影響平均餘命增長之生命表特性及其相關死亡率模式分析

Effect of life table indices and a related mortality model on increase of life expectancy

10.6288/TJPH.202002_39(1).108052

林正祥(CHENG-HSIANG LIN)；張怡陵(YI-LING CHANG)

平均餘命 ； 存活曲線矩形化 ； 死亡變異 ； 混合模式 ； 遲緩衰老 ； life expectancy ； rectangularity of the survival curves ； variability in the distribution of ages at death ； hybrid model of mortality ； senescence-slowing

台灣公共衛生雜誌

39卷1期（2020 / 02 / 26）

74 - 89

繁體中文

目標：探討死亡年齡變異、存活曲線矩形化間之生命表特性及相關的死亡率模式對平均餘命的影響。方法：利用1998－2016年台灣生命表資料，以各類相關指標測量存活曲線矩形化與死亡年齡變異趨勢。並以相關死亡率模式中重要的混合模式，探討平均餘命增長變化受到死亡率下降與遲緩衰老步調下降消長影響情況。結果：存活曲線間逐漸呈現矩形化的情況，且死亡年齡變異也呈下降狀態；以年齡95歲為上限利用面積差異百分比來檢測矩形化，結果顯示矩形化逐漸趨向平均餘命極限。另透過死亡率混合模式的分析結果得知平均餘命增長趨勢，其中32%是受到死亡率下降的影響，而受到延遲老化的影響則為68%。結論：各種指標均顯示存活曲線有逐漸矩形化的情況，死亡年齡的變異則是呈現下降的趨勢，平均餘命的增長受到一定的限制。從死亡率混合模式分析結果顯示這些年來平均餘命受到遲緩衰老的影響遠較死亡率下降來的大，對於平均餘命的展延，遲緩衰老當扮演舉足重的角色。

Objectives: To investigate the effect of variation in age at death and rectangularity in the survival curve on the increase of life expectancy and further investigate this phenomenon by using a hybrid mortality model. Methods: By using life table data in Taiwan, we measured the rectangular trend in survival curves and variation of age at death on the basis of related life table indices. We then applied a hybrid mortality model to interpret the effects of declining mortality and senescence-slowing on life expectancy. Results: The survival curve, which is closely related to life expectancy, gradually became rectangular from 1998 to 2016, and the variation of age at death declined. We measured the rectangularity of survival curve by setting the upper limit age of 95 years through using the percentage difference in area and found that rectangularity gradually approached the limit. Analysis using the hybrid mortality model revealed that 32% and 68% of the increase of life expectancy resulted from declining mortality and senescence-slowing, respectively. Conclusions: All indicators pointed to the survival curve gradually becoming rectangular and the variation of age at death trending downward, implying that human life expectancy is approaching a certain limit. The hybrid model of mortality revealed that the increase of life expectancy was affected more by senescence-slowing than by declining mortality.

1. 王德睦, TM,李大正, TC(2009)。台灣的存活曲線矩形化與壽命延長。人口學刊，38，1-31。
   連結：
2. 林正祥, CH,謝尚儒, SJ(2016)。台灣死亡率與平均餘命變動速率關係趨勢－生命表熵的應用。台灣衛誌，35，477-486。
   連結：
3. 劉士嘉, SC,林正祥, CH(2017)。人類壽命上限值探討—以台灣為例。人口學刊，55，133-163。
   連結：
4. Baudisch, A(2008).Inevitable Aging? Contributions to Evolutionary-Demographic Theory.Berlin, Germany:Springer.
5. Bergerson, M,Ebeling, M,Canudas-Romo, V(2015).Decomposing changes in life expectancy: Compression versus shifting mortality.Demographic Res,33,391-424.
6. Butler, RN,Miller, RA,Perry, D(2008).New model of health promotion and disease prevention for the 21th century.BMJ,377,a399.
7. Chen, YQ,Wang, MC(2000).Analysis of accelerated hazards models.J Am Stat Assoc,95,608-618.
8. Cheung, SL,Robine, JM,Tu, EJ,Caselli, G(2005).Three dimensions of the survival curve: horizontalization, verticalization, and longevity extension.Demography,42,243-258.
9. Coale, AJ,Kisker, EE(1990).Defects in data on old-age mortality in the United States: new procedures for calculating mortality schedules and life tables at the highest ages.Asian Pac Popul Forum,4,1-31.
10. Cox, DR(1972).Regression models and life tables.J Roy Stat Soc B,34,187-220.
11. Demetrius, L(1979).Relations between demographic parameters.Demography,16,329-338.
12. Demetrius, L(1974).Demograhic parameters and natural selection.Proc Natl Acad Sci U.S.A,71,4645-4647.
13. Fries, JF(1980).Aging, nature death, and the compression of morbidity.N Engl J Med,303,130-135.
14. Goldman, N,Lord, G(1986).A new look at entropy and life table.Demography,23,275-282.
15. Goldstein, JR,Cassidy, T(2012).How slowing senescence translates into longer life expectancy.Popul Stud,66,29-37.
16. Janssen, F,de Beer, J(2019).The timing of the transition from mortality compression to mortality delay in Europe, Japan and the United States.Genus,75,10.
17. Kalbfleisch, JD,Prentice, RL(2002).The Statistical Analysis of Failure Time Data.New York, NY:John Wiley & Sons.
18. Kannisto, V(2000).Measuring the compression of mortality.Demogr Res,3,24.
19. Keyfitz, N(1977).Applied Mathematical Demography.New York, NY:Springer.
20. Mitra, S(1978).A short note on the taeuber paradox.Demography,15,621-623.
21. Mueller, LD,Drapeau, MD,Adams, CS(2003).Statistical tests of demographic heterogeneity theories.Exp Gerontol,38,373-386.
22. Myers, GC,Manton, KG(1984).Compression of mortality: myth or reality?.Gerontologist,24,346-353.
23. Myers, GC,Manton, KG(1984).Recent changes in the U.S. age at death distribution: further observations.Gerontologist,24,572-575.
24. Namboodiri, K,Suchindran, CM(1987).Life Table Techniques and their Applications.Florida, FL:Academic Press.
25. Shkolnikov, V,Andreev, EM.MPIDR Technical ReportMPIDR Technical Report,未出版
26. Vaupel, JW(1986).How change in age-specific mortality Affects life expectancy.Popul Stud,40,147-157.
27. Wald A, Wolfowitz J. On a test whether two samples are from the same population. Ann Math Stat 1940;11:147-62. doi:10.1214/aoms/1177731909
28. Wilmoth, JR,Horiuchi, S(1999).Rectangularization revisited: variability of age at death within human populations.Demography,36,475-495.
29. 內政部戶政司：年中人口按性別及五齡組。https://www.ris.gov.tw/app/portal/346。引用2018/08/20。Department of Household Registration, Ministry of the Interior, R.O.C. (Taiwan). Mid-year population distribution by gender and the five age groups. Available at: https://www.ris.gov.tw/app/portal/346. Accessed August 20, 2018. [In Chinese]
30. 內政部戶政司：死亡數及粗死亡率（按登記及發生）。https://www.ris.gov.tw/app/portal/346。引用2018/08/20。Department of Household Registration, Ministry of the Interior, R.O.C. (Taiwan). Mortality and crude death rate. Available at: https://www.ris.gov.tw/app/portal/346. Accessed August 20, 2018. [In Chinese]
31. 內政部統計處：台灣地區簡易生命表。https://www.moi.gov.tw/stat/node.aspx?sn=4883。引用2018/8/20。Department of Statistics, Ministry of the Interior, R.O.C. (Taiwan). Abridged life table, Taiwan Area. Available at: https://www.moi.gov.tw/stat/node.aspx?sn=4883. Accessed August 20, 2018. [In Chinese]
32. 陳寬政, KC(2014)。科技部補助專題研究計畫成果報告科技部補助專題研究計畫成果報告,台北=Taipei:科技部=Ministry of Health and Welfare, R.O.C. (Taiwan)。
33. 陳寬政, KC,董宜禎, YC(2014)。高齡死亡率的趨平發展。健康，2，23-45。
34. 董宜禎, YC(2014)。嘉義=Chiayi，中正大學社會福利研究所=Department and Graduate Institute of Social Welfare, National Chung Cheng University。
35. 羅紀瓊（編）, JC(ed.)(2009).台灣人口老化問題.台北=Taipei:中央研究院經濟研究所=Institute of Economics, Academia Sinica, R.O.C. (Taiwan).