The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

A Method for Construction of Life Table in Korea

우리나라 자료에 적합한 생명표 작성방법에 대한 연구

  • Received : 20110600
  • Accepted : 20110800
  • Published : 2011.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

The life table is a statistical model for life expectancy and reflects mortality experiences exposed to a particular group of people. The following three issues are prerequisite for constructing the life table : a selection of how to estimate the death probability from observed death rates, a graduation method to smooth irregularity of the death probabilities, and an extension method of the death probabilities for oldest-old ages. To construct the life table that is fittest to Korean mortality experiences, we examine five estimation methods such as Chiang's and Greville's for the death probability, three graduation techniques including Beer's and Greville's formulae, and twelve mathematical functions for the extension of death probabilities for oldest-old ages. We also propose a method to resolve the cross-over problem arising from construction the life table.

생명표는 특정 집단의 사망 경험(mortality expereience)을 반영하여 각 연령에서의 기대여명을 추정하는 통계적 모형이다. 사망 경험은 사망확률(death probability)을 통해 반영되는데, 사망확률을 추정하기 위해서는 세 가지 사항이 고려되어야 한다. 첫째는 사망률(death rate)로부터 사망확률을 추정하는 방법의 선택이며, 둘째는 사망확률의 불규칙성을 해결하기 위한 평활 방법, 셋째는 초고령 자료의 신뢰성 문제를 해결하기 위한 사망확률 추정 및 확장 문제이다. 본 논문에서는 사망확률 추정방법의 선택을 위해 Chiang 방법, 상수방법, Greville 방법, Reed and Merrell 방법 및 Keyfitz and Frauenthal 방법을 비교하며, 평활 방법으로는 Beers 방법, Greville 방법 및 이동평균 방법을 비교하도록 한다. 또한 초고령에서 사망확률 추정 및 확장을 위해 총 12가지 수학적 함수를 비교한다. 본 논문에서는 각 방법들을 비교함으로써 우리나라에 적합한 생명표 작성 방법을 제시하고, 이를 이용하여 2005년부터 2009년까지의 생명표를 작성하도록 한다. 또한 기간별 성별 기대여명의 역전현상(cross-over)현상을 해결하기 위한 방법을 제시한다.

Keywords

References

  1. 박유성, 박성근, 최보승, 김기환 (2009). Beers와 Greville 보정방법에 의한 사망확률 보정방법 비교 연구, Journal of the Korean Data Analysis Society, 11, 97-110.
  2. 통계청 (2010). <2009년 생명표>, 통계청.
  3. Anderson, R. N. (1999). A method for constructing complete annual U.S. life tables, Vital Health Statistics, Series 2, No.129, NCHS.
  4. Anderson, R. N. and Arias, E. (2003). The effect of revised populations on mortality statistics for the United States, 2000, National Vital Statistics Reports, 51, No 9.
  5. Arias, E. (2010). United states life table 2006, National Vital Statistics Reports, 58, No 21.
  6. Beard, R. E. (1971). Some aspects of theories of mortality, cause of death analysis, forecasting and stochastic processes, In W.Brass (Eds.), Biological Aspects of Demography, Taylor and Francis, London.
  7. Beers, H. S. (1944). Six-term formulas for routine actuarial interpolation, American Institute of Actuaries, 33, 245-260.
  8. Boleslawski, L. and Tabeau, E. (2001). Comparing theoretical age patterns of mortality beyond the age of 80, In E. Tabeau, A. Van Den Berg Jeths, and C. Heathcote (Eds.), Forecasting Mortality in Developed Countries: Insights from a Statistical, Demographic and Epidemiological Perspective, Kluwer Academic Publishers, Dordrecht.
  9. Buettner, T. (2002). Approaches and experiences in projecting mortality patterns for the oldest-old, North American Actuarial Journal, 6, 14-29. https://doi.org/10.1080/10920277.2002.10596053
  10. Chiang, C. L. (1968). Introduction to Stochastic Processes in Biostatistics, John Wiley and Sons, New York.
  11. Chiang, C. L. (1984). The Life Table and its Applications, Robert E. Krieger Publishing Co., Malabar, Florida.
  12. Coale, A. J. and Demeny, P. (1983). Regional Model Life Tables and Stable Populations, Academic Press, New York.
  13. Coale, A. J. and Kisker, E. E. (1986). Mortality crossovers: Reality or bad data?, Population Studies, 40, 389-401. https://doi.org/10.1080/0032472031000142316
  14. Coale, A. J. and Kisker, E. E. (1990). Defects in data on old-age mortality in the United States: New procedures for calculating schedules and life tables at the highest ages, Asian and Pacific Population Forum, 4, 1-31.
  15. Condran, G., Himes, C. L. and Preston, S. H. (1991). Old age mortality patterns in low-mortality countries: An evaluation of population and death data at advanced ages, 1950 to present, Population Bulletin of the United Nations, 30, 23-61.
  16. Gompertz, B. (1825). On the nature of the function expressive of the law of mortality, Philosophical Transactions, 27, 513-585.
  17. Greville, T. N. E. (1943). Short methods of constructing abridged life tables, The Record of the American Institute of Actuaries, 32, 29-42.
  18. Greville, T. N. E. (1945). Actuarial Note : Some Extensions of Mr. Beers's Method of Interpolation, American Institute of Actuaries, 34, 21-34.
  19. Heligman, L. and Pollard, J. H. (1980). The age pattern of mortality, Journal of the Institute of Actuaries, 107, 49-80. https://doi.org/10.1017/S0020268100040257
  20. Hill, K. (1999). The Measurement of Adult Mortality: An Assessment of Data Availability, Data Quality and Estimation Methods. In Health and Mortality Issues of Global Concerns, Proceedings of the Symposium on Health and Mortality, Brussels: Population and Family Study Centre.
  21. Himes, C. L., Preston, S. H. and Condran, G. (1994). A relational model of mortality at older ages in low mortality countries, Population Studies, 2, 269-291.
  22. Keyfitz, N. (1966). A life table that agrees with the data, Journal of the American Statistical Association, 61, 305-12. https://doi.org/10.2307/2282820
  23. Keyfitz, N. and Frauenthal, J. (1975). An improved life table method, Biometrics, 31, 889-899. https://doi.org/10.2307/2529814
  24. London, R. L. (1981). In defense of minimum-Ro linear compound graduation, and a simple modification for its improvement, ARCH, Chicago: Society of Actuaries, 75-88.
  25. Makeham, W. (1860). On the law of mortality and the construction of annuity tables, Journal of the Institute of Actuaries, 13, 325-358.
  26. Ng, E. and Gentleman, J. F. (1995). The impact of estimation method and population adjustment on Canadian life table estimates, Health Reports, 7, 15-21.
  27. Perks, W. (1932). On some experiments in the graduation of mortality statistics, Journal of the Institute of Actuaries, 63, 12-27. https://doi.org/10.1017/S0020268100046680
  28. Preston, S. H., Heuveline, P. and Guillot, M. (2000). Demography: Measuring and Modeling Population Processes, Blackwell Publishing Ltd, Oxford.
  29. Reed, L. J. and Merrell, M. (1939). A short method for constructing an abridged life table, American Journal of Hygiene, 30, 33-62.
  30. Shryock, H. S., Siegel, J. S. and Associates (1993). Interpolation: Selected General Methods, In: D.J. Bogue, E.E. Arriaga, D.L. Anderton and G.W. Rumsey (Eds.), Readings in Population Research Methodology. Vol. 1: Basic Tools. Social Development, Center / UN Population Fund, Chicago.
  31. Siegel, J. S. and Swanson, D. A. (2004). The Methods and Materials of Demography, Elsevier Academic Press, San Diego.
  32. Sprague, T. B. (1881). Explanation of a new formula for interpolation, Journal of the Institute of Actuaries, 22, 1880-1881.
  33. Weibull, W. (1951). A statistical distribution function of wide applicability, Journal of Applied Mechanics, 18, 293-297.
  34. Wilmoth, J. R. (1995). Are mortality rates falling at extremely high ages? An investigation based on a model proposed by Coale and Kisker, Population Studies, 49, 281-295. https://doi.org/10.1080/0032472031000148516
  35. World Health Organization (1977). Manual of Mortality Analysis, WHO, Geneva.

Cited by

  1. Benefit-Cost Analysis of National Pensioners by Income and Life Expectancy vol.27, pp.2, 2014, https://doi.org/10.5351/KJAS.2014.27.2.211
  2. A review of life table applications and an introduction of its application method vol.24, pp.6, 2013, https://doi.org/10.7465/jkdi.2013.24.6.1159