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Logistic and CSG Growth Models for Predicting Life Expectancy

Year 2024, Volume: 29 Issue: 2, 503 - 513, 31.08.2024
https://doi.org/10.53433/yyufbed.1432156

Abstract

The tables that allow calculating the probability of death at a certain age by recording the number of births/deaths in a population are called life tables. The concept of life expectancy, which is a measure that determines how long a creature will live, is also determined by mortality rates obtained from life tables. It is also possible to model the expected lifetime with some nonlinear mathematical functions. One of the functions that is often used in modeling mortality rates is the logistic growth function. This study aims to propose a model that can be used as an alternative to the logistic growth model and to interpret the mortality rates of countries. In this study, the life expectancy of males and females in Türkiye, Singapore, Norway, and China was modeled using the logistic and the CSG growth model, which was newly introduced to the literature. When modeling the life expectancy of countries, the adjusted graph was drawn following the data of each growth model. Then, the performances of the logistic growth model and the CSG growth model were compared with R^2, RMSE, and MAPE statistical criteria. As a result of the comparison, it was revealed that the CSG growth model is more suitable than the logistic model for estimating life expectancy for overall data and for each gender. The originality of this study is the CSG model which is a new nonlinear model that predicts life expectancy effectively for related datasets.

Project Number

FBA-2022-14131

References

  • Aje, O. G., Akanni, S. B., Abdualazeez, I. A., Ibrahim, R. A., & Adebayo, A. A. (2024). Forecasting of male life expectancy in Nigeria: Box-Jenkins approach. International Journal of Development Mathematics (IJDM), 1(1). https://doi.org/10.62054/ijdm/0101.20
  • Arosio, P., Knowles, T. P., & Linse, S. (2015). On the lag phase in amyloid fibril formation. Physical Chemistry Chemical Physics, 17(12), 7606-7618. https://doi.org/10.1039/C4CP05563B
  • Barnston, A. (1992). Correspondence among the Correlation [root mean square error] and Heidke Verification Measures; Refinement of the Heidke Score. Weather and Forecasting, 7(4), 699-709. https://doi.org/10.1175/1520-0434(1992)007<0699:CATCRA>2.0.CO;2
  • Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A., & Nesbitt, C. J. (1997). Actuarial mathematics (2nd ed.). Schaumburg: The Society of Actuaries.
  • Burton, J. K., Reid, M., Gribben, C., Caldwell, D., Clark, D. N., Hanlon, P., … & McAllister, D. A. (2021). Impact of COVID-19 on care-home mortality and life expectancy in Scotland. Age and Ageing, 50(4), 1029-1037. https://doi.org/10.1093/ageing/afab080
  • Carla, S. A., & Sumathi, M. (2021). Maximum lifespan prediction of women from Modified Weibull Distribution. International Research Journal on Advanced Science Hub (IRJASH), 3(3), 56-60.
  • Chai, T., & Draxler, R. R. (2014). Root mean square error (RMSE) or mean absolute error (MAE)?–Arguments against avoiding RMSE in the literature. Geoscientific Model Development, 7(3), 1247-1250. https://doi.org/10.5194/gmd-7-1247-2014
  • Chen, H. (2007). Use of linear, Weibull, and log-logistic functions to model pressure inactivation of seven foodborne pathogens in milk. Food Microbiology, 24(3), 197-204. https://doi.org/10.1016/j.fm.2006.06.004
  • Dinçer K. S. (1998). The Investigation of the life expectancy variation from 1970 to 1986 in Eskişehir and Turkey. (Master thesis), Anadolu University Institute of Health Sciences, Eskişehir, Turkey.
  • Gavrilov, L. A., & Gavrilova, N. S. (2019). New trend in old-age mortality: Gompertzialization of mortality trajectory. Gerontology, 65(5), 451-457. https://doi.org/10.1159/000500141
  • Hifzan, R. M., Hamidi, K. M., Aida, M. N., & Salisi, M. S. (2024). Analysis of growth curve with non-linear models of gompertz and logistics model in female katjang X boer goats in Malaysia. Tropical Animal Science Journal, 47(2), 155-160. https://doi.org/10.5398/tasj.2024.47.2.155
  • Huishuo, G., Yuepeng, S., Xuehui, S., Deqiang, Z., & Xiaoyu, Z. (2020). Optimal growth model of Populus simonii seedling combination based on Logistic and Gompertz models. Journal of Beijing Forestry University, 42(5), 59-70. https://dx.doi.org/10.12171/j.1000-1522.20190296
  • İskender, C. (2021). Mathematical study of the verhulst and gompertz growth functions and their contemporary applications. Ekoist: Journal of Econometrics and Statistics, 34, 73-102. http://dx.doi.org/10.26650/ekoist.2021.34.876749
  • Levantesi, S., Nigri, A., Piscopo, G., & Spelta, A. (2023). Multi-country clustering-based forecasting of healthy life expectancy. Quality & Quantity, 57(2), 189-215. https://doi.org/10.1007/s11135-022-01611-6
  • Lee, K., Choi, K., & Cho, D. (2021). A study on the numerical approach for industrial life Cycle: Empirical evidence from Korea. The Journal of Asian Finance, Economics and Business, 8(5), 667-678. https://doi.org/10.13106/jafeb.2021.vol8.no5.0667
  • Longhi, D. A., Dalcanton, F., Aragão, G. M. F. D., Carciofi, B. A. M., & Laurindo, J. B. (2017). Microbial growth models: A general mathematical approach to obtain μ max and λ parameters from sigmoidal empirical primary models. Brazilian Journal of Chemical Engineering, 34, 369-375. https://doi.org/10.1590/0104-6632.20170342s20150533
  • Makgopa, L. F., Mathapo, M. C., & Tyasi, T. L. (2024). A systematic review of estimation of growth curve in goats. Tropical Animal Health and Production, 56(1), 14. https://doi.org/10.1007/s11250-023-03857-0
  • Namboodiri, K., & Suchindran, C. M. (2013). Life table techniques and their applications. Academic Press.
  • National Bureau of Statistics of China (NBS) (2021). Life Tables. Access date: 12 August 2022. https://www.moi.gov.tw/english/cl.aspx?n=7780
  • Panik, M. J. (2014). Growth curve modeling: Theory and applications. John Wiley and Sons.
  • Pham, H. (2011). Modeling U.S. mortality and risk-cost optimization on life expectancy. IEEE Transactions on Reliability, 60(1), 125-133. https://doi.org/10.1109/TR.2010.2103990
  • Prasad, K. V. (2022). Characters of population. In insect ecology: Concepts to Management. Springer, Singapore.
  • Santos, A. L. P. dos, Ferreira, T. A. E., de Brito, C. C. R., Gomes-Silva, F., & Moreira, G. R. (2024). Proposal for a new non-linear model to describe growth curves. Bioscience Journal, 40(e40011), 1981-3163. https://doi.org/10.14393/BJ-v40n0a2024-68936
  • Schacht, R. M. (1980). Two models of population growth. American Anthropologist, 82(4), 782-798. https://doi.org/10.1525/aa.1980.82.4.02a00040
  • Şençelikel, T., & Öner, K. S. (2017). Türkiye’de 2007-2014 yılları arası yaşam ümidinin farklı yaşam tablosu hazırlama yöntemleri ile değerlendirilmesi. Osmangazi Tıp Dergisi, 39(3), 9-17. https://doi.org/10.20515/otd.317151
  • Singapore Department of Statistics (DOS) (2021). Life tables. Access date: 12 August 2022. https://www.singstat.gov.sg/publications/population/complete-life-table
  • Statistics Norway (SSB) (2021). Life tables. Access date: 12 August 2022. https://www.ssb.no/en/statbank/table/07902/
  • Taylan, H., & Yapar, G. (2013). Türkiye geneli ölüm verileri kullanılarak yaşam tablosunun oluşturulması. İstatistik Araştırma Dergisi, 10(2), 1-24.
  • Trappey, C. V., & Wu, H.-Y. (2008). An evaluation of the time-varying extended logistic, simple logistic, and Gompertz models for forecasting short product lifecycles. Advanced Engineering Informatics, 22(4), 421-430. https://doi.org/10.1016/j.aei.2008.05.007
  • Tsoularis, A., & Wallace, J. (2002). Analysis of logistic growth models. Mathematical Biosciences, 179(1), 21-55. https://doi.org/10.1016/S0025-5564(02)00096-2
  • Turkish Statistical Institute (TUIK) (2020). Life tables. Access date: 12 August 2022. https://data.tuik.gov.tr/Kategori/GetKategori?p=Nufus-ve-Demografi-109
  • Ünal, D., & Çığşar, B. (2021). CSG: Towards a comprehensive model of growth. New Trends in Mathematical Sciences, 9(1), 130- 135. https://doi.org/10.20852/ntmsci.2021.440
  • Vanfleteren, J. R., De Vreese, A., & Braeckman, B. P. (1998). Two-parameter logistic and weibull equations provide better fits to survival data from isogenic populations of caenorhabditis elegans in axenic culture than does the gompertz model. The Journals of Gerontology, 53A(6), B393-B403. https://doi.org/10.1093/gerona/53A.6.B393
  • Weon, B. M., & Je, J. H. (2009). Theoretical estimation of maximum human lifespan. Biogerontology, 10(1), 65-71. https://doi.org/10.1007/s10522-008-9156-4
  • Windarto, E., Eridani, E., & Purwati, U. D. (2018). A new modified logistic growth model for empirical use. Communication in Biomathematical Sciences, 1(2), 122-131. https://doi.org/10.5614/cbms.2018.1.2.5

Yaşam Beklentisi Tahmininde Lojistik ve CSG Modelleri

Year 2024, Volume: 29 Issue: 2, 503 - 513, 31.08.2024
https://doi.org/10.53433/yyufbed.1432156

Abstract

Bir popülasyondaki doğum/ölüm sayıları kullanılarak belirli bir yaştaki ölüm olasılığının hesaplanmasını sağlayan tablolara yaşam tabloları denir. Bir canlının ne kadar yaşayıp yaşamayacağının ölçüsü olan yaşam beklentisi, yaşam tablolarından elde edilen ölüm oranıyla hesaplanmaktadır. Beklenen yaşam süresini, lineer olmayan fonksiyonlarla modellemek mümkündür. Ölüm oranlarının modellenmesinde sıklıkla kullanılan fonksiyonlardan biri lojistik büyüme modelidir. Bu çalışma ile lojistik büyüme modeline alternatif olarak kullanılabilecek literatüre yeni kazandırılan bir model kullanarak Türkiye, Singapur, Norveç ve Çin’e ait ölüm oranlarını yorumlamak amaçlanmıştır. Ülkelerin total ve cinsiyete göre yaşam beklentileri lojistik ve CSG büyüme modelleri kullanılarak tahmin edilmiştir. Ülkelerin yaşam beklentileri tahmin edilirken her büyüme modelinin tahmini grafiklerle desteklenmiştir. Daha sonra lojistik ve CSG büyüme modellerinin performansları R^2, RMSE ve MAPE istatistikleri kullanılarak karşılaştırılmıştır Karşılaştırma sonucunda CSG büyüme modelinin yaşam beklentisi tahmininde hem total veri hem de cinsiyetler açısından lojistik büyüme modeline göre daha iyi tahminde bulunduğu tespit edilmiştir. Bu çalışmanın özgünlüğü, çalışmada kullanılan veri kümeleri için yaşam beklentisini etkili bir şekilde tahmin edebilen yeni bir doğrusal olmayan büyüme modelinin sunulmasıdır.

Supporting Institution

Çukurova Üniversitesi

Project Number

FBA-2022-14131

References

  • Aje, O. G., Akanni, S. B., Abdualazeez, I. A., Ibrahim, R. A., & Adebayo, A. A. (2024). Forecasting of male life expectancy in Nigeria: Box-Jenkins approach. International Journal of Development Mathematics (IJDM), 1(1). https://doi.org/10.62054/ijdm/0101.20
  • Arosio, P., Knowles, T. P., & Linse, S. (2015). On the lag phase in amyloid fibril formation. Physical Chemistry Chemical Physics, 17(12), 7606-7618. https://doi.org/10.1039/C4CP05563B
  • Barnston, A. (1992). Correspondence among the Correlation [root mean square error] and Heidke Verification Measures; Refinement of the Heidke Score. Weather and Forecasting, 7(4), 699-709. https://doi.org/10.1175/1520-0434(1992)007<0699:CATCRA>2.0.CO;2
  • Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A., & Nesbitt, C. J. (1997). Actuarial mathematics (2nd ed.). Schaumburg: The Society of Actuaries.
  • Burton, J. K., Reid, M., Gribben, C., Caldwell, D., Clark, D. N., Hanlon, P., … & McAllister, D. A. (2021). Impact of COVID-19 on care-home mortality and life expectancy in Scotland. Age and Ageing, 50(4), 1029-1037. https://doi.org/10.1093/ageing/afab080
  • Carla, S. A., & Sumathi, M. (2021). Maximum lifespan prediction of women from Modified Weibull Distribution. International Research Journal on Advanced Science Hub (IRJASH), 3(3), 56-60.
  • Chai, T., & Draxler, R. R. (2014). Root mean square error (RMSE) or mean absolute error (MAE)?–Arguments against avoiding RMSE in the literature. Geoscientific Model Development, 7(3), 1247-1250. https://doi.org/10.5194/gmd-7-1247-2014
  • Chen, H. (2007). Use of linear, Weibull, and log-logistic functions to model pressure inactivation of seven foodborne pathogens in milk. Food Microbiology, 24(3), 197-204. https://doi.org/10.1016/j.fm.2006.06.004
  • Dinçer K. S. (1998). The Investigation of the life expectancy variation from 1970 to 1986 in Eskişehir and Turkey. (Master thesis), Anadolu University Institute of Health Sciences, Eskişehir, Turkey.
  • Gavrilov, L. A., & Gavrilova, N. S. (2019). New trend in old-age mortality: Gompertzialization of mortality trajectory. Gerontology, 65(5), 451-457. https://doi.org/10.1159/000500141
  • Hifzan, R. M., Hamidi, K. M., Aida, M. N., & Salisi, M. S. (2024). Analysis of growth curve with non-linear models of gompertz and logistics model in female katjang X boer goats in Malaysia. Tropical Animal Science Journal, 47(2), 155-160. https://doi.org/10.5398/tasj.2024.47.2.155
  • Huishuo, G., Yuepeng, S., Xuehui, S., Deqiang, Z., & Xiaoyu, Z. (2020). Optimal growth model of Populus simonii seedling combination based on Logistic and Gompertz models. Journal of Beijing Forestry University, 42(5), 59-70. https://dx.doi.org/10.12171/j.1000-1522.20190296
  • İskender, C. (2021). Mathematical study of the verhulst and gompertz growth functions and their contemporary applications. Ekoist: Journal of Econometrics and Statistics, 34, 73-102. http://dx.doi.org/10.26650/ekoist.2021.34.876749
  • Levantesi, S., Nigri, A., Piscopo, G., & Spelta, A. (2023). Multi-country clustering-based forecasting of healthy life expectancy. Quality & Quantity, 57(2), 189-215. https://doi.org/10.1007/s11135-022-01611-6
  • Lee, K., Choi, K., & Cho, D. (2021). A study on the numerical approach for industrial life Cycle: Empirical evidence from Korea. The Journal of Asian Finance, Economics and Business, 8(5), 667-678. https://doi.org/10.13106/jafeb.2021.vol8.no5.0667
  • Longhi, D. A., Dalcanton, F., Aragão, G. M. F. D., Carciofi, B. A. M., & Laurindo, J. B. (2017). Microbial growth models: A general mathematical approach to obtain μ max and λ parameters from sigmoidal empirical primary models. Brazilian Journal of Chemical Engineering, 34, 369-375. https://doi.org/10.1590/0104-6632.20170342s20150533
  • Makgopa, L. F., Mathapo, M. C., & Tyasi, T. L. (2024). A systematic review of estimation of growth curve in goats. Tropical Animal Health and Production, 56(1), 14. https://doi.org/10.1007/s11250-023-03857-0
  • Namboodiri, K., & Suchindran, C. M. (2013). Life table techniques and their applications. Academic Press.
  • National Bureau of Statistics of China (NBS) (2021). Life Tables. Access date: 12 August 2022. https://www.moi.gov.tw/english/cl.aspx?n=7780
  • Panik, M. J. (2014). Growth curve modeling: Theory and applications. John Wiley and Sons.
  • Pham, H. (2011). Modeling U.S. mortality and risk-cost optimization on life expectancy. IEEE Transactions on Reliability, 60(1), 125-133. https://doi.org/10.1109/TR.2010.2103990
  • Prasad, K. V. (2022). Characters of population. In insect ecology: Concepts to Management. Springer, Singapore.
  • Santos, A. L. P. dos, Ferreira, T. A. E., de Brito, C. C. R., Gomes-Silva, F., & Moreira, G. R. (2024). Proposal for a new non-linear model to describe growth curves. Bioscience Journal, 40(e40011), 1981-3163. https://doi.org/10.14393/BJ-v40n0a2024-68936
  • Schacht, R. M. (1980). Two models of population growth. American Anthropologist, 82(4), 782-798. https://doi.org/10.1525/aa.1980.82.4.02a00040
  • Şençelikel, T., & Öner, K. S. (2017). Türkiye’de 2007-2014 yılları arası yaşam ümidinin farklı yaşam tablosu hazırlama yöntemleri ile değerlendirilmesi. Osmangazi Tıp Dergisi, 39(3), 9-17. https://doi.org/10.20515/otd.317151
  • Singapore Department of Statistics (DOS) (2021). Life tables. Access date: 12 August 2022. https://www.singstat.gov.sg/publications/population/complete-life-table
  • Statistics Norway (SSB) (2021). Life tables. Access date: 12 August 2022. https://www.ssb.no/en/statbank/table/07902/
  • Taylan, H., & Yapar, G. (2013). Türkiye geneli ölüm verileri kullanılarak yaşam tablosunun oluşturulması. İstatistik Araştırma Dergisi, 10(2), 1-24.
  • Trappey, C. V., & Wu, H.-Y. (2008). An evaluation of the time-varying extended logistic, simple logistic, and Gompertz models for forecasting short product lifecycles. Advanced Engineering Informatics, 22(4), 421-430. https://doi.org/10.1016/j.aei.2008.05.007
  • Tsoularis, A., & Wallace, J. (2002). Analysis of logistic growth models. Mathematical Biosciences, 179(1), 21-55. https://doi.org/10.1016/S0025-5564(02)00096-2
  • Turkish Statistical Institute (TUIK) (2020). Life tables. Access date: 12 August 2022. https://data.tuik.gov.tr/Kategori/GetKategori?p=Nufus-ve-Demografi-109
  • Ünal, D., & Çığşar, B. (2021). CSG: Towards a comprehensive model of growth. New Trends in Mathematical Sciences, 9(1), 130- 135. https://doi.org/10.20852/ntmsci.2021.440
  • Vanfleteren, J. R., De Vreese, A., & Braeckman, B. P. (1998). Two-parameter logistic and weibull equations provide better fits to survival data from isogenic populations of caenorhabditis elegans in axenic culture than does the gompertz model. The Journals of Gerontology, 53A(6), B393-B403. https://doi.org/10.1093/gerona/53A.6.B393
  • Weon, B. M., & Je, J. H. (2009). Theoretical estimation of maximum human lifespan. Biogerontology, 10(1), 65-71. https://doi.org/10.1007/s10522-008-9156-4
  • Windarto, E., Eridani, E., & Purwati, U. D. (2018). A new modified logistic growth model for empirical use. Communication in Biomathematical Sciences, 1(2), 122-131. https://doi.org/10.5614/cbms.2018.1.2.5
There are 35 citations in total.

Details

Primary Language English
Subjects Computational Statistics, Statistical Analysis, Statistical Theory, Applied Statistics
Journal Section Natural Sciences and Mathematics / Fen Bilimleri ve Matematik
Authors

Begüm Çığşar 0000-0002-8453-985X

Deniz Ünal 0000-0002-4095-3039

Abdel-hack Bıo Boulou 0000-0001-9054-0390

Bassel Alshahaby 0000-0002-4568-8959

Project Number FBA-2022-14131
Publication Date August 31, 2024
Submission Date February 6, 2024
Acceptance Date July 1, 2024
Published in Issue Year 2024 Volume: 29 Issue: 2

Cite

APA Çığşar, B., Ünal, D., Bıo Boulou, A.-h., Alshahaby, B. (2024). Logistic and CSG Growth Models for Predicting Life Expectancy. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 29(2), 503-513. https://doi.org/10.53433/yyufbed.1432156