Pomiar rektangularyzacji krzywej przeżycia – stan wiedzy i analiza wyników
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Published:
Dec 1, 2019
Keywords:
rectangularization of the survival curve, mortality compression, dispersion of age at death, modal age at death, maximum life span
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Abstract
This article is a result of a methodological literature review concerning the compression of mortality and rectangularization of the survival curve concepts. It aims to identify the current state of knowledge – key definitions, existing tools of measurement and analysis of empirical research conducted so far in Europe. The process of gathering and selecting scientific literature is precisely described so that one can easily understand the obtained knowledge synthesis and possibly improve further research. The first part of this paper includes definitions of the rectangularization of the survival curve, its dimensions, and related terminology. Then, 26 measures and indicators of the phenomenon, found in existing scientific literature, are described individually and gathered in a comparative table. Finally, the results of reviewing empirical research of 11 European countries are presented: Sweden, France, Switzerland, Great Britain, the Netherlands, Italy, Finland, Denmark, Norway, Spain, and Poland. The results are further discussed on the example of France. The analysis shows that some of the rectangularization measures are still rarely used empirically, some being only theoretically formulated. Moreover, these studies have small to none representation of some European countries. As a result of this literature review, new interesting paths for further research are formulated.
Article Details
How to Cite
Wnuk, A. . (2019). Pomiar rektangularyzacji krzywej przeżycia – stan wiedzy i analiza wyników. Studia Demograficzne, (1(175), 27–61. https://doi.org/10.33119/SD.2019.1.2
Section
Original research papers & review papers
References
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[32] Shkolnikov, V. M, Andreev, E. E., Begun, A. Z. (2003). Gini coefficient as a life table function: computation from discrete data, decomposition of differences and empirical examples, Demographic Research, vol. 8, article 11, s. 305–358.
[33] Siegel, J. S. (2012). The Life Table. W: The Demography and Epidemiology of Human Health and Aging (s. 135–216), J. S. Siegel (Ed.). New York: Springer, https://doi.org/10.1007/978-94-007-1315-4 (dostęp: 20.12.2018).
[34] Szukalski, P. (2008). Ewolucja umieralności i niepełnosprawności w Polsce w świetle koncepcji rektangularyzacji krzywej przeżycia. W: Starzenie się ludności Polski – między demografią a gerontologią społeczną (s. 89–123), J. T. Kowaleski, P. Szukalski (red.). Łodź: Wydawnictwo Uniwersytetu Łodzkiego.
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[36] Upton, A. C. (1977). Pathology. W: Handbook of Biology of Aging (s. 513–535), C. E. Finch, L. Hayflick (Eds.). New York: Van Nostrand Reinhold.
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[38] Wroblewska, W. (2009). Teoria przejścia epidemiologicznego oraz fakty na przełomie wieków w Polsce, Studia Demograficzne, 1 (155), s. 110–159.
[39] Wroblewska, W. (2017). Pomiar dyspersji wieku w momencie zgonu. Przyczynek do analizy kompresji umieralności w Polsce, Studia Demograficzne, 1 (171), s. 3–25.
[40] Yue, J. C. (2012). Mortality Compression and Longevity Risk, North American Actuarial Journal, 16 (4), s. 434–448.
[2] Bell, F. C., Miller, M. L. (2005). Life tables for the United States social security area, Social Security Administration Publications, 3, https://www.ssa.gov/oact/NOTES/pdf_studies/study120.pdf (dostęp: 10.02.2019).
[3] Camarda, C. G. (2008). Smoothing methods for the analysis of mortality development. Rozprawa doktorska. Madrid: Universidad Carlos III de Madrid, Department of Statistics.
[4] Canudas-Romo, V. (2008). The modal age at death and the shifting mortality hypothesis, Demographic Research, vol. 19, article 30, s. 1179–1204.
[5] Canudas-Romo, V. (2010). Three measures of longevity: time trends and record values, Demography, 47 (2), s. 299–312.
[6] Cheung, S. L. K., Robine, J. M., Jow-Ching Tu, E., Caselli, G. (2005). Three dimension of the survival curve: horizontalization, verticalization, and longevity extension, Demography, 42 (2), s. 243–258, https://link.springer.com/content/pdf/10.1353/dem.2005.0012.pdf (dostęp: 13.09.2018).
[7] Cheung, S. L. K., Robine, J. M., Paccaud, F., Marazzi, A. (2009). Dissecting the compression of mortality in Switzerland, 1876–2005, Demographic Research, vol. 21, article 19, s. 569– 598.
[8] Comfort, A. (1979). The Biology of Senescence. New York: Elsevier.
[9] Currie, I. D., Durban, M., Eilers, P. H. C. (2004). Smoothing and forecasting mortality rates, Statistical Modelling, 4 (4), s. 279–298. DOI:10.1191/1471082X04st080oa (dostęp: 15.01.2019).
[10] Debon, A., Martinez-Ruiz, F., Montes, F. (2012). Temporal evolution of mortality indicators: application to Spanish data, North American Actuarial Journal, 16 (3), s. 364–377.
[11] Eakin, T., Witten, M. (1995). How Square Is the Survival Curve of a Given Species?, Experimental Gerontology, 30 (1), s. 33–64.
[12] Ebeling, M., Rau, R., Baudisch, A. (2013). The maximized inner rectangle approach (MIRA): disentangling rectangularization, https://iussp.org/sites/default/files/event_call_for_papers/MIRAEbelingRauBaudisch.pdf (dostęp: 20.12.2018).
[13] Ebeling, M., Rau, R., Baudisch, A. (2018). Rectangularization of the survival curve reconsidered: The maximum inner rectangle approach, Population Studies, vol. 72, no. 3, s. 369–379, doi.org/10.1080/00324728.2017.1414299 (dostęp: 14.12.2018).
[14] Engelaer, F. M., van Bodegom, D., Kirkwood, T. B. L., Westendorp, R. G. J. (2014). Limits to the compression of human mortality. W: Compression and plasticity of old-age mortality (s. 63–76), F. M. Engelaer (Ed.). Leiden: Leiden University.
[15] Fries, J. F. (1980). Aging, Natural Death and the Compression of Morbidity, New England Journal of Medicine, 303 (3), s. 130–135.
[16] Fries, J. F., Crapo, L. M. (1981). Vitality and Aging: Implications of the Rectangular Curve. Reprint, Pine Forge Press, 2006, s. 43–50.
[17] Hill, G. (1993). The entropy of the survival curve: an alternative measure, Canadian Studies in Population, 20 (1), s. 43–57.
[18] Kannisto, V. (2000). Measuring the Compression of Mortality, Demographich Research, vol. 3, article 6, 10.4054/DemRes.2000.3.6 (dostęp: 15.09.2018).
[19] Kannisto, V. (2007). Central and dispersion indicators of individual life duration: New methods. W: In Human longevity, individual life duration, and the growth of the oldest-old population, Vol. 4 (s. 111–129), J. M. Robine, E. M. Crimmins, S. Horiuchi, Y. Zeng (Eds.). Springer: Dordrecht.
[20] Manton, K. G., Tolley, H. D. (1991). Rectangularization of the Survival Curve: Implications of an Ill-Posed Question, Journal of Aging and Health, 3 (2), s. 172–193.
[21] Myers, G. C., Manton, K. G. (1984). Compression of Mortality: Myth or Reality?, The Gerontologist, 24 (4), s. 346–353.
[22] Nagnur, D. (1986). Rectangularization of the survival curve and entropy: the Canadian experience, 1921–1981, Canadian Studies in Population, 13 (1), s. 83–102.
[23] Nusselder, W. J., Mackenbach, J. P. (1996). Rectangularization of the survival Curve in the Netherlands, 1950–1992, The Gerontologist, vol. 36, no. 6, s. 773–781.
[24] Nusselder, W. J. (2007). Recent trends in life expectancy and rectangularisation of the survival curve at advanced ages in the Netherlands. W: In Human longevity, individual life duration, and the growth of the oldest-old population. Vol. 4 (s. 131–146), J. M. Robine, E. M. Crimmins, S. Horiuchi, Y. Zeng (Eds.). Springer: Dordrecht. Ouellette, N., Bourbeau, R. (2011). Changes in the age-at-death distribution in four low mortality countries: A nonparametric approach, Demographic Research, vol. 25, article 19, s. 595–628.
[25] Paccaud, F., Pinto, C. S., Marazzi, A., Mili, J. (1998). Age at death and rectangularization of the survival curve: trends in Switzerland, 1969–1994, Journal of Epidemiology & Community Health, 52 (7), s. 412–415.
[26] Pearl, R. ([1923] 1940). Introduction to Medical Biometry and Statistics, 3 rd ed. Philadelphia: Saunders.
[27] Randolph, J. J. (2009). A Guide to Writing the Dissertation Literature Review, Practical Assessment, Research & Evaluation, 14 (13), s. 1–13, http://pareonline.net/getvn.asp?v=14&n=13 (dostęp: 15.06.2018).
[28] Robine, J. M. (2001). Redefining the Stages of the Epidemiological Transition by a Study of the Dispersion of Life Spans: The Case of France, Population: An English Selection, 13 (1), s. 173–194.
[29] Rossi, I. A., Rousson, V., Paccaud, F. (2013). The contribution of rectangularization to the secular increase of life expectancy: an empirical study, International Journal of Epidemiology, 42 (1), s. 250–258.
[30] Rousson, V., Paccaud, F. (2010). A set of indicators for decomposing the secular increase of life expectancy, Population Health Metrics, 8:18, s. 1–9. http://www.pophealthmetrics.com/content/8/1/18 (dostęp: 3.01.2019).
[31] Schalkwijk, F. H., Koopman, J. J. E., Ghariq, E., de Beer, J. A. A., van Bodegom, D., Westendorp, R. G. J. (2016). Disentangling rectangularization and life span extension with the moving rectangle method, Annals of Epidemiology, 26 (3), s. 218–221.
[32] Shkolnikov, V. M, Andreev, E. E., Begun, A. Z. (2003). Gini coefficient as a life table function: computation from discrete data, decomposition of differences and empirical examples, Demographic Research, vol. 8, article 11, s. 305–358.
[33] Siegel, J. S. (2012). The Life Table. W: The Demography and Epidemiology of Human Health and Aging (s. 135–216), J. S. Siegel (Ed.). New York: Springer, https://doi.org/10.1007/978-94-007-1315-4 (dostęp: 20.12.2018).
[34] Szukalski, P. (2008). Ewolucja umieralności i niepełnosprawności w Polsce w świetle koncepcji rektangularyzacji krzywej przeżycia. W: Starzenie się ludności Polski – między demografią a gerontologią społeczną (s. 89–123), J. T. Kowaleski, P. Szukalski (red.). Łodź: Wydawnictwo Uniwersytetu Łodzkiego.
[35] Thatcher, A. R., Cheung, S. L. K., Horiuchi, S., Robine, J. M. (2010). The compression of deaths above the mode, Demographic Research, vol. 22, article 17, s. 505–538.
[36] Upton, A. C. (1977). Pathology. W: Handbook of Biology of Aging (s. 513–535), C. E. Finch, L. Hayflick (Eds.). New York: Van Nostrand Reinhold.
[37] Wilmoth, J. R., Horiuchi, S. (1999). Rectangularization revisited: variability of age at death within human populations, Demography, 36 (4), s. 475–495.
[38] Wroblewska, W. (2009). Teoria przejścia epidemiologicznego oraz fakty na przełomie wieków w Polsce, Studia Demograficzne, 1 (155), s. 110–159.
[39] Wroblewska, W. (2017). Pomiar dyspersji wieku w momencie zgonu. Przyczynek do analizy kompresji umieralności w Polsce, Studia Demograficzne, 1 (171), s. 3–25.
[40] Yue, J. C. (2012). Mortality Compression and Longevity Risk, North American Actuarial Journal, 16 (4), s. 434–448.