Indonesian National Mortality Rates using the Whittaker-Henderson Graduation Method

Gabrielle Aretha Setiady, Felivia Kusnadi

Abstract


In this paper, we aim to present a graph depicting the quantified mortality rates for the entire population of Indonesia, derived from the 2019 World Health Organization (WHO) mortality data for Indonesia. First, the mortality rates which consisted of five-year age groups were interpolated to determine the rates for each individual age. Next, these rates were extrapolated to extend the data from age 85 up to age 110. The resulting crude rates were adjusted with the Whittaker-Henderson smoothing technique by utilizing Python and MS Excel. The refined results were then compared to the insured lives from the fourth Indonesian Mortality Rates Table (TMI IV). This assessment supplied the government with insights to help shape health policies and inform economic forecasts. The results indicated that male mortality rates were higher than those of females, although no significant difference was observed among the younger generation. On the contrary, mortality rates of old people were significantly greater compared to the insured lives which was due to WHO’s limited data availability and more comprehensive data collection process, compared to TMI IV’s insured lives through the underwriting process.

Keywords


Mortality Rates; Whittaker-Henderson Graduation Method; Indonesia; World Health Organization.

Full Text:

DOWNLOAD [PDF]

References


Agustina, R.; Dartanto, T.; Sitompul, R.; Susiloretni, K. A.; Suparmi, M.K.M.; Achadi, E. L.; Taher, A.; Wirawan, F.; Sungkar, S.; Sudarmono, P.; Shankar, A.H.; Thabrany, H. (2018). Universal Health Coverage in Indonesia: Concept, Progress, and Challenges. The Lancet, 393(10166), 75–102. https://doi.org/10.1016/s0140-6736(18)31647-7

Ahmadi, S.; Li, J. S.-H. (2014). Coherent Mortality Forecasting with Generalized Linear Models: A Modified Time-Transformation Approach. Insurance: Mathematics and Economics, 59(1), 194–221. https://doi.org/10.1016/j.insmatheco.2014.09.007

Alexopoulos, A.; Dellaportas, P.; Forster, J. J. (2019). Bayesian Forecasting of Mortality Rates by Using Latent Gaussian Models. Journal of the Royal Statistical Society Series A: Statistics in Society, 182(2), 689–711. https://doi.org/10.1111/rssa.12422

Asamoah Owusu, D.; S. K. Appiah, S.K.; Danso, A. A. A. (2019). Estimating Exposures for a Mortality Study of a National Pension Scheme. Journal of Mathematical and Statistical Analysis, 2(2), 204. https://article.scholarena.com/Estimating-Exposures-for-a-Mortality-Study-of-a-National-Pension-Scheme.pdf

Cantiello, J.; Fottler, M. D.; Oetjen, D.; Zhang, N. J. (2015). The Impact of Demographic and Perceptual Variables on A Young Adult’s Decision to Be Covered by Private Health Insurance. BMC Health Services Research, 15(1), 1–15. https://doi.org/10.1186/s12913-015-0848-6

Chanco, M. E. (2016). Mortality Rates Estimation Using Whittaker-Henderson Graduation Technique. Journal of the Mathematical Society of the Philippines, 39(1), 7–16. https://mathsociety.ph/matimyas/images/vol39/ChancoM-Matimyas.pdf

Chapra, S. (2018). Applied Numerical Methods with MATLAB for Engineers and Scientists (5th ed). McGraw-Hill. https://www.mheducation.com/highered/product/applied-numerical-methods-matlab-engineers-scientists-chapra/M9781264162604.html

Dickson, D.C.M.; Hardy, M.R.; Waters, H. R. (2020). Actuarial Mathematics for Life Contingent Risks. Cambridge University Press. https://assets.cambridge.org/97811084/78083/frontmatter/9781108478083_frontmatter.pdf

Dzupire, N. C.; Gunde, R.; Chirwa, P. B. (2024). Constructing Malawian Ordinary Actuarial Tables: Reflection of the COVID-19 Era. African Journal of Education, 7(4), 107–115. https://doi.org/10.2022/ajest.v7i4.1029

Ferezagia, D. V. (2018). The Dynamics of Life-Insurance Penetration in ASEAN Countries. International Journal of Basic & Applied Sciences, 18(4), 15–19. https://www.academia.edu/65774776/The_Dynamics_of_Life_Insurance_Penetration_in_ASEAN_Countries?hb-sb-sw=26972707

Hainaut, D. (2018). A Neural-Network Analyzer for Mortality Forecast. ASTIN Bulletin: The Journal of the IAA, 48(2), 481–508. https://doi.org/10.1017/asb.2017.45

Hodson, T. O. (2022). Root-mean-square error (RMSE) or mean absolute error (MAE): when to use them or not. Geoscientific Model Development, 15(14), 5481–5487. https://doi.org/10.5194/gmd-15-5481-2022

Joseph, A. W. (1952). The Whittaker-Henderson method of graduation. Journal of the Institute of Actuaries, 78(1), 99–114. https://doi.org/10.1017/S0020268100052495

Kong, Q.; Siaw, T.; Bayen, A. Y. (2020). Python programming and numerical methods: A guide for engineers and scientists. Addison-Wesley. https://pythonnumericalmethods.studentorg.berkeley.edu/notebooks/Index.html

Lan, T. T. (2022). Risk Awareness for Vietnamese’s Life Insurance on Financial Protection: The Case Study of Daklak Province, Vietnam. International Journal of Financial Studies, 10(4), 84. https://doi.org/10.3390/ijfs10040084

Liu, Y; Li, J. S. H. (2017). The Locally Linear Cairns–Blake–Dowd Model: A Note on Delta–Nuga Hedging of Longevity Risk. ASTIN Bulletin: The Journal of the IAA, 47(1), 79–151. https://doi.org/10.1017/asb.2016.33

London, D. (1997). Survival Models and Their Estimation (3rd ed). ACTEX Publications, Inc. https://www.studocu.com/id/document/universitas-riau/matematika-aktuaria-2/survival-models/46312749

Macdonald, A.S.; Richards, S.J.;Currie, I. D. (2018). Modelling Mortality with Actuarial Applications. Cambridge University Press. https://doi.org/10.1017/9781107051386

Manejero, J. L.; Mendoza, R. (2020). Variational Approach to Data Graduation. Philippine Journal of Science, 149(2), 431–450. https://philjournalsci.dost.gov.ph/images/pdf/pjs_pdf/vol149no2/variational_approach_to_data_graduation_.pdf

Nazhifa, A. . R. A. B. (2022). The influence of economic conditions on the penetration and density of life insurance companies in Indonesia for the period 2016–2020. In Sustainable Future: Trends, Strategies and Development. Routledge. https://doi.org/10.1201/9781003335832-37

Nigri, A.; Levantesi, S.; Marino, M.; Scognamiglio, S.; Perla, F. (2019). A Deep Learning Integrated Lee–Carter Model. Risks, 7(1), 33. https://doi.org/10.3390/risks7010033

Odhiambo, J.; Weke, P.; Ngare, P.; Naryongo, R.; Sewe, S. (2022). Poisson incorporated credibility regression modelling of systematic mortality risk for populations with finite data. Mathematical Problems in Engineering, 1(1), 1–14. https://doi.org/10.1155/2022/1753542

Odhiambo, J. O. (2023). Deep Learning Incorporated Bühlmann Credibility in the Modified Lee–Carter Mortality Model. Mathematical Problems in Engineering, 1(1), 1–8. https://doi.org/10.1155/2023/8543909

Organization, W. H. (2023). Data Collection and Analysis Tools. World Health Organization.

Perdana, N. R.; Adhasari, G.; Mahadewi, E. P. (2022). Challenges and Implementation of Universal Health Coverage Program in Indonesia. International Journal of Health and Pharmaceutical, 2(3), 589–596. https://doi.org/10.51601/ijhp.v2i3.97

Pisani, E.; Olivier Kok, M.; Nugroho, K. (2017). Indonesia’s road to universal health coverage: a political journey. Health Policy and Planning, 32(2), 267–276. https://doi.org/10.1093/heapol/czw120

Safitri, K. A. (2019). The contribution of life and non-life insurances on ASEAN economic growth. Management Science Letters, 9(1), 957–966. https://doi.org/10.5267/j.msl.2019.4.009

Schultz, T. P. (1993). Mortality decline in the low-income world: causes and consequences. The American Economic Review, 83(2), 337–342. https://www.jstor.org/stable/2117687

Şenol, Z.; Zeren, F.; Canakci, M. (2020). The relationship between insurance and economic growth. Montenegrin Journal of Economics, 16(4), 145–155. https://doi.org/10.14254/1800-5845/2020.16-4.12

Suwondo, A.; Munandar, A.; Jamil, A.R.;Ridwan, M.;Pebrianto, P.S.; Supriatni, Y.; Dwihapsari, P.M.; Fahmi, M.A.;Kosasih, N.;Elviroza, R.; Hadiwibowo, B.; Yogo, H.D.; Pasaribu, T.; Sianturi, M.; Pertiwi, R.A.; Demus, N.; Hadi, N.; Ubadah; Kalla, Y.H.; Jala, B. . F. (2019). Tabel Mortalitas Indonesia IV.

Whittaker, E. T. (1922). On a new method of graduation. Proceedings of the Edinburgh Mathematical Society, 41(1), 63–75. https://doi.org/10.1017/S0013091500077853

Woolhandler, S.; Himmelstein, D. U. (2017). The Relationship of Health Insurance and Mortality: Is Lack of Insurance Deadly? Annals of Internal Medicine, 167(6), 424–431. https://doi.org/10.7326/M17-1403




DOI: https://doi.org/10.31764/jtam.v8i4.26316

Refbacks

  • There are currently no refbacks.


Copyright (c) 2024 Gabrielle Aretha Setiady, Felivia Kusnadi

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

_______________________________________________

JTAM already indexing:

                     


_______________________________________________

 

Creative Commons License

JTAM (Jurnal Teori dan Aplikasi Matematika) 
is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License

______________________________________________

_______________________________________________

_______________________________________________ 

JTAM (Jurnal Teori dan Aplikasi Matematika) Editorial Office: