; Millossovich, P.; Kaishev, V. StMoMo: An R Package for Stochastic Mortality Modelling. 2016. Available online: Https://cran.r-project.org/web/packages/StMoMo/StMoMo.pdf (accessed on 25 July 2024).
- Wood, S.N. Generalized Additive Models: An Introduction with R; Chapman and Hall/CRC: Boca Raton, FL, USA, 2006; R package version 1.8-23, 2015; Available online: https://cran.r-project.org/web/packages/mgcv/index.html (accessed on 1 October 2023).
- Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V.; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P.; Weiss, R.; Dubourg, V.; et al. Scikit-learn: Machine learning in Python. J. Mach. Learn. Res. 2011, 12, 2825–2830. [Google Scholar]
- Bergstra, J.; Komer, B.; Eliasmith, C.; Yamins, D.; Cox, D.D. Hyperopt: A python library for model selection and hyperparameter optimization. Comput. Sci. Discov. 2015, 8, 014008. [Google Scholar] [CrossRef]
- Hamilton, A.D.; Jang, J.B.; Patrick, M.E.; Schulenberg, J.E.; Keyes, K.M. Age, period and cohort effects in frequent cannabis use among US students: 1991–2018. Addiction 2019, 114, 1763–1772. [Google Scholar] [CrossRef]
- Crimmins, E.M.; Shim, H.; Zhang, Y.S.; Kim, J.K. Differences between men and women in mortality and the health dimensions of the morbidity process. Clin. Chem. 2019, 65, 135–145. [Google Scholar] [CrossRef]
- Trovato, F.; Lalu, N.M. Narrowing sex differentials in life expectancy in the industrialized world: Early 1970’s to early 1990’s. Soc. Biol. 1996, 43, 20–37. [Google Scholar] [CrossRef]
- Rosella, L.C.; Calzavara, A.; Frank, J.W.; Fitzpatrick, T.; Donnelly, P.D.; Henry, D. Narrowing mortality gap between men and women over two decades: A registry-based study in Ontario, Canada. BMJ Open 2016, 6, e012564. [Google Scholar] [CrossRef]
- Perls, T.T.; Fretts, R.C. Why Women Live Longer than Men-What gives women the extra years? Sci. Am. 1998, 2, 100–103. [Google Scholar]
- Sudre, C.H.; Murray, B.; Varsavsky, T.; Graham, M.S.; Penfold, R.S.; Bowyer, R.C.E.; Pujol, J.C.; Klaser, K.; Antonelli, M.; Canas, L.S.; et al. Attributes and predictors of Long-COVID. Nat. Med. 2021, 27, 626–631. [Google Scholar] [CrossRef]
- Kunzler, A.M.; Röthke, N.; Günthner, L.; Stoffers-Winterling, J.; Tüscher, O.; Coenen, M.; Rehfuess, E.; Schwarzer, G.; Binder, H.; Schmucker, C.; et al. Mental burden and its risk and protective factors during the early phase of the SARS-CoV-2 pandemic: Systematic review and meta-analyses. Glob. Health 2021, 17, 1–29. [Google Scholar] [CrossRef] [PubMed]
- Polack, F.P.; Thomas, S.J.; Kitchin, N.; Absalon, J.; Gurtman, A.; Lockhart, S.; Perez, J.L.; Pérez Marc, G.; Moreira, E.D.; Zerbini, C.; et al. Safety and efficacy of the BNT162b2 mRNA Covid-19 vaccine. N. Engl. J. Med. 2020, 383, 2603–2615. [Google Scholar] [CrossRef] [PubMed]
- Johns Hopkins University. COVID-19 Dashboard. 2021. Available online: https://coronavirus.jhu.edu/map.html (accessed on 1 October 2024).
- Boudourakis, L.; Uppal, N. Decreased COVID-19 mortality—A cause for optimism. JAMA Intern. Med. 2021, 181, 478–479. [Google Scholar] [CrossRef] [PubMed]
- Telenti, A.; Arvin, A.; Corey, L.; Corti, D.; Diamond, M.S.; Garcìa-Sastre, A.; Garry, R.F.; Holmes, E.C.; Pang, P.S.; Virgin, H.W. After the pandemic: Perspectives on the future trajectory of COVID-19. Nature 2021, 596, 495–504. [Google Scholar] [CrossRef] [PubMed]
- Hastie, T.; Tibshirani, R.; Friedman, J.H. The Elements of Statistical Learning: Data Mining, Inference, and Prediction; Springer: New York, NY, USA, 2009; Volume 2. [Google Scholar]
- Deprez, P.; Shevchenko, P.V.; Wüthrich, M.V. Machine learning techniques for mortality modeling. Eur. Actuar. J. 2017, 7, 337–352. [Google Scholar] [CrossRef]
- Oram, E.; Dash, P.B.; Naik, B.; Nayak, J.; Vimal, S.; Nataraj, S.K. Light gradient boosting machine-based phishing webpage detection model using phisher website features of mimic URLs. Pattern Recognit. Lett. 2021, 152, 100–106. [Google Scholar] [CrossRef]
- Bergstra, J.; Yamins, D.; Cox, D. Making a science of model search: Hyperparameter optimization in hundreds of dimensions for vision architectures. In Proceedings of the International Conference on Machine Learning, Atlanta, GA, USA, 17–19 June 2013. [Google Scholar]
- Bergstra, J.; Bardenet, R.; Bengio, Y.; Kégl, B. Algorithms for hyper-parameter optimization. In Proceedings of the 25th Annual Conference on Neural Information Processing Systems 2011, Granada, Spain, 12–14 December 2011. [Google Scholar]
Model | Country | Training Set (Fitting Period) | Test Set (Forecast Period) |
---|---|---|---|
LC, APC, GBM | Finland, Italy, Netherlands, US | 1950–2010 | 2011–2019 |
LC, APC, GBM | Germany | 1990–2010 | 2011–2019 |
GAM | Finland, Italy, Netherlands, US, Germany | 1990–2015 | 2016–2019 |
Metric | LC | APC | GBM | GAM |
---|---|---|---|---|
Runtime (s) | 63.15 | 87.31 | 799.75 | 412.49 |
Memory (MB) | 17.9 | 20.3 | 301 | 76.2 |
Storage (MB) | 0.0274 | 0.0308 | 72.10 | 11.78 |
Country | Female | Male | ||||||
---|---|---|---|---|---|---|---|---|
LC | APC | GBM | GAM | LC | APC | GBM | GAM | |
FIN | 0.0021 | 0.0029 | 0.0028 | 0.0012 | 0.0029 | 0.0029 | 0.0027 | 0.0015 |
DE | 0.0048 | 0.0046 | 0.0039 | 0.0021 | 0.0052 | 0.0045 | 0.0045 | 0.002 |
ITA | 0.0045 | 0.0025 | 0.0044 | 0.0016 | 0.0042 | 0.0021 | 0.0026 | 0.0013 |
NLD | 0.003 | 0.0020 | 0.0024 | 0.0013 | 0.0035 | 0.0038 | 0.0027 | 0.0011 |
US | 0.0023 | 0.0018 | 0.0014 | 0.0010 | 0.0054 | 0.0020 | 0.0031 | 0.0016 |
Assumption | Description |
---|---|
Scenario 1: Complete disappearance of COVID-19 | |
No long-term effects | Assumes no long-term health consequences for recovered individuals, despite evidence of “Long Covid” [37]. Assumes no lasting psychological or social impacts from lockdowns [38]. |
Vaccination effectiveness | Assumes widespread vaccination will lead to the abrupt disappearance of the pandemic, despite uncertainties about long-term vaccine efficacy. |
Excess mortality | Assumes excess mortality will average out in the coming years, with no rapid population reductions. |
Scenario 2: Continuous COVID-19 impact | |
Viral variants | Acknowledges that while vaccines reduce infection risk [39], rising incidence rates suggest ongoing challenges [40]. Considers the potential for emerging variants to undermine vaccine effectiveness. |
Consistent mortality impact | Assumes the impact on mortality will remain unchanged over the next years, despite short-term decreases and uncertainties as well as advancements in science and medicine [41]. |
Economic and health consequences | Recognizes the negative economic and health impacts of prolonged lockdowns and containment measures. |
Scenario 3: Gradual decline in COVID-19 impact | |
Medical progress and behavioral changes | Credits medical advancements, behavioral changes, and herd or vaccine immunity for the reduced impact. |
Residual effect | Recognizes a residual effect of the pandemic but anticipates it will diminish over time. |
Scenario 4: Adjustment for 2020/2021 excess mortality | |
Disappearance of adverse effects | Assumes the adverse health effects of the pandemic will disappear with no long-term consequences. |
Explicit excess mortality accounting | Assumes excess mortality from 2020 and 2021 will not average out and must be explicitly accounted for. |
Unchanged baseline mortality | Assumes baseline mortality remains unchanged, discounting behavioral changes (e.g., reduced traffic fatalities, fewer influenza deaths due to hygiene, and quarantine measures). |
Scenario | Fitting Period | Forecast Period | Validation Period |
---|---|---|---|
1—Without COVID-effect | 1990–2019 | 2020–2025 | 2022–2023 |
2—Full COVID-effect | 1990–2021 | 2022–2025 | 2022–2023 |
3—Flattening COVID-effect | 1990–2021 | 2022–2025 | 2022–2023 |
4—Excess mortality | 1990–2019 | 2020–2025 | 2022–2023 |
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Nalmpatian, A.; Heumann, C.; Pilz, S. Forecasting Mortality Trends: Advanced Techniques and the Impact of COVID-19. Stats 2024, 7, 1172-1188. https://doi.org/10.3390/stats7040069
Nalmpatian A, Heumann C, Pilz S. Forecasting Mortality Trends: Advanced Techniques and the Impact of COVID-19. Stats. 2024; 7(4):1172-1188. https://doi.org/10.3390/stats7040069
Chicago/Turabian StyleNalmpatian, Asmik, Christian Heumann, and Stefan Pilz. 2024. "Forecasting Mortality Trends: Advanced Techniques and the Impact of COVID-19" Stats 7, no. 4: 1172-1188. https://doi.org/10.3390/stats7040069
APA StyleNalmpatian, A., Heumann, C., & Pilz, S. (2024). Forecasting Mortality Trends: Advanced Techniques and the Impact of COVID-19. Stats, 7(4), 1172-1188. https://doi.org/10.3390/stats7040069