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

Trends in the relationship between the proportional rate of change in force of mortality and life expectancy: an application of life-table entropy

10.6288/TJPH201635105040

林正祥(Cheng-Hsiang Lin)；謝尚儒(Shang-Ju Hsieh)

死亡率 ； 平均餘命 ； 生命表熵 ； 惡性腫瘤熵 ； mortality rate ； life expectancy ； life table entropy ； cancer entropy

台灣公共衛生雜誌

35卷5期（2016 / 10 / 01）

477 - 486

繁體中文

目標：熵在熱力學的領域中，指的是失去的熱量或無法利用的能量的量測，應用於人口學中，其可視為生命表中損失之人年數相對於平均餘命之比率，若喪失的人年數的比率(熵)愈小，則人們所能生存的平均餘命(功)就會愈大，反之則會愈小。本文旨在探討出生及中、老年時期生命表熵及惡性腫瘤熵之變化趨勢。方法：闡述說明生命表中平均餘命，死亡率變化速率與熵的關係及其特性，並利用台灣生命表相關資料探討生命表熵及疾病熵(惡性腫瘤)變化趨勢。結果：研究結果顯示1952年至2014年生命表熵H_0(0歲熵)男、女性皆呈平穩曲線下降，H_(40)(40歲熵)男、女性則有震盪起伏現象，H_(65)(65歲熵)是震盪起伏上升，幅度較H_(40)為大；HE係指因死亡率減少所能增加的平均餘命，其變動趨勢顯示HE_0呈現下降趨勢，而在HE_(40)與HE_(65)則是上升的；1975年至2014年惡性腫瘤熵，男、女性均呈上升趨勢，其對平均餘命的影響亦然。以2014年平均餘命推算，若當年所有死亡率悉數去除(免死一次)，則男、女性平均壽命分別為89.8年及94.92年。結論：本研究初步檢視生命表中熵的變動趨勢，發現中、老年人熵值高(特別是中年人)，意謂較少的系統能量可以轉化為功(存活的生命年數)，因此延遲老化應是未來努力的目標；惡性腫瘤熵男、女均呈上升趨勢，且男性高於女性。另外，2014年資料顯示，惡性腫瘤熵影響中年時期的減損甚鉅，顯然中年時期的預防應重於一切，至於其對老年男、女性平均餘命的影響分別為18%及10.7%，亦不容小覷。延遲衰老及癌症預防應列為政府健康促進政策要務。

Objectives: In thermodynamics, entropy is heat loss or lack of availability of thermal energy needed for activity within a given operating system. It is viewed as the percentage of the average years of future lost by the observed deaths to the life expectancy in Demograph. If loss of person-years is less, then people will survive longer, and vice versa. This study aimed to evaluate the long-term trends in entropy and cancer entropy at birth, middle age and advanced age in Taiwan. Methods: Interpret how the life table entropy derived from the relationship between the proportional rate of progress in force of mortality and life expectancy. The Taiwan life table and cancer data set was used to explore long-term trends in entropy and cancer entropy based on number of deaths recorded at birth, middle age and older age (age 65 years and older). Results: From 1952 to 2014, trends in birth entropy for males and females declined steadily; at middle age, trends in entropy for males and females fluctuated up and down; trends in entropy among older adults was similar to middle age fluctuated up and down but with a wider margin. Mortality rates are declining in all age groups, while life expectancy is increasing for both sexes. From 1975 to 2014, trends in cancer entropy and life expectancy affected by cancer were increasing for both sexes. In 2014, life expectancy was estimated to be 89.8 and 94.92 years at birth for males and females, respectively, when the mortality rate is reduced completely (saved from death once) for the whole first year. Conclusions: This study found a high percentage of entropy in middle aged and older adults, showing that loss of person years is higher for middle-aged men and women especially. Trends in cancer entropy are rising and are higher among males than females. In 2014, cancer entropy was the major effect on middle age life expectancy. However, the effects of cancer on life expectancy among older adults (18% for males, 10.7% for females) should still not be overlooked. Results suggest that reducing senescence and cancer prevention should be the main purpose of long-term health promotion by the government in the future.

1. 林正祥、劉士嘉(2013)。台灣老人成功與活躍老化之健康餘命探討。台灣衛誌，32，562-75。
   連結：
2. 衛生福利部統計處：死因統計。http://www.mohw.gov.tw/cht/DOS/Statistic.aspx? f_list_no=312&fod_list_no=1601。引用2015/10/20。Department of Statistics, Ministry of Health and Welfare, R.O.C. (Taiwan). The cause of death statistics. Available at: http://www.mohw.gov.tw/cht/DOS/Statistic.aspx? f_list_no=312&fod_list_no=1601. Accessed October 20, 2015. [In Chinese]
3. Greenwood M. Medical statistics from Graunt to Farr. Biometrika 1948;32:101-27, 203-25. doi:10.1093/biomet/32.3-4.203.
4. Clausius R. XIII. On the application of the theorem of the Equivalence of Transformations to the internal work of a mass of matter. Phil Mag 1862;24:81-97.
5. Shannon CE. A symbolic analysis of relay and switching circuits. Trans AIEE 1938;57:713-23. doi:10.1109/EE.1938.6431064.
6. 內政部統計處：台灣地區簡易生命表。http://www.moi.gov.tw/stat/life.aspx。引用2015/10/20。Department of Statistics, Ministry of the Interior, R.O.C. (Taiwan). Abridged life table, Taiwan Area. Available at: http://www.moi.gov.tw/stat/life.aspx. Accessed October 20, 2015. [In Chinese]
7. Farr W. Life Tables. Fifth Annual Report of the Registrar General. London: Her Majesty's Stationery Office, 1843; 16-9.
8. Ben-Naim, A(2008).Entropy Demystified: The Second Law Reduced to Plain Common Sense.Singapore:World Scientific.
9. Chiang, CL(1984).The Life Table and Its Applications.Malabar, FL:Robert E. Krieger Publishing.
10. Cooper, LN,Gilbert, IH(1969).An introduction to the meaning and structure of physics.Am J Phys,37,458.
11. de Castro, MC(2001).Changes in mortality and life expectancy: some methodological issues.Math Popul Stud,9,181-208.
12. Demetrius, L(2001).Mortality plateaus and directionality theory.Proc Biol Sci,268,2029-37.
13. Demetrius, L(1979).Relations between demographic parameters.Demography,16,329-38.
14. Demetrius, L(1974).Demograhic parameters and natural selection.Proc Nat Acad Sci USA,71,4645-7.
15. Demetrius, L,Legendre, S,Harremöes, P(2009).Evolutionary entropy: a predictor of body size, metabolic rate and maximal life span.Bull Math Biol,71,800-18.
16. Goldman, N,Lord, G(1986).A new look at entropy and life table.Demography,23,275-82.
17. Hakkert, R(1987).Life table transformations and inequality measures: some noteworthy formal relationships.Demography,24,615-22.
18. Keyfitz, N(1977).Applied Mathematical Demography.New York, NY:John Wiley and Sons.
19. Mitra, S(1978).A short note on the taeuber paradox.Demography,15,621-3.
20. Nagnur, D(1986).Rectangularization of the survival curve and entropy: the Canadian experience, 1921-1981.Can Stud Popul,13,83-102.
21. Nagnur, D,Nagrodski, M(1987).Cause-Deleted Life Tables for Canada (1921 to 1981): An Approach Towards Analysing Epidemiologic Transition.Ottawa, Ontario:Social and Economic Studies Division, Analytical Studies Branch, Statistics Canada.
22. Newman, SC(1986).A generalization of life expectancy which incorporates the age distribution of the poppulation and its use in the measurement of the impact of mortality reduction.Demography,23,261-74.
23. Nusselder, WJ,Mackenbach, JP(1996).Rectangularization of the survival curve in the Netherlands, 1950-1992.Gerontologist,36,773-82.
24. Pearson, K(1978).The History of Statistics in the 17th and 18th Centuries Against the Changing Background of Intellectual, Scientific and Religious Thought.New York, NY:Macmillan Publishing.
25. Smith, D,Keyfitz, N(1977).Mathematical Demography: Selected Paper.Berlin:Springer-Verlag.
26. Tsai, SP,Lee, ES,Hardy, RJ(1978).The effect of a reduction in leading causes of death: potential gains in life expectancy.Am J Public Health,68,966-71.
27. Vaupel, JW(1986).How change in age-specific mortality a ffects life expectancy.Popul Stud,40,147-57.
28. Vaupel, JW,Yashin, AI(1987).Repeated resuscitation: how lifesaving alters life tables.Demography,24,123-35.
29. Vaupel, JW,Yashin, AI(1986).Targeting lifesaving: demographic linkages between population structure and life expectancy.Eur J Popul,2,335-60.
30. 林正祥(1996)。台灣地區三大死因部分去除對平均壽命增加之影響。國家科學委員會研究彙刊：人文及社會科學，2，250-60。

1. 張怡陵,林正祥(2020)。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。台灣公共衛生雜誌，39(1)，74-89。