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Years of Potential Life Lost (YPLL)—What Does it Measure?
潛在生命年損失（YPLL）—它測量了什麼？

John W. Gardner and Jill S. Sanborn
約翰·W·加德納和吉爾·S·桑伯恩

Abstract 摘要

The concept of years of potential life lost (YPLL) involves estimating the average time a person would have lived had he or she not died prematurely. This measure is used to help quantify social and economic loss owing to premature death, and it has been promoted to emphasize specific causes of death affecting younger age groups. YPLL inherently incorporates age at death, and its calculation mathematically weights the total deaths by applying values to death at each age. The method of calculating YPLL varies from author to author, each producing different rankings of leading causes of premature death. One can choose between heart disease, cancer, or accidents as the leading cause of premature death, depending on which method is used. Confusion in the use of this measure stems from a misunderstanding of the value system inherent in the calculation, as well as from differing views as to values that should be applied to each age at death. (Epidemiology 1990;1:322-329)
潛在生命損失年數（YPLL）的概念涉及估算一個人如果沒有過早去世，平均可以活多久。這一指標用於量化因過早死亡而造成的社會和經濟損失，並被推廣以強調影響年輕年齡群體的特定死亡原因。YPLL 本質上包含死亡年齡，其計算方法通過對每個年齡的死亡賦予權重來數學上加權總死亡人數。計算 YPLL 的方法因作者而異，每位作者產生的過早死亡主要原因的排名也不同。根據所使用的方法，可以選擇心臟病、癌症或意外作為過早死亡的主要原因。對這一指標使用的混淆源於對計算中固有價值體系的誤解，以及對應該對每個死亡年齡賦予何種價值的不同看法。（流行病學 1990;1:322-329）

Keywords: health priorities, health resources, health status indicators, mortality.
關鍵詞：健康優先事項、健康資源、健康狀態指標、死亡率。
For decades, public health workers have been interested in quantifying the health of populations. Historically, mortality rates have been the central index of health status in a community. In recent years, attention has expanded to include measures that assess the impact of major causes of death on populations. Years of potential life lost (YPLL) is currently in vogue, with several impact measures arising from various modifications of this concept. In this paper, we explore the concept of YPLL, try to illustrate what it is measuring, and discuss the rationale for its use.
數十年來，公共衛生工作者一直對量化人口健康感興趣。歷史上，死亡率一直是社區健康狀況的核心指標。近年來，關注的範圍擴大到包括評估主要死亡原因對人口影響的指標。潛在生命損失年數（YPLL）目前正受到重視，並且基於這一概念的各種修改衍生出幾個影響指標。在本文中，我們探討 YPLL 的概念，試圖說明它所測量的內容，並討論其使用的理由。
The concept of YPLL entails estimating the average time a person would have lived had he or she not died prematurely. This estimation inherently incorporates age at death, rather than merely the occurrence of death itself. Use of the YPLL measures has been promoted in an attempt to emphasize specific causes of death in proportion to their burden on society. Crude and specific mortality rates describe the amount of death in a population, but they fail to quantify the burden of loss resulting from this mortality. YPLL, in contrast, is presented as an index that focuses on the social and economic consequences of mortality. Most health care workers would consider prevention of premature death as an important goal. In terms of social and economic loss, this goal is the prevention of death before its “natural” time, so the individual can contribute maximally to society.
YPLL 的概念涉及估算一個人如果沒有過早去世，平均會活多久。這一估算本質上包含了死亡年齡，而不僅僅是死亡事件的發生。YPLL 指標的使用被推廣，以強調特定死亡原因對社會的負擔。粗死亡率和特定死亡率描述了人口中的死亡數量，但未能量化由此死亡所帶來的損失負擔。相對而言，YPLL 被呈現為一個專注於死亡的社會和經濟後果的指標。大多數醫療工作者會認為預防過早死亡是一個重要目標。在社會和經濟損失方面，這一目標是防止在其“自然”時間之前的死亡，以便個體能夠最大限度地為社會做出貢獻。
It was recognized early that evaluation of competing claims for allocation of health resources requires consideration not only of the number of deaths from each cause, but also their distribution by age. No single index is completely adequate in quantifying the social and economic impact of mortality in a society, but YPLL and future income sacrificed have been proposed as aids to be used in these estimations, since they focus on the burden of lost productivity ( 1 − 2 1 − 2 1-21-2 ). The competition for health resources often relates to programs directed at specific diseases, so a ranking of these diseases (causes of death) according to their impact on society’s productivity can be useful.
早期就已認識到，評估健康資源分配的競爭要求不僅考慮每種原因造成的死亡人數，還要考慮其年齡分佈。沒有單一指標能完全充分地量化社會中死亡率的社會和經濟影響，但已提出 YPLL 和未來收入損失作為這些估算的輔助工具，因為它們專注於生產力損失的負擔（ 1 − 2 1 − 2 1-21-2 ）。健康資源的競爭通常與針對特定疾病的計劃有關，因此根據這些疾病（死亡原因）對社會生產力的影響進行排名可能會很有用。
In 1982, the Centers for Disease Control (CDC) (3) introduced a YPLL measure to its standard set of tables of reported diseases, with the justification that, “by displaying a variety of measures that gauge the importance and relative magnitude of certain public health issues, this table will call attention to those issues where strategies for prevention are needed. Publication of this table reflects CDC’s increased responsibility for promoting action to reduce unnecessary morbidity and premature mortality. . . . To this end, the new table provides information regarding areas that provide the greatest potential for health improvement.” In 1986, further discussion (4) declared that, “since most deaths occur among persons in older age groups, crude and ageadjusted mortality data are dominated by the underlying disease processes of the elderly. Alternative measures have been proposed to reflect the mortality trends of younger age groups. These measures provide a more accurate picture of premature mortality by weighting deaths occurring at younger ages more heavily than those occurring in older populations. . . . The major strengths of YPLL are that it is simple to compute and
在 1982 年，疾病控制中心（CDC）引入了一項 YPLL 指標，作為其報告疾病的標準表格之一，理由是：“通過展示各種衡量某些公共衛生問題重要性和相對規模的指標，這個表格將引起對那些需要預防策略的問題的關注。這個表格的發布反映了 CDC 在促進減少不必要的疾病和過早死亡方面的責任增加……為此，新的表格提供了有關健康改善潛力最大的領域的信息。”在 1986 年，進一步的討論宣稱：“由於大多數死亡發生在年長者中，粗死亡率和年齡調整死亡率數據主要受到老年人潛在疾病過程的影響。已提出替代指標以反映年輕年齡組的死亡趨勢。這些指標通過對年輕年齡段的死亡進行更重的加權，提供了更準確的過早死亡圖景……YPLL 的主要優勢在於其計算簡單。
comprehend and it effectively emphasizes deaths of younger persons, in contrast to usual mortality statistics, which are dominated by deaths of the elderly.”
理解並有效強調年輕人的死亡，與通常由老年人死亡主導的死亡統計形成對比。

What Does YPLL Measure? YPLL 測量什麼？

The method of calculating YPLL varies from author to author. Each method is a function of age at death and the number of deaths at that age. The number of deaths at each age is multiplied by an indicator of years of potential life remaining for that age, and the terms are summed to get the total YPLL. This calculation is a weighted total of the number of deaths by age, with the weights for each age determined by the particular method of valuing potential remaining years of life. That is,
計算潛在生命損失年數（YPLL）的方法因作者而異。每種方法都是死亡年齡和該年齡死亡人數的函數。每個年齡的死亡人數乘以該年齡的潛在剩餘生命年數指標，然後將這些項相加以獲得總 YPLL。這一計算是按年齡加權的死亡人數總和，每個年齡的權重由特定的潛在剩餘生命年數評估方法決定。也就是說，
YPLL = = == sum(deaths at a given age) ⋅ ⋅ *\cdot
YPLL = = == 在特定年齡的死亡總數 ⋅ ⋅ *\cdot
(weight for that age) ] = Σ ( d i ) ( w i ) ] = Σ d i w i ]=Sigma(d_(i))(w_(i))]=\Sigma\left(d_{i}\right)\left(w_{i}\right).
（該年齡的體重） ] = Σ ( d i ) ( w i ) ] = Σ d i w i ]=Sigma(d_(i))(w_(i))]=\Sigma\left(d_{i}\right)\left(w_{i}\right) 。
This calculation is similar to that of an age-adjusted rate (which uses r i r i r_(i)r_{i} rather than d i d i d_(i)d_{i} ). It is of interest to explore the weights ( w i w i w_(i)w_{i} ) used in the various YPLL calculations. First of all, these measures use the number of deaths at each age ( d i ) d i (d_(i))\left(d_{i}\right), rather than mortality risk (or rate, r i r i r_(i)r_{i} ) at each age. The fundamental health characteristic of a population is its specific mortality rates ( r i r i r_(i)r_{i} ). The number of deaths that occur in a population is a function of these rates, the population size, and its age distribution; therefore, all YPLL calculations reflect the age distribution of the population [ie, d i = ( r i ) ( n i ) ] d i = r i n i {:d_(i)=(r_(i))(n_(i))]\left.d_{i}=\left(r_{i}\right)\left(n_{i}\right)\right]. This inherent inclusion of age-specific populations ( n i ) n i (n_(i))\left(n_{i}\right) in the YPLL calculations make them applicable only to that population. In an impact evaluation, this specificity is what one desires, since the objective is to sum the burden of loss for each death in a given population. This loss is a function of the mortality risk at each age in the population, the size and age distribution of the population, the age distribution of the cause of death, and the value attached to death at each age.
這個計算類似於年齡調整率的計算（使用 r i r i r_(i)r_{i} 而不是 d i d i d_(i)d_{i} ）。探索在各種 YPLL 計算中使用的權重（ w i w i w_(i)w_{i} ）是有趣的。首先，這些指標使用每個年齡的死亡人數 ( d i ) d i (d_(i))\left(d_{i}\right) ，而不是每個年齡的死亡風險（或比率， r i r i r_(i)r_{i} ）。一個人口的基本健康特徵是其特定的死亡率（ r i r i r_(i)r_{i} ）。在一個人口中發生的死亡人數是這些死亡率、人口規模及其年齡分佈的函數；因此，所有 YPLL 計算都反映了該人口的年齡分佈[即， d i = ( r i ) ( n i ) ] d i = r i n i {:d_(i)=(r_(i))(n_(i))]\left.d_{i}=\left(r_{i}\right)\left(n_{i}\right)\right] 。這種在 YPLL 計算中固有的年齡特定人口 ( n i ) n i (n_(i))\left(n_{i}\right) 的包含，使得它們僅適用於該人口。在影響評估中，這種特異性是所期望的，因為目標是總結給定人口中每次死亡的損失負擔。這種損失是人口中每個年齡的死亡風險、人口的規模和年齡分佈、死亡原因的年齡分佈以及每個年齡對死亡的價值的函數。
We have categorized the various methods used to calculate YPLL in Table 1, which also defines notation and abbreviations. Dempsey (5) calculated life expectancy at birth, less age of death (PYPLL, with N = L 0 N = L 0 N=L_(0)N=L_{0} ). He was criticized by Greville (6), who calculated life expectancy at age of death (YPLL). Logan and Benjamin (7) calculated years of life lost to the age at which 90 % 90 % 90%90 \% of males and females died, respectively, according to the 1952 life tables (PYPLL, with N = 85 N = 85 N=85N=85 for males and N = 88 N = 88 N=88N=88 for females). They also calculated the years of life lost during “the working age period” (WYPLL, with W = 15 W = 15 W=15W=15 and N = 65 N = 65 N=65N=65 ). Stickle (2) used life expectancy at age of death (YPLL), but also extended the working years of life lost concept by calculating future income sacrificed, ie , the number of years of life lost times the average income for each year taken from a 1963 survey of personal income by age (VYPLL, with I ( j ) = I ( j ) = I(j)=I(j)= average annual income). Romeder and McWhinnie (8) calculated years of life lost from age 1 to 70 , eliminating deaths in the first year and after age 70 ( PYPLL ∘ ∘ ^(@)^{\circ}, with N = 70 N = 70 N=70N=70 ). Perloff et al (9) included deaths occurring under age 1 , but calculated only “potentially productive years of life lost” (WYPLL, with W = 15 W = 15 W=15W=15 and N = 70 N = 70 N=70N=70 ). The CDC, in its MMWR tables introduced in 1982 (3), calculated years of life lost from age 1 to 65 (PYPLL* with N = N = N=N= 65), but changed in 1986 (10) to include infant deaths (PYPLL with N = 65 N = 65 N=65N=65 ). This change moved sudden infant death syndrome and prematurity into the ten leading causes of premature death in the MMWR tables.
我們已在表 1 中對計算 YPLL 的各種方法進行了分類，並定義了符號和縮寫。Dempsey（5）計算了出生時的預期壽命減去死亡年齡（PYPLL，帶有 N = L 0 N = L 0 N=L_(0)N=L_{0} ）。他受到 Greville（6）的批評，後者計算了死亡年齡的預期壽命（YPLL）。Logan 和 Benjamin（7）根據 1952 年的生命表計算了男性和女性分別在 90 % 90 % 90%90 \% 歲時的生命損失年數（PYPLL，男性為 N = 85 N = 85 N=85N=85 ，女性為 N = 88 N = 88 N=88N=88 ）。他們還計算了在“工作年齡期間”損失的生命年數（WYPLL，帶有 W = 15 W = 15 W=15W=15 和 N = 65 N = 65 N=65N=65 ）。Stickle（2）使用了死亡年齡的預期壽命（YPLL），但還通過計算未來收入的損失來擴展了損失工作年限的概念，即損失的生命年數乘以根據 1963 年按年齡進行的個人收入調查的平均收入（VYPLL，帶有 I ( j ) = I ( j ) = I(j)=I(j)= 的平均年收入）。Romeder 和 McWhinnie（8）計算了從 1 歲到 70 歲的生命損失年數，排除了第一年和 70 歲以後的死亡（PYPLL ∘ ∘ ^(@)^{\circ} ，帶有 N = 70 N = 70 N=70N=70 ）。 Perloff 等人（9）包括了 1 歲以下的死亡，但僅計算“潛在生產性生命損失年數”（WYPLL，參見 W = 15 W = 15 W=15W=15 和 N = 70 N = 70 N=70N=70 ）。疾病控制與預防中心（CDC）在 1982 年引入的 MMWR 表格中（3），計算了從 1 歲到 65 歲的生命損失年數（PYPLL* 參見 N = N = N=N= 65），但在 1986 年（10）改為包括嬰兒死亡（PYPLL 參見 N = 65 N = 65 N=65N=65 ）。這一變更使得嬰兒猝死症和早產成為 MMWR 表格中十大過早死亡原因之一。
The formula given for VYPLL is in fact a general formula from which any of the other YPLL calculations can be derived, each using different values for the function I ( j ) I ( j ) I(j)I(j). For example, the YPLL formula uses I ( j ) = 1 I ( j ) = 1 I(j)=1I(j)=1 for all j j jj; PYPLL uses I ( j ) = 1 I ( j ) = 1 I(j)=1I(j)=1 for j < N j < N j < Nj<N and I ( j ) = 0 I ( j ) = 0 I(j)=0I(j)=0 for j ⩾ N j ⩾ N j >= Nj \geqslant N; PYPLL* is the same as PYPLL except that it uses I ( j ) = 0 I ( j ) = 0 I(j)=0I(j)=0 for all j j jj when i = 0 i = 0 i=0i=0; WYPLL uses I ( j ) = 1 I ( j ) = 1 I(j)=1I(j)=1 for w ⩽ j < N w ⩽ j < N w <= j < Nw \leqslant j<N and I ( j ) = 0 I ( j ) = 0 I(j)=0I(j)=0 otherwise; and the crude total deaths use this formula with I ( j ) = 1 I ( j ) = 1 I(j)=1I(j)=1 when j = i j = i j=ij=i and I ( j ) I ( j ) I(j)I(j) = 0 = 0 =0=0 otherwise. So the weights used in each calculation are
VYPLL 的公式實際上是一個通用公式，從中可以推導出其他任何 YPLL 計算，每個計算使用不同的 I ( j ) I ( j ) I(j)I(j) 值。例如，YPLL 公式對所有 j j jj 使用 I ( j ) = 1 I ( j ) = 1 I(j)=1I(j)=1 ；PYPLL 對 j < N j < N j < Nj<N 使用 I ( j ) = 1 I ( j ) = 1 I(j)=1I(j)=1 ，對 j ⩾ N j ⩾ N j >= Nj \geqslant N 使用 I ( j ) = 0 I ( j ) = 0 I(j)=0I(j)=0 ；PYPLL*與 PYPLL 相同，只是當 i = 0 i = 0 i=0i=0 時對所有 j j jj 使用 I ( j ) = 0 I ( j ) = 0 I(j)=0I(j)=0 ；WYPLL 對 w ⩽ j < N w ⩽ j < N w <= j < Nw \leqslant j<N 使用 I ( j ) = 1 I ( j ) = 1 I(j)=1I(j)=1 ，對 I ( j ) = 0 I ( j ) = 0 I(j)=0I(j)=0 則使用其他值；而粗略總死亡人數在 j = i j = i j=ij=i 時使用此公式，當 I ( j ) I ( j ) I(j)I(j) = 0 = 0 =0=0 時則使用 I ( j ) = 1 I ( j ) = 1 I(j)=1I(j)=1 。因此，每個計算中使用的權重為
weight i = n i ( ∑ j = i i + L 1 I ( j ) )  weight  i = n i ∑ j = i i + L 1   I ( j ) " weight "_(i)=n_(i)(sum_(j=i)^(i+L_(1))I(j))\text { weight }_{i}=n_{i}\left(\sum_{j=i}^{i+L_{1}} I(j)\right)
and the differences between methods are due solely to the different values of I ( j ) I ( j ) I(j)I(j) assigned to each year of age. Note that only the YPLL formula values each year of life lost equally, while PYPLL, WYPLL, and VYPLL do not put equal value on each year of life lost. In addition, none of these methods takes into account the effect of competing causes of death. For example, PYPLL assumes that all individuals will live to age N N NN, except those dying from the cause of interest.
方法之間的差異僅僅是由於每個年齡所分配的 I ( j ) I ( j ) I(j)I(j) 的不同值。請注意，只有 YPLL 公式對每一年失去的生命賦予相等的價值，而 PYPLL、WYPLL 和 VYPLL 則不對每一年失去的生命賦予相等的價值。此外，這些方法都沒有考慮到競爭性死亡原因的影響。例如，PYPLL 假設所有個體都會活到 N N NN 歲，除了因所關心的原因而死亡的人。

Why Different Weichting Methods?
為什麼有不同的加權方法？

Authors have disagreed on what ages social and economic losses begin and end, as well as the value of productivity at each age. For example, some authors use life expectancy at birth ( L 0 L 0 L_(0)L_{0} ) for N N NN (currently 74.8 ; or - 71.3 for males and 78.3 for females), while others have arbitrarily selected 65,70 , or some other age. The CDC ( 3 , 4 ) ( 3 , 4 ) (3,4)(3,4) argued that, "If deaths of persons older than 65 years were included, greater weight would be given to
作者對於社會和經濟損失的開始和結束年齡，以及每個年齡的生產力價值存在分歧。例如，一些作者使用出生時的預期壽命（ L 0 L 0 L_(0)L_{0} ）作為 N N NN （目前為 74.8；男性為 71.3，女性為 78.3），而其他人則隨意選擇 65、70 或其他年齡。CDC ( 3 , 4 ) ( 3 , 4 ) (3,4)(3,4) 辯稱：“如果將 65 歲以上的死亡人數納入考量，將會給予更大的權重。”
TABLE 1. Formulas for Alternative YPLL Summary Measures*
表 1. 替代 YPLL 摘要指標的公式*
Abbreviation † † †\dagger 縮寫 † † †\dagger Name 名稱 Formula 公式
YPLL ( 6 , 2 ) YPLL ( 6 , 2 ) YPLL(6,2)\operatorname{YPLL}(6,2) Years of potential life lost
潛在生命損失年數
∑ i = 0 ∞ d i ( L i ) ∑ i = 0 ∞   d i L i sum_(i=0)^(oo)d_(i)(L_(i))\sum_{i=0}^{\infty} d_{i}\left(L_{i}\right)
sum_(i=0)^(oo)d_(i)(L_(i))| $\sum_{i=0}^{\infty} d_{i}\left(L_{i}\right)$ | | :--- |
PYPLL ( 5 , 7 , 10 ) ( 5 , 7 , 10 ) (5,7,10)(5,7,10) Premature (to N N NN ) years of potential life lost
過早（至 N N NN ）年潛在生命損失
∑ i = 0 N d i ( N − i ) ∑ i = 0 N   d i ( N − i ) sum_(i=0)^(N)d_(i)(N-i)\sum_{i=0}^{N} d_{i}(N-i)
sum_(i=0)^(N)d_(i)(N-i)| $\sum_{i=0}^{N} d_{i}(N-i)$ | | :--- |
PYPLL ( 8 , 3 ) ( 8 , 3 ) (8,3)(8,3) Premature (to N N NN ) years of potential life lost ‡ ‡ ‡\ddagger
過早（至 N N NN ）年潛在生命損失 ‡ ‡ ‡\ddagger
∑ i = 1 N d i ( N − i ) ∑ i = 1 N   d i ( N − i ) sum_(i=1)^(N)d_(i)(N-i)\sum_{i=1}^{N} d_{i}(N-i)
sum_(i=1)^(N)d_(i)(N-i)| $\sum_{i=1}^{N} d_{i}(N-i)$ | | :--- |
WYPLL ( 7 , 9 ) ( 7 , 9 ) (7,9)(7,9) Working ( W W WW to N N NN ) years of potential life lost
工作（ W W WW 到 N N NN 年）潛在生命損失
∑ i = 0 W − 1 d i ( N − W ) + ∑ i = W N d i ( N − i ) ∑ i = 0 W − 1   d i ( N − W ) + ∑ i = W N   d i ( N − i ) sum_(i=0)^(W-1)d_(i)(N-W)+sum_(i=W)^(N)d_(i)(N-i)\sum_{i=0}^{W-1} d_{i}(N-W)+\sum_{i=W}^{N} d_{i}(N-i)
sum_(i=0)^(W-1)d_(i)(N-W)+sum_(i=W)^(N)d_(i)(N-i)| $\sum_{i=0}^{W-1} d_{i}(N-W)+\sum_{i=W}^{N} d_{i}(N-i)$ | | :--- |
VYPLL ( 2 ) Valued years of potential life lost
失去的潛在生命年數
∑ i = 0 ∞ d i [ ∑ j = i i + L I ( j ) ] ∑ i = 0 ∞   d i ∑ j = i i + L   I ( j ) sum_(i=0)^(oo)d_(i)[sum_(j=i)^(i+L)I(j)]\sum_{i=0}^{\infty} d_{i}\left[\sum_{j=i}^{i+L} I(j)\right]
sum_(i=0)^(oo)d_(i)[sum_(j=i)^(i+L)I(j)]| $\sum_{i=0}^{\infty} d_{i}\left[\sum_{j=i}^{i+L} I(j)\right]$ | | :--- |
CRUDE (14) 原油 (14) Crude death rate 粗死亡率
∑ d 1 ∑ n 1 = ∑ ( r i ) ( n 1 ) ∑ n i ∑ d 1 ∑ n 1 = ∑ r i n 1 ∑ n i (sumd_(1))/(sumn_(1))=(sum(r_(i))(n_(1)))/(sumn_(i))\frac{\sum d_{1}}{\sum n_{1}}=\frac{\sum\left(r_{i}\right)\left(n_{1}\right)}{\sum n_{i}}
(sumd_(1))/(sumn_(1))=(sum(r_(i))(n_(1)))/(sumn_(i))| $\frac{\sum d_{1}}{\sum n_{1}}=\frac{\sum\left(r_{i}\right)\left(n_{1}\right)}{\sum n_{i}}$ | | :--- |
ADJ (14) Adjusted death rate 調整後死亡率
Σ ( r i ) ( w i ) Σ w i Σ r i w i Σ w i (Sigma(r_(i))(w_(i)))/(Sigmaw_(i))\frac{\Sigma\left(r_{i}\right)\left(w_{i}\right)}{\Sigma w_{i}}
(Sigma(r_(i))(w_(i)))/(Sigmaw_(i))| $\frac{\Sigma\left(r_{i}\right)\left(w_{i}\right)}{\Sigma w_{i}}$ | | :--- |
CI L CI L CI_(L)\mathrm{CI}_{\mathrm{L}} (14) Lifetime cumulative incidence rate
終生累積發生率
1 − exp ⁡ ( − ∑ i = 0 L r i ) 1 − exp ⁡ − ∑ i = 0 L   r i 1-exp(-sum_(i=0)^(L)r_(i))1-\exp \left(-\sum_{i=0}^{L} r_{i}\right)
1-exp(-sum_(i=0)^(L)r_(i))| $1-\exp \left(-\sum_{i=0}^{L} r_{i}\right)$ | | :--- |
Abbreviation † Name Formula YPLL(6,2) Years of potential life lost "sum_(i=0)^(oo)d_(i)(L_(i))" PYPLL (5,7,10) Premature (to N ) years of potential life lost "sum_(i=0)^(N)d_(i)(N-i)" PYPLL (8,3) Premature (to N ) years of potential life lost ‡ "sum_(i=1)^(N)d_(i)(N-i)" WYPLL (7,9) Working ( W to N ) years of potential life lost "sum_(i=0)^(W-1)d_(i)(N-W)+sum_(i=W)^(N)d_(i)(N-i)" VYPLL ( 2 ) Valued years of potential life lost "sum_(i=0)^(oo)d_(i)[sum_(j=i)^(i+L)I(j)]" CRUDE (14) Crude death rate "(sumd_(1))/(sumn_(1))=(sum(r_(i))(n_(1)))/(sumn_(i))" ADJ (14) Adjusted death rate "(Sigma(r_(i))(w_(i)))/(Sigmaw_(i))" CI_(L) (14) Lifetime cumulative incidence rate "1-exp(-sum_(i=0)^(L)r_(i))"| Abbreviation $\dagger$ | Name | Formula | | :---: | :---: | :---: | | $\operatorname{YPLL}(6,2)$ | Years of potential life lost | $\sum_{i=0}^{\infty} d_{i}\left(L_{i}\right)$ | | PYPLL $(5,7,10)$ | Premature (to $N$ ) years of potential life lost | $\sum_{i=0}^{N} d_{i}(N-i)$ | | PYPLL $(8,3)$ | Premature (to $N$ ) years of potential life lost $\ddagger$ | $\sum_{i=1}^{N} d_{i}(N-i)$ | | WYPLL $(7,9)$ | Working ( $W$ to $N$ ) years of potential life lost | $\sum_{i=0}^{W-1} d_{i}(N-W)+\sum_{i=W}^{N} d_{i}(N-i)$ | | VYPLL ( 2 ) | Valued years of potential life lost | $\sum_{i=0}^{\infty} d_{i}\left[\sum_{j=i}^{i+L} I(j)\right]$ | | CRUDE (14) | Crude death rate | $\frac{\sum d_{1}}{\sum n_{1}}=\frac{\sum\left(r_{i}\right)\left(n_{1}\right)}{\sum n_{i}}$ | | ADJ (14) | Adjusted death rate | $\frac{\Sigma\left(r_{i}\right)\left(w_{i}\right)}{\Sigma w_{i}}$ | | $\mathrm{CI}_{\mathrm{L}}$ (14) | Lifetime cumulative incidence rate | $1-\exp \left(-\sum_{i=0}^{L} r_{i}\right)$ |
natural causes of death, and premature and preventable causes of death would no longer be distinguishable. . . . Thus, deaths in older age groups are underrepresented by the upper age limit of 65 years. However, this method preserves the emphasis on causes of mortality among younger persons." Another argument for excluding those over age 70 in YPLL calculations has been that diagnosis may be inaccurate in those ages, so deaths are more difficult to attribute to the proper cause and thus ought to be excluded from the calculations ( 8 , 9 ) ( 8 , 9 ) (8,9)(8,9).
自然死亡原因，以及過早和可預防的死亡原因將不再可區分……因此，年齡較大的群體的死亡在 65 歲的上限下被低估。然而，這種方法仍然強調年輕人中的死亡原因。另一個排除 70 歲以上人群在 YPLL 計算中的理由是，這個年齡段的診斷可能不準確，因此更難將死亡歸因於正確的原因，因此應該從計算中排除。
Some of the arguments for using 65 or 70 as a cutoff age relate to time of retirement when job productivity ceases. For example, Perloff et al (9) stated, “We decided to use seventy rather than sixty-five as the cutoff age because our analysis focuses on the loss of productive years, and many people in the sixty-five to sixty-nine age category are still economically active.” The working years of life lost formula implements this argument by decreasing the weights during childhood, where potential productivity is future, not current. Again Perloff et al (9) explained, “We have decided to give the deaths of children this smaller weight because we thought it inconsistent to exclude the deaths of people over seventy because they were no longer economically active and, at the same time, to include in the weights for children the childhood years in which they are not economically active.”
一些使用 65 或 70 作為截止年齡的論點與退休時間有關，當工作生產力停止時。例如，Perloff 等人（9）表示：“我們決定使用七十而不是六十五作為截止年齡，因為我們的分析集中在生產年限的損失上，而許多六十五到六十九歲的人仍然在經濟上活躍。” 失去的工作年限公式通過在童年期間減少權重來實施這一論點，因為潛在的生產力是未來的，而不是當前的。再次，Perloff 等人（9）解釋道：“我們決定給予兒童死亡這個較小的權重，因為我們認為排除七十歲以上不再經濟活躍的人的死亡是不一致的，同時又將他們在經濟上不活躍的童年年限納入兒童的權重中。”
Some authors have chosen to exclude infant deaths, while others have not. Romeder and McWhinnie (8) reasoned that, "each infant death would account for
一些作者選擇排除嬰兒死亡，而另一些則沒有。Romeder 和 McWhinnie (8) 理論認為，「每一例嬰兒死亡都會佔據」
TABLE 2. Age-Specific Weights Used in VYPLL Calculation of Investment-Producer-Consumer Model
表 2. 用於投資-生產者-消費者模型的 VYPLL 計算的年齡特定權重

死亡年齡 (1)
Age at
Death
(1)
Age at Death (1)| Age at | | :--- | | Death | | (1) |

中世紀 (2)
Mid-
Age
(2)
Mid- Age (2)| Mid- | | :--- | | Age | | (2) |

生活 期待 ∘ ∘ ^(@){ }^{\circ} (3)
Life
Expectancy ∘ ∘ ^(@){ }^{\circ}
(3)
Life Expectancy ^(@) (3)| Life | | :--- | | Expectancy ${ }^{\circ}$ | | (3) |
 0-19 20-64 65 + 65 + 65+65+

網絡 投資 † † ^(†){ }^{\dagger} (10)
Net
Investment † † ^(†){ }^{\dagger}
(10)
Net Investment ^(†) (10)| Net | | :--- | | Investment ${ }^{\dagger}$ | | (10) |

潛在損失† (11)
Potential
Loss†
(11)
Potential Loss† (11)| Potential | | :--- | | Loss† | | (11) |
 收到 (4)
Received
(4)
Received (4)| Received | | :--- | | (4) |

未收到 (5)
Didn't
Receive
(5)
Didn't Receive (5)| Didn't | | :--- | | Receive | | (5) |
 生產 (6)
Produced
(6)
Produced (6)| Produced | | :--- | | (6) |

未生產 (7)
Didn't
Produce
(7)
Didn't Produce (7)| Didn't | | :--- | | Produce | | (7) |
 消耗 (8)
Consumed
(8)
Consumed (8)| Consumed | | :--- | | (8) |

未消耗 (9)
Didn't
Consume
(9)
Didn't Consume (9)| Didn't | | :--- | | Consume | | (9) |
0 0.5 75 0.5 19.5 0.0 45.0 0.0 10.5 0.5 15.5
1-4 3.0 73 3.0 17.0 0.0 45.0 0.0 11.0 3.0 20.0
5-14 10.0 66 10.0 10.0 0.0 45.0 0.0 11.0 10.0 34.0
15-24 20.0 56 20.0 0.0 0.0 45.0 0.0 11.0 20.0 54.0
25-34 30.0 47 20.0 0.0 10.0 35.0 0.0 12.0 10.0 33.0
35-44 40.0 37 20.0 0.0 20.0 25.0 0.0 12.0 0.0 13.0
45-54 50.0 29 20.0 0.0 30.0 15.0 0.0 14.0 -10.0 -9.0
55-64 60.0 20 20.0 0.0 40.0 5.0 0.0 15.0 -20.0 -30.0
65-74 70.0 14 20.0 0.0 45.0 0.0 5.0 14.0 -20.0 -34.0
75-84 80.0 8 20.0 0.0 45.0 0.0 15.0 8.0 -10.0 - 18.0
85 + 85 + 85+85+ 88.0 6 20.0 0.0 45.0 0.0 23.0 6.0 -2.0 -8.0
"Age at Death (1)" "Mid- Age (2)" "Life Expectancy ^(@) (3)" 0-19 20-64 65+ "Net Investment ^(†) (10)" "Potential Loss† (11)" "Received (4)" "Didn't Receive (5)" "Produced (6)" "Didn't Produce (7)" "Consumed (8)" "Didn't Consume (9)" 0 0.5 75 0.5 19.5 0.0 45.0 0.0 10.5 0.5 15.5 1-4 3.0 73 3.0 17.0 0.0 45.0 0.0 11.0 3.0 20.0 5-14 10.0 66 10.0 10.0 0.0 45.0 0.0 11.0 10.0 34.0 15-24 20.0 56 20.0 0.0 0.0 45.0 0.0 11.0 20.0 54.0 25-34 30.0 47 20.0 0.0 10.0 35.0 0.0 12.0 10.0 33.0 35-44 40.0 37 20.0 0.0 20.0 25.0 0.0 12.0 0.0 13.0 45-54 50.0 29 20.0 0.0 30.0 15.0 0.0 14.0 -10.0 -9.0 55-64 60.0 20 20.0 0.0 40.0 5.0 0.0 15.0 -20.0 -30.0 65-74 70.0 14 20.0 0.0 45.0 0.0 5.0 14.0 -20.0 -34.0 75-84 80.0 8 20.0 0.0 45.0 0.0 15.0 8.0 -10.0 - 18.0 85+ 88.0 6 20.0 0.0 45.0 0.0 23.0 6.0 -2.0 -8.0| Age at <br> Death <br> (1) | Mid- <br> Age <br> (2) | Life <br> Expectancy ${ }^{\circ}$ <br> (3) | 0-19 | | 20-64 | | $65+$ | | Net <br> Investment ${ }^{\dagger}$ <br> (10) | Potential <br> Loss† <br> (11) | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | | | | Received <br> (4) | Didn't <br> Receive <br> (5) | Produced <br> (6) | Didn't <br> Produce <br> (7) | Consumed <br> (8) | Didn't <br> Consume <br> (9) | | | | 0 | 0.5 | 75 | 0.5 | 19.5 | 0.0 | 45.0 | 0.0 | 10.5 | 0.5 | 15.5 | | 1-4 | 3.0 | 73 | 3.0 | 17.0 | 0.0 | 45.0 | 0.0 | 11.0 | 3.0 | 20.0 | | 5-14 | 10.0 | 66 | 10.0 | 10.0 | 0.0 | 45.0 | 0.0 | 11.0 | 10.0 | 34.0 | | 15-24 | 20.0 | 56 | 20.0 | 0.0 | 0.0 | 45.0 | 0.0 | 11.0 | 20.0 | 54.0 | | 25-34 | 30.0 | 47 | 20.0 | 0.0 | 10.0 | 35.0 | 0.0 | 12.0 | 10.0 | 33.0 | | 35-44 | 40.0 | 37 | 20.0 | 0.0 | 20.0 | 25.0 | 0.0 | 12.0 | 0.0 | 13.0 | | 45-54 | 50.0 | 29 | 20.0 | 0.0 | 30.0 | 15.0 | 0.0 | 14.0 | -10.0 | -9.0 | | 55-64 | 60.0 | 20 | 20.0 | 0.0 | 40.0 | 5.0 | 0.0 | 15.0 | -20.0 | -30.0 | | 65-74 | 70.0 | 14 | 20.0 | 0.0 | 45.0 | 0.0 | 5.0 | 14.0 | -20.0 | -34.0 | | 75-84 | 80.0 | 8 | 20.0 | 0.0 | 45.0 | 0.0 | 15.0 | 8.0 | -10.0 | - 18.0 | | $85+$ | 88.0 | 6 | 20.0 | 0.0 | 45.0 | 0.0 | 23.0 | 6.0 | -2.0 | -8.0 |
  • Life expectancies taken at midpoint age from U.S. 1986 life tables (11).
    根據美國 1986 年生命表（11）在中點年齡所計算的預期壽命。
    † † †\dagger Net investment ( 10 ) = [ ( 10 ) = [ (10)=[(10)=[ received ] + [ ] + [ ]+[]+[ consumed ] − [ ] − [ ]-[]-[ produced] = ( 4 ) + ( 8 ) − ( 6 ) = ( 4 ) + ( 8 ) − ( 6 ) =(4)+(8)-(6)=(4)+(8)-(6).
    † † †\dagger 淨投資 ( 10 ) = [ ( 10 ) = [ (10)=[(10)=[ 收到 ] + [ ] + [ ]+[]+[ 消耗 ] − [ ] − [ ]-[]-[ 生產] = ( 4 ) + ( 8 ) − ( 6 ) = ( 4 ) + ( 8 ) − ( 6 ) =(4)+(8)-(6)=(4)+(8)-(6) .
    Potential loss (11) = [net investment] + [didn’t produce] - [didn’t receive] - [didn’t consume] = ( 10 ) + ( 7 ) − ( 5 ) − ( 9 ) = Σ I ( j ) = ( 10 ) + ( 7 ) − ( 5 ) − ( 9 ) = Σ I ( j ) =(10)+(7)-(5)-(9)=Sigma I(j)=(10)+(7)-(5)-(9)=\Sigma I(j).
    潛在損失 (11) = [淨投資] + [未生產] - [未收到] - [未消耗] = ( 10 ) + ( 7 ) − ( 5 ) − ( 9 ) = Σ I ( j ) = ( 10 ) + ( 7 ) − ( 5 ) − ( 9 ) = Σ I ( j ) =(10)+(7)-(5)-(9)=Sigma I(j)=(10)+(7)-(5)-(9)=\Sigma I(j) 。
    (Note: negative investments and negative losses are gains to society.)
    （注意：負投資和負損失對社會來說是收益。）
    almost 70 years lost giving a weight double that of a death berween ages 30 and 40 . This appears to be an overestimation of the value accepted by society for such a loss in light of the fact that a ‘very early death is often replaced’ by another birth. Therefore, from the point of view of social criteria, infant mortality is less disrupting than mortality of older children and adults." Initially, CDC (3) stated that, “If deaths of persons younger than one year were included, causes of death affecting this age group would be weighted heavily and would therefore contribute a disproportionately large share of potential years of life lost.” But, as mentioned above, in 1986 CDC (10) changed its method from PYPLL* to PYPLL, which includes infant deaths. Perloff et al (9) stated, “We did not want to exclude deaths under the age of one because infant mortality results in a considerable number of lost years of life, and because we felt it illogical to exclude infant deaths from a discussion of premature deaths.” No one has yet included lost productivity from stillbirths, miscarriages, or abortions in any YPLL computations.
    幾乎 70 年的損失，造成 30 至 40 歲之間死亡的體重是其兩倍。這似乎是對社會對此類損失所接受的價值的高估，因為“非常早逝的生命常常被另一個出生所取代”。因此，從社會標準的角度來看，嬰兒死亡率對社會的影響比年長兒童和成人的死亡率小。最初，CDC（3）表示：“如果將一歲以下的死亡納入考量，影響這個年齡組的死亡原因將會被重視，因此將對潛在生命損失年數的貢獻過於龐大。”但如上所述，1986 年 CDC（10）將其方法從 PYPLL*改為 PYPLL，這包括了嬰兒死亡。Perloff 等（9）表示：“我們不想排除一歲以下的死亡，因為嬰兒死亡導致了相當多的生命年損失，並且我們認為在討論過早死亡時排除嬰兒死亡是不合邏輯的。”至今尚無人將死產、流產或墮胎造成的生產力損失納入任何 YPLL 計算中。
The historical example that addresses lost economic productivity most fully is that of Stickle (2), where he calculated “future income sacrificed.” Although his methods are not described in detail in his paper, it is clear that he utilized a formula similar to that given in Table 1 for VYPLL. His values for the function I ( j ) I ( j ) I(j)I(j) were determined from a survey of personal monetary income by age and sex. Perhaps the following model will be useful as an example that directly addresses the value function.
針對失去的經濟生產力，最完整的歷史例子是 Stickle (2)，他計算了“未來收入的犧牲”。雖然他的論文中沒有詳細描述其方法，但顯然他使用了一個類似於表 1 中 VYPLL 的公式。他對函數 I ( j ) I ( j ) I(j)I(j) 的值是根據年齡和性別的個人貨幣收入調查得出的。也許以下模型將作為一個直接針對價值函數的例子而有用。
INVESTMENT-PRODUCER-CONSUMER (IPC) MODEL
投資-生產者-消費者 (IPC) 模型
Consider dividing the lifetime of each individual into three segments: Investment years (ages 0 − 19 0 − 19 0-190-19 ), Producer years (ages 20-64), and Consumer years (ages 65 + 65 + 65+65+ ). For simplicity, consider the value for each year to be equal. During the investment and consumer years, the individual is receiving from society (negative value), while during the producer years the individual is giving to society (positive value). We then calculate the VYPLL weights for each age as shown in Table 2, which illustrates this model using 1986 U.S. life expectancies (11). The net investment made by society is the amount received by the individual during years 0 − 19 0 − 19 0-190-19 and 65 + 65 + 65+65+, less the amount produced during age 20 − 64 20 − 64 20-6420-64. The total potential loss to society is the net investment at death plus the amount that would have been produced, less the additional amount that would have been consumed, up to life expectancy. If an individual lives to the average life expectancy of 75 , the net contribution to society is − 20 + 45 − 10 = + 15 − 20 + 45 − 10 = + 15 -20+45-10=+15-20+45-10=+15 years. An infant who dies at birth, then, results in a net loss of 15 years, while an individual dying at age 20 results in a net loss of 54 years ( + 20 + 45 − 11 = 54 ) ( + 20 + 45 − 11 = 54 ) (+20+45-11=54)(+20+45-11=54), and at age 50 a net gain of 9 years ( + 20 − 30 + 15 − 14 = − 9 ) ( + 20 − 30 + 15 − 14 = − 9 ) (+20-30+15-14=-9)(+20-30+15-14=-9), while dying at age 65 gives a net gain of 42 years ( + 20 − 45 − 17 = ( + 20 − 45 − 17 = (+20-45-17=(+20-45-17= -42 ), and at 80 a net gain of 18 years ( + 20 − 45 + 15 + 20 − 45 + 15 +20-45+15+20-45+15 − 8 = − 18 − 8 = − 18 -8=-18-8=-18 ). As can be seen from these calculations, the worst case of social and economic loss is death at age 20 (after full investment, but before any productivity) and best at age 65 (after maximum productivity, but before entering consumerism stage). Although this is an
考慮將每個個體的生命週期分為三個階段：投資年（年齡 0 − 19 0 − 19 0-190-19 ）、生產年（年齡 20-64）、消費年（年齡 65 + 65 + 65+65+ ）。為了簡化，假設每年的價值相等。在投資年和消費年期間，個體從社會中獲得（負價值），而在生產年期間，個體則向社會貢獻（正價值）。然後，我們計算每個年齡的 VYPLL 權重，如表 2 所示，該表使用 1986 年美國的預期壽命（11）來說明這一模型。社會所做的淨投資是個體在 0 − 19 0 − 19 0-190-19 年和 65 + 65 + 65+65+ 年期間獲得的金額，減去在 20 − 64 20 − 64 20-6420-64 年期間所產生的金額。對社會的總潛在損失是死亡時的淨投資加上本來會產生的金額，減去到預期壽命為止本來會消耗的額外金額。如果一個人活到平均壽命 75 歲，對社會的淨貢獻為 − 20 + 45 − 10 = + 15 − 20 + 45 − 10 = + 15 -20+45-10=+15-20+45-10=+15 年。 一名在出生時死亡的嬰兒，最終造成 15 年的淨損失，而一名 20 歲去世的個體則造成 54 年的淨損失 ( + 20 + 45 − 11 = 54 ) ( + 20 + 45 − 11 = 54 ) (+20+45-11=54)(+20+45-11=54) ，50 歲去世則有 9 年的淨增益 ( + 20 − 30 + 15 − 14 = − 9 ) ( + 20 − 30 + 15 − 14 = − 9 ) (+20-30+15-14=-9)(+20-30+15-14=-9) ，65 歲去世則有 42 年的淨增益 ( + 20 − 45 − 17 = ( + 20 − 45 − 17 = (+20-45-17=(+20-45-17= ，而 80 歲去世則有 18 年的淨增益 + 20 − 45 + 15 + 20 − 45 + 15 +20-45+15+20-45+15 − 8 = − 18 − 8 = − 18 -8=-18-8=-18 。從這些計算中可以看出，社會和經濟損失最嚴重的情況是 20 歲去世（在完全投資後，但在任何生產力之前），而最佳情況是 65 歲去世（在最大生產力後，但在進入消費階段之前）。雖然這是一個
TABLE 3. Total YPLL for 12 Causes of Death* in the U.S. in 1986, Using the YPLL Formulas from Table 1 and 1986 Life Expectancies
表 3. 1986 年美國 12 種死亡原因的總失去潛在壽命年數*，使用表 1 中的失去潛在壽命年數公式和 1986 年預期壽命
Method 方法 Heart 心臟 Cancer 癌症 CVD Accidents 事故 COPD
YPLL 9,295,896 7,391,289 1,640,579 3,451,137 967,090
PYPLL(85) 8,387,691 7 , 840 , 850 7 , 840 , 850 7,840,8507,840,850 1,337,160 3,939,854 928,078
PYPLL(75) 3,923,651 4 , 178 , 200 4 , 178 , 200 4,178,2004,178,200 590,600 3,106,919 396,878
PYPLL(65) 1,558,251 1 , 832 , 725 1 , 832 , 725 1,832,7251,832,725 246,170 2,364,644 128,548
PYPLL・(65) 1,494,912 1,826,468 239,139 2,306,013 124,678
PYPLL (70) 2,220,772 2,631,713 339,699 2,651,358 193,878
WYPLL (15-65) 1,538,070 1,818,665 243,780 2,295,125 126,740
WYPLL(15-70) 2,268,840 2,624,395 344,885 2,645,015 196,240
CRUDE 765,490 469,376 149,643 95,277 76,559
Cl(75) † † †\dagger 15.34 % 15.34 % 15.34%15.34 \% 14.15% 2.45 % 2.45 % 2.45%2.45 \% 2.56% 2.07%
Cl(55) † † †\dagger 1.96% 2.32% 0.31% 1.74% 0.13%
VYPLL(IPC) − 14 , 792 , 439 − 14 , 792 , 439 -14,792,439-14,792,439 − 10 , 206 , 502 − 10 , 206 , 502 -10,206,502-10,206,502 − 2 , 608 , 096 − 2 , 608 , 096 -2,608,096-2,608,096 1,173,576 − 1 , 744 , 728 − 1 , 744 , 728 -1,744,728-1,744,728
Method Heart Cancer CVD Accidents COPD YPLL 9,295,896 7,391,289 1,640,579 3,451,137 967,090 PYPLL(85) 8,387,691 7,840,850 1,337,160 3,939,854 928,078 PYPLL(75) 3,923,651 4,178,200 590,600 3,106,919 396,878 PYPLL(65) 1,558,251 1,832,725 246,170 2,364,644 128,548 PYPLL・(65) 1,494,912 1,826,468 239,139 2,306,013 124,678 PYPLL (70) 2,220,772 2,631,713 339,699 2,651,358 193,878 WYPLL (15-65) 1,538,070 1,818,665 243,780 2,295,125 126,740 WYPLL(15-70) 2,268,840 2,624,395 344,885 2,645,015 196,240 CRUDE 765,490 469,376 149,643 95,277 76,559 Cl(75) † 15.34% 14.15% 2.45% 2.56% 2.07% Cl(55) † 1.96% 2.32% 0.31% 1.74% 0.13% VYPLL(IPC) -14,792,439 -10,206,502 -2,608,096 1,173,576 -1,744,728| Method | Heart | Cancer | CVD | Accidents | COPD | | :---: | :---: | :---: | :---: | :---: | :---: | | YPLL | 9,295,896 | 7,391,289 | 1,640,579 | 3,451,137 | 967,090 | | PYPLL(85) | 8,387,691 | $7,840,850$ | 1,337,160 | 3,939,854 | 928,078 | | PYPLL(75) | 3,923,651 | $4,178,200$ | 590,600 | 3,106,919 | 396,878 | | PYPLL(65) | 1,558,251 | $1,832,725$ | 246,170 | 2,364,644 | 128,548 | | PYPLL・(65) | 1,494,912 | 1,826,468 | 239,139 | 2,306,013 | 124,678 | | PYPLL (70) | 2,220,772 | 2,631,713 | 339,699 | 2,651,358 | 193,878 | | WYPLL (15-65) | 1,538,070 | 1,818,665 | 243,780 | 2,295,125 | 126,740 | | WYPLL(15-70) | 2,268,840 | 2,624,395 | 344,885 | 2,645,015 | 196,240 | | CRUDE | 765,490 | 469,376 | 149,643 | 95,277 | 76,559 | | Cl(75) $\dagger$ | $15.34 \%$ | 14.15% | $2.45 \%$ | 2.56% | 2.07% | | Cl(55) $\dagger$ | 1.96% | 2.32% | 0.31% | 1.74% | 0.13% | | VYPLL(IPC) | $-14,792,439$ | $-10,206,502$ | $-2,608,096$ | 1,173,576 | $-1,744,728$ |
⋅ ⋅ *\cdot Disease groupings correspond to those used by MMWR (10) and/or NCHS (12), as follows (ICD-9 codes): Diseases of the Heart (390-398, 402, 404-429), Malignant Neoplasms, including neoplasms of lymphatic and hematopoietic tissues (Cancer) (140-208), Cerebrovascular Diseases (CVD) (430-438), Accidents & Adverse Effects (E800-E949), Chronic Obstructive Pulmonary Diseases and Allied Conditions (COPD) (490496), Pneumonia and Influenza (P/I) (480-487), Suicide/Homicide and Legal Intervention (S/Hom.) (E950-E978), Diabetes Mellitus (250), Chronic Liver Disease and Cirrhosis (571), Certain Conditions Originating in the Perinatal Period (760-779), Congenital Anomalies (740-759), Sudden Infant Death Syndrome (SIDS) (798.0).
疾病分組對應於 MMWR (10) 和/或 NCHS (12) 使用的分組，如下所示（ICD-9 代碼）：心臟疾病 (390-398, 402, 404-429)、惡性腫瘤，包括淋巴和造血組織的腫瘤（癌症）(140-208)、腦血管疾病 (CVD) (430-438)、意外事故與不良影響 (E800-E949)、慢性阻塞性肺病及相關疾病 (COPD) (490-496)、肺炎和流感 (P/I) (480-487)、自殺/謀殺及法律介入 (S/Hom.) (E950-E978)、糖尿病 (250)、慢性肝病及肝硬化 (571)、某些起源於圍產期的疾病 (760-779)、先天性畸形 (740-759)、嬰兒猝死症候群 (SIDS) (798.0)。
† † †\dagger Cumulative incidence calculations [ ( Cl = 1 − exp ⁡ ( − Σ 1 ) ] Cl = 1 − exp ⁡ − Σ 1 [(Cl=1-exp(-Sigma_(1))]:}\left[\left(\mathrm{Cl}=1-\exp \left(-\Sigma_{1}\right)\right]\right. represent the average risk of death due to the specific cause from birth to age 55 or 75 , respectively, assuming no deaths from other causes.
† † †\dagger 累積發生率計算 [ ( Cl = 1 − exp ⁡ ( − Σ 1 ) ] Cl = 1 − exp ⁡ − Σ 1 [(Cl=1-exp(-Sigma_(1))]:}\left[\left(\mathrm{Cl}=1-\exp \left(-\Sigma_{1}\right)\right]\right. 代表從出生到 55 歲或 75 歲因特定原因死亡的平均風險，假設沒有其他原因的死亡。
artificial example, with a value scale chosen somewhat arbitrarily, it illustrates a process of defining social and economic loss in a way that can incorporate investment and consumerism concepts.
人為範例，選擇了一個稍微隨意的價值尺度，展示了一個定義社會和經濟損失的過程，這個過程可以納入投資和消費主義的概念。

Illustration of DifFerences Between Calculation Methods
計算方法之間差異的插圖

The weights for each age group using various YPLL measures can be derived using the formulas in Table 1 and life expectancies from the desired population. Table 3 uses these weights to calculate the total YPLL by each method for twelve causes of death in the United States using 1986 life table and final mortality data ( 11 , 12 ) ( 11 , 12 ) (11,12)(11,12). Table 4 ranks the top ten causes of death by each method.
每個年齡組的權重可以使用表 1 中的公式和所需人口的預期壽命來推導。表 3 使用這些權重計算 1986 年生命表和最終死亡數據下，美國十二種死亡原因的總 YPLL。表 4 則根據每種方法對十大死亡原因進行排名。
We see in Tables 3 and 4 that the relative ranking of causes of death is changed when one uses a different YPLL method. Comparing the number of crude deaths (which emphasizes deaths in the elderly) with the PYPLL(65) method used by CDC (which emphasizes deaths in the young), one sees the leading cause of death change from heart disease to accidents. In fact, one can choose between heart disease, cancer, or accidents as the leading cause of death, depending on which method one chooses for calculation. Looking at the VYPPL (Investment-Producer-Consumer) model, one sees that heart disease and cancer drop from the list entirely, as do five of the other causes of death that also have negative VYPLL (ie, net gain, rather than loss). We are left then, in this model, with the main causes of death in the young working ages (accidents and suicide/homicide) and the early deaths (perinatal, congenital anomalies, and sudden infant death syndrome). With this model those diseases largely attributable to aging drop from the top rankings because of the negative weights in the older age groups.
我們在表 3 和表 4 中看到，當使用不同的 YPLL 方法時，死亡原因的相對排名會發生變化。比較粗死亡人數（強調老年人的死亡）與 CDC 使用的 PYPLL(65)方法（強調年輕人的死亡），可以看到主要死亡原因從心臟病變為意外事故。事實上，根據所選擇的計算方法，可以在心臟病、癌症或意外事故之間選擇作為主要死亡原因。查看 VYPPL（投資-生產者-消費者）模型，可以看到心臟病和癌症完全從名單中消失，其他五種也有負 VYPLL（即淨增益，而非損失）的死亡原因也同樣消失。因此，在這個模型中，我們剩下的主要死亡原因是年輕工作年齡的意外事故和自殺/他殺，以及早期死亡（圍產期、先天性畸形和嬰兒猝死症候群）。在這個模型中，主要歸因於老化的疾病因為在老年組的負權重而從排名中下降。
Using the U.S. 1986 final mortality statistics from NCHS (12), we calculated VYPLL using the Investment-Producer-Consumer model for each of the 72 cause-of-death categories that had more than 1000 deaths. Of these, only nine produced positive VYPLL values; they are given in Table 5. This analysis illustrates that external causes of death, rather than deaths from disease, have by far the largest impact by this measure ( 79 % 79 % 79%79 \% of the positive VYPLLs), followed by causes of death in infancy and early childhood. The remaining causes of death (including subcategories of cancer, heart disease, etc) all have negative VYPLL, indicating no net productivity loss.
使用美國 1986 年 NCHS 的最終死亡統計數據，我們針對 72 個死亡原因類別（死亡人數超過 1000）的每一類別，使用投資-生產者-消費者模型計算了 VYPLL。在這些類別中，只有九個產生了正的 VYPLL 值；這些數據列在表 5 中。這項分析顯示，外部死亡原因對這一指標的影響遠大於疾病造成的死亡（正 VYPLL 的 79 % 79 % 79%79 \% ），其次是嬰兒和幼兒的死亡原因。其餘的死亡原因（包括癌症、心臟病等的子類別）均有負的 VYPLL，表明沒有淨生產力損失。

Discussion 討論

YPLL is generally used to emphasize deaths at younger ages, which is an important consideration when one notes that 71 % 71 % 71%71 \% of deaths in the United States in 1986 occurred at age 65 or greater. From the formulas in Ta ble 1, we see that the younger ages always receive the highest weights for YPLL, PYPLL, PYPLL ∙ ∙ ^(∙){ }^{\bullet}, and WYPLL. If the objective is simply to emphasize deaths at younger ages, however, then the more straightforward approach is to present the specific mortality rates for those ages rather than use a YPLL measure.
YPLL 通常用來強調年輕年齡的死亡，這是一個重要的考量，因為在注意到 1986 年美國的死亡中有 71 % 71 % 71%71 \% 是在 65 歲或更大年齡時。從表 1 的公式中，我們可以看到年輕年齡總是對 YPLL、PYPLL、PYPLL ∙ ∙ ^(∙){ }^{\bullet} 和 WYPLL 具有最高的權重。然而，如果目標僅僅是強調年輕年齡的死亡，那麼更直接的方法是呈現這些年齡的具體死亡率，而不是使用 YPLL 指標。
YPLL is not an inferential statistic; it is an impact
YPLL 不是一種推論統計；它是一種影響
P/I S/Hom. Diabetes 糖尿病 Liver 肝臟 Perinatal 圍產期 Anom. 異常。 SIDS
787,710 1 , 998 , 984 1 , 998 , 984 1,998,9841,998,984 529,499 574,094 1 , 378 , 232 1 , 378 , 232 1,378,2321,378,232 802,517 395,850
617,672 2 , 336 , 330 2 , 336 , 330 2,336,3302,336,330 528,887 668,035 1 , 552 , 806 1 , 552 , 806 1,552,8061,552,806 906,196 445,991
316,507 1 , 831 , 560 1 , 831 , 560 1,831,5601,831,560 271,737 426,555 1 , 368 , 921 1 , 368 , 921 1,368,9211,368,921 783,291 393,211
176,087 1 , 361 , 150 1 , 361 , 150 1,361,1501,361,150 121,172 231,600 1 , 185 , 046 1 , 185 , 046 1,185,0461,185,046 664,606 340,431
133,323 1 , 343 , 219 1 , 343 , 219 1,343,2191,343,219 121,043 230,310 9,469 132,868 0
174,833 1 , 566 , 604 1 , 566 , 604 1,566,6041,566,604 170,643 311,550 10,274 149,793 0
163,350 1 , 349 , 365 1 , 349 , 365 1,349,3651,349,365 120,910 231,170 919,120 532,255 263,900
23,175 1 , 574 , 140 1 , 574 , 140 1,574,1401,574,140 170,520 312,510 1 , 011 , 055 1 , 011 , 055 1,011,0551,011,055 590,400 290,290
69,812 52,635 37,184 26,159 18,391 12,638 5,278
0.92 % 0.92 % 0.92%0.92 \% 1.59 % 1.59 % 1.59%1.59 \% 1.00 % 1.00 % 1.00%1.00 \% 1.02 % 1.02 % 1.02%1.02 \% 0.49 % 0.49 % 0.49%0.49 \% 0.35 % 0.35 % 0.35%0.35 \% 0.14 % 0.14 % 0.14%0.14 \%
0.16 % 0.16 % 0.16%0.16 \% 1.13 % 1.13 % 1.13%1.13 \% 0.15 % 0.15 % 0.15%0.15 \% 0.33 % 0.33 % 0.33%0.33 \% 0.49 % 0.49 % 0.49%0.49 \% 0.30 % 0.30 % 0.30%0.30 \% 0.14 % 0.14 % 0.14%0.14 \%
− 1 , 035 , 036 − 1 , 035 , 036 -1,035,036-1,035,036 775,715 − 743 , 539 − 743 , 539 -743,539-743,539 − 447 , 150 − 447 , 150 -447,150-447,150 286,075 166,096 81,809
P/I S/Hom. Diabetes Liver Perinatal Anom. SIDS 787,710 1,998,984 529,499 574,094 1,378,232 802,517 395,850 617,672 2,336,330 528,887 668,035 1,552,806 906,196 445,991 316,507 1,831,560 271,737 426,555 1,368,921 783,291 393,211 176,087 1,361,150 121,172 231,600 1,185,046 664,606 340,431 133,323 1,343,219 121,043 230,310 9,469 132,868 0 174,833 1,566,604 170,643 311,550 10,274 149,793 0 163,350 1,349,365 120,910 231,170 919,120 532,255 263,900 23,175 1,574,140 170,520 312,510 1,011,055 590,400 290,290 69,812 52,635 37,184 26,159 18,391 12,638 5,278 0.92% 1.59% 1.00% 1.02% 0.49% 0.35% 0.14% 0.16% 1.13% 0.15% 0.33% 0.49% 0.30% 0.14% -1,035,036 775,715 -743,539 -447,150 286,075 166,096 81,809| P/I | S/Hom. | Diabetes | Liver | Perinatal | Anom. | SIDS | | :---: | :---: | :---: | :---: | :---: | :---: | ---: | | 787,710 | $1,998,984$ | 529,499 | 574,094 | $1,378,232$ | 802,517 | 395,850 | | 617,672 | $2,336,330$ | 528,887 | 668,035 | $1,552,806$ | 906,196 | 445,991 | | 316,507 | $1,831,560$ | 271,737 | 426,555 | $1,368,921$ | 783,291 | 393,211 | | 176,087 | $1,361,150$ | 121,172 | 231,600 | $1,185,046$ | 664,606 | 340,431 | | 133,323 | $1,343,219$ | 121,043 | 230,310 | 9,469 | 132,868 | 0 | | 174,833 | $1,566,604$ | 170,643 | 311,550 | 10,274 | 149,793 | 0 | | 163,350 | $1,349,365$ | 120,910 | 231,170 | 919,120 | 532,255 | 263,900 | | 23,175 | $1,574,140$ | 170,520 | 312,510 | $1,011,055$ | 590,400 | 290,290 | | 69,812 | 52,635 | 37,184 | 26,159 | 18,391 | 12,638 | 5,278 | | $0.92 \%$ | $1.59 \%$ | $1.00 \%$ | $1.02 \%$ | $0.49 \%$ | $0.35 \%$ | $0.14 \%$ | | $0.16 \%$ | $1.13 \%$ | $0.15 \%$ | $0.33 \%$ | $0.49 \%$ | $0.30 \%$ | $0.14 \%$ | | $-1,035,036$ | 775,715 | $-743,539$ | $-447,150$ | 286,075 | 166,096 | 81,809 |
measure quantifying the burden of social and economic loss from premature mortality within a given population. Some inappropriate uses of YPLL include descriptive and analytic analysis of specific causes of death. For example, an analysis using YPLL of subgroups of congenital anomalies is inappropriate since most of those subgroups have the same ages at death and thus the differences in YPLL reflect primarily differences in the numbers of deaths (13). Another inappropriate use of YPLL is in etiologic assessment, where death risk (or rate, r i r i r_(i)r_{i} ) is the variable of interest, not an impact measure like YPLL. YPLL should never be used as a substitute for careful examination of the age-specific rates to determine time-trends and other variability that might reflect etiologic characteristics.
衡量特定人群中因過早死亡所造成的社會和經濟損失的負擔。一些不當使用 YPLL 的情況包括對特定死亡原因的描述性和分析性分析。例如，對先天性畸形亞組使用 YPLL 進行分析是不恰當的，因為這些亞組的大多數死亡年齡相同，因此 YPLL 的差異主要反映的是死亡人數的差異（13）。另一個不當使用 YPLL 的情況是在病因評估中，死亡風險（或比率， r i r i r_(i)r_{i} ）是關注的變量，而不是像 YPLL 這樣的影響指標。YPLL 絕不應該用作仔細檢查年齡特定比率的替代品，以確定時間趨勢和其他可能反映病因特徵的變異性。
YPLL inherently incorporates values attached to each age at death. The quantification of the value of life in each age range is difficult, since it involves synthesizing widely differing value systems and quantifying inherently qualitative issues. There are good arguments for emphasizing each age group. For example, infants and children should be emphasized because of their innocence, dependence, and future potential; young adults should be emphasized because they are in the workforce, are often parents of young children, and have been trained for lifelong productivity; older adults should be emphasized because they have valuable work experience, are often breadwinners for large families, and continue in the workforce; seniors should be emphasized because of their valuable wisdom from long life experience, and retirees should be emphasized as a reward for lifelong productivity.
YPLL 本質上包含了與每個死亡年齡相關的價值。對於每個年齡範圍的生命價值進行量化是困難的，因為這涉及到合成截然不同的價值體系並量化本質上質性的問題。強調每個年齡組別都有其合理的論據。例如，應該強調嬰兒和兒童，因為他們的無辜、依賴性和未來潛力；年輕成年人應該受到重視，因為他們在勞動力市場中，通常是年幼孩子的父母，並且已經接受了終身生產力的培訓；老年人應該受到重視，因為他們擁有寶貴的工作經驗，通常是大家庭的經濟支柱，並且仍然在勞動力市場中；老年人應該受到重視，因為他們擁有來自長期生活經驗的寶貴智慧，而退休者則應該受到重視，作為對終身生產力的獎勵。
The important point here is that utilization of any YPLL method (including crude or adjusted death rates) inherently weights the age-specific deaths. By using these summary measures, one is placing values on the different ages at death. In practice, it seems that authors are often unaware of what value scale is being used, or even that a value scale is inherent in their calculations. The method used to calculate YPLL determines both the total number of years of potential life lost and the relative rankings for each cause of premature death.
這裡的重要點是，使用任何 YPLL 方法（包括粗略或調整後的死亡率）本質上會對年齡特定的死亡進行加權。通過使用這些摘要指標，人們對不同的死亡年齡賦予了價值。在實踐中，作者似乎經常不知道使用了什麼價值尺度，甚至不知道他們的計算中固有的價值尺度。計算 YPLL 的方法決定了潛在生命損失的總年數以及每種過早死亡原因的相對排名。
Romeder and McWhinnie (8) state that “the concept of potential years of life lost . . . originated with the primary objective of comparing the relative importance of different causes of death for a particular population.” If one can manipulate the leading causes of premature death so easily by changing the method of YPLL calculation, then of what use is it in helping to set health priorities? In using a summary measure of deaths to rank different causes, one must first address the value scale for age at death, then implement a weighting method that utilizes those values.
Romeder 和 McWhinnie (8) 指出「潛在生命損失年數的概念……最初的目的是比較特定人群中不同死亡原因的相對重要性。」如果通過改變 YPLL 計算方法可以如此輕易地操控過早死亡的主要原因，那麼這對於幫助設定健康優先事項有何用處？在使用死亡的綜合指標來排名不同原因時，必須首先處理死亡年齡的價值尺度，然後實施一種利用這些價值的加權方法。

Value Scale: EQUality Versus lost Productivity
價值尺度：平等與失去的生產力

Owing to the scarcity of health care resources and the need to ensure maximal societal benefit from their use, health planners assign priorities for the allocation of resources to those causes of death that they believe have the largest impact on society. Mooney and McGuire (1) identified four criteria commonly used in determining allocation of resources: equality, future contribution, past contribution, and individual need. The crude number of deaths, used most often to rank the leading causes of death, treats each death equally. This index emphasizes causes of death in the elderly because that is where most deaths occur. A second method of equality is to count each year of age equally, since each individual passes through each year of age once. This measure is the cumulative incidence of death (14) from birth to life expectancy ( L 0 L 0 L_(0)L_{0} ), which estimates each individual’s average lifetime risk of dying from a specific cause. Cumulative incidence provides more “equality” than does crude deaths because it addresses each individual’s average lifetime risk, rather than the current age-mixture of deaths in the population.
由於醫療資源的稀缺以及確保其使用能帶來最大的社會效益的需要，健康規劃者為資源的分配設定優先順序，將其分配給他們認為對社會影響最大的死亡原因。Mooney 和 McGuire (1) 確定了四個常用於資源分配的標準：平等、未來貢獻、過去貢獻和個人需求。最常用來排名主要死亡原因的粗死亡數字，對每一個死亡事件一視同仁。這一指標強調老年人的死亡原因，因為大多數死亡發生在這個年齡段。第二種平等的方法是將每一歲的年齡視為相等，因為每個人都只經歷每一歲一次。這一衡量標準是從出生到預期壽命的死亡累積發生率 (14)，它估算了每個人因特定原因死亡的平均終生風險。與粗死亡數相比，累積發生率提供了更多的“平等”，因為它考慮了每個人的平均終生風險，而不是當前人口中死亡的年齡組合。
TABLE 4. Top Ten Ranking of 12 Causes of Death ∗ ∗ ^(**){ }^{*} Using the Various YPLL Methods
表 4. 12 種死亡原因的前十名排名 ∗ ∗ ^(**){ }^{*} 使用各種 YPLL 方法
RANK YPLL PYPLL(85) PYPLL(75) PYPLL(65) PYPLL*(65) PYPLL* (70)
1 Heart 心臟 Heart 心臟 Cancer 癌症 Accidents 事故 Accidents 事故 Accidents 事故
3 Cancer 癌症 Cancer 癌症 Heart 心臟 Cancer 癌症 Cancer 癌症 Cancer 癌症
3 Accidents 事故 Accidents 事故 Accidents 事故 Heart 心臟 Heart 心臟 Heart 心臟
4 S/hom. S/hom. S/hom. Shom. S/hom. S/hom.
5 CVD Perinatal 圍產期 Perinatal 圍產期 Perinatal 圍產期 CVD CVD
6 Perinatal 圍產期 CVD Anom. 異常。 Anom. 異常。 Liver 肝臟 Liver 肝臟
7 COPD COPD CVD SIDS P / I P / I P//I\mathrm{P} / \mathrm{I} COPD
8 Anom. 異常。 Anom. 異常。 Liver 肝臟 CVD Anom. 異常。
9 P/I Liver 肝臟 COPD Liver 肝臟 COPD Diabetes 糖尿病
10 Liver 肝臟 P/I SIDS P/I Diabetes 糖尿病 Anom. 異常。
RANK WPYLL(15-65) WPYLL(15-70) CRUDE Cl (to 75) Cl (至 75) Cl (to 55) Cl (至 55) VYPLL(IPC)
1 Accidents 事故 Accidents 事故 Heart 心臟 Heart 心臟 Cancer 癌症 Accidents 事故
2 Cancer 癌症 Cancer 癌症 Cancer 癌症 Cancer 癌症 Heart 心臟 S/hom.
3 Heart 心臟 Heart 心臟 CVD Accidents 事故 Accidents 事故 Perinatal 圍產期
4 S/hom. S/hom. Accidents 事故 CVD S/hom. Anom. 異常。
5 Perinatal 圍產期 Perinatal 圍產期 COPD COPD Perinatal 圍產期 SIDS
6 Anom. 異常。 Anom. 異常。 P/I S/hom. Liver 肝臟
7 SIDS CVD S/hom. Liver 肝臟 CVD
8 CVD Liver 肝臟 Diabetes 糖尿病 Diabetes 糖尿病 Anom. 異常。
9 Liver 肝臟 SIDS Liver 肝臟 P/I P/I
10 P/I P/I Perinatal 圍產期 Perinatal 圍產期 Diabetes 糖尿病
RANK YPLL PYPLL(85) PYPLL(75) PYPLL(65) PYPLL*(65) PYPLL* (70) 1 Heart Heart Cancer Accidents Accidents Accidents 3 Cancer Cancer Heart Cancer Cancer Cancer 3 Accidents Accidents Accidents Heart Heart Heart 4 S/hom. S/hom. S/hom. Shom. S/hom. S/hom. 5 CVD Perinatal Perinatal Perinatal CVD CVD 6 Perinatal CVD Anom. Anom. Liver Liver 7 COPD COPD CVD SIDS P//I COPD 8 Anom. Anom. Liver CVD Anom. 9 P/I Liver COPD Liver COPD Diabetes 10 Liver P/I SIDS P/I Diabetes Anom. RANK WPYLL(15-65) WPYLL(15-70) CRUDE Cl (to 75) Cl (to 55) VYPLL(IPC) 1 Accidents Accidents Heart Heart Cancer Accidents 2 Cancer Cancer Cancer Cancer Heart S/hom. 3 Heart Heart CVD Accidents Accidents Perinatal 4 S/hom. S/hom. Accidents CVD S/hom. Anom. 5 Perinatal Perinatal COPD COPD Perinatal SIDS 6 Anom. Anom. P/I S/hom. Liver 7 SIDS CVD S/hom. Liver CVD 8 CVD Liver Diabetes Diabetes Anom. 9 Liver SIDS Liver P/I P/I 10 P/I P/I Perinatal Perinatal Diabetes | RANK | YPLL | PYPLL(85) | PYPLL(75) | PYPLL(65) | PYPLL*(65) | PYPLL* (70) | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | 1 | Heart | Heart | Cancer | Accidents | Accidents | Accidents | | 3 | Cancer | Cancer | Heart | Cancer | Cancer | Cancer | | 3 | Accidents | Accidents | Accidents | Heart | Heart | Heart | | 4 | S/hom. | S/hom. | S/hom. | Shom. | S/hom. | S/hom. | | 5 | CVD | Perinatal | Perinatal | Perinatal | CVD | CVD | | 6 | Perinatal | CVD | Anom. | Anom. | Liver | Liver | | 7 | COPD | COPD | CVD | SIDS | $\mathrm{P} / \mathrm{I}$ | COPD | | 8 | Anom. | Anom. | Liver | CVD | Anom. | | | 9 | P/I | Liver | COPD | Liver | COPD | Diabetes | | 10 | Liver | P/I | SIDS | P/I | Diabetes | Anom. | | RANK | WPYLL(15-65) | WPYLL(15-70) | CRUDE | Cl (to 75) | Cl (to 55) | VYPLL(IPC) | | 1 | Accidents | Accidents | Heart | Heart | Cancer | Accidents | | 2 | Cancer | Cancer | Cancer | Cancer | Heart | S/hom. | | 3 | Heart | Heart | CVD | Accidents | Accidents | Perinatal | | 4 | S/hom. | S/hom. | Accidents | CVD | S/hom. | Anom. | | 5 | Perinatal | Perinatal | COPD | COPD | Perinatal | SIDS | | 6 | Anom. | Anom. | P/I | S/hom. | Liver | | | 7 | SIDS | CVD | S/hom. | Liver | CVD | | | 8 | CVD | Liver | Diabetes | Diabetes | Anom. | | | 9 | Liver | SIDS | Liver | P/I | P/I | | | 10 | P/I | P/I | Perinatal | Perinatal | Diabetes | |
  • Disease groupings correspond to those given in Table 3.
    疾病分組與表 3 中所列的相符。
TABLE 5. Ranking of Causes of Death* with Positive VYPLL, Using Investment-Producer-Consumer Model
表 5. 使用投資-生產者-消費者模型的正向 VYPLL 死亡原因排名*
Rank 排名 Cause of Death 死亡原因 ICD Codes ICD 代碼 VYPLL
1 Motor vehicle accidents 機動車輛事故 E810-E825 1,048,643
2 Homicide/legal intervention
謀殺/法律介入		 E960-E978 512,811
3 Suicide 自殺 E950-E959 262,904
4 Other conditions-perinatal
其他情況-圍產期		 760-766, 770-779 212,972
5 Congenital anomalies 先天性畸形 740-759 166,096
6 Other accidents/adverse effects
其他意外/不良反應		 E800-E807, E826-E949 124,933
7 Sudden infant death syndrome
嬰兒猝死症候群		 798.0 81,809
8 Birth-relared conditions 出生相關情況 767-769 73,103
9 Other external causes 其他外部原因 E980-E999 44,497
Rank Cause of Death ICD Codes VYPLL 1 Motor vehicle accidents E810-E825 1,048,643 2 Homicide/legal intervention E960-E978 512,811 3 Suicide E950-E959 262,904 4 Other conditions-perinatal 760-766, 770-779 212,972 5 Congenital anomalies 740-759 166,096 6 Other accidents/adverse effects E800-E807, E826-E949 124,933 7 Sudden infant death syndrome 798.0 81,809 8 Birth-relared conditions 767-769 73,103 9 Other external causes E980-E999 44,497| Rank | Cause of Death | ICD Codes | VYPLL | | :---: | :---: | :---: | :---: | | 1 | Motor vehicle accidents | E810-E825 | 1,048,643 | | 2 | Homicide/legal intervention | E960-E978 | 512,811 | | 3 | Suicide | E950-E959 | 262,904 | | 4 | Other conditions-perinatal | 760-766, 770-779 | 212,972 | | 5 | Congenital anomalies | 740-759 | 166,096 | | 6 | Other accidents/adverse effects | E800-E807, E826-E949 | 124,933 | | 7 | Sudden infant death syndrome | 798.0 | 81,809 | | 8 | Birth-relared conditions | 767-769 | 73,103 | | 9 | Other external causes | E980-E999 | 44,497 |
  • Disease groupings correspond to those used by NCHS (12).
    疾病分組與 NCHS 使用的分組相符（12）。
The YPLL concept assigns priority to causes of death according to future contribution lost. This approach emphasizes causes of death occurring in younger age groups because of their larger potential for future contribution. The YPLL formula in Table 1, however, is the only one that assigns equal value to each year of life lost. The other formulas assign different values to years of life lost at different ages; this is a productivity assessment that attaches value to each age according to someone’s concept of potential contribution to society. Society recognizes that potential contribution and invests in the upbringing and education of children so it can reap the benefits of productivity during their adult years. This investment was emphasized by Dickinson in 1948 (15), and restated by Stickle (2) in 1965 as follows, “It may be argued that the concepts of life-years lost and future income sacrificed do not take into account sufficiently the social and economic consequences of deaths during the middle years of life. These deaths often involve heads of families and other individuals from whom the yield of investments in education and training has not been fully realized.” The VYPLL formula allows weighting along these economic lines, as illustrated with the Investment-Producer-Consumer model.
YPLL 概念根據未來貢獻的損失為死亡原因分配優先權。這種方法強調年輕年齡組的死亡原因，因為他們對未來貢獻的潛力更大。然而，表 1 中的 YPLL 公式是唯一一個對每一年生命損失賦予相等價值的公式。其他公式則根據不同年齡對生命損失的年份賦予不同的價值；這是一種生產力評估，根據某人對社會潛在貢獻的概念，對每個年齡賦予價值。社會認識到這種潛在貢獻，並投資於兒童的成長和教育，以便在他們成年後獲得生產力的收益。這項投資在 1948 年由 Dickinson 強調（15），並在 1965 年由 Stickle 重新表述如下：“可以說，生命年損失和未來收入犧牲的概念並未充分考慮到中年死亡的社會和經濟後果。這些死亡通常涉及家庭的主要成員和其他個體，這些人的教育和培訓投資的收益尚未完全實現。”VYPLL 公式允許沿著這些經濟線進行加權，如投資-生產者-消費者模型所示。

Conclusion 結論

YPLL has been promoted as “simple to compute and comprehend” (4), but it is neither simple to compute nor to comprehend. The divergence in computational methods reflects either a lack of understanding of the
YPLL 被宣傳為「計算和理解都很簡單」（4），但它既不簡單計算，也不簡單理解。計算方法的差異反映了對於這一概念的理解不足。
underlying value scales or disagreement about the values to be utilized. Comprehension of the concept becomes clear only after recognizing that YPLL is a method of assigning social value to each age at death. The difficulty in assigning those values is clear, and YPLL is a complex measure incorporating subtle value judgments that are often inapparent to the casual observer. The YPLL concept can be beneficial only if used in the correct context with an appropriate and explicit value scale.
潛在的價值尺度或對應使用的價值的分歧。只有在認識到 YPLL 是一種為每個死亡年齡分配社會價值的方法後，對該概念的理解才會變得清晰。分配這些價值的困難是顯而易見的，而 YPLL 是一種複雜的衡量標準，包含了對價值的微妙判斷，這些判斷對於普通觀察者來說往往不明顯。只有在正確的背景下使用適當且明確的價值尺度，YPLL 概念才能發揮其益處。
It is important to emphasize that YPLL addresses only the impact of social and economic loss from early death, and not the cost of death, preventability of death, or morbidity associated with specific causes of death. Medical and other economic costs related to death from specific causes are not included in any of the YPLL measures, nor are any quality-of-life values. A thorough economic analysis must address all of these issues to evaluate the full economic impact of specific causes of death (16). For example, the economic impact of a sudden death at age 45 from an accident or heart attack may differ greatly from the same individual’s death at the same age from long-standing cancer or organ disease. The medical costs involved in the terminal care, the disability, and other quality-of-life issues will be quite different depending on the cause and circumstances of the death.
重要的是要強調，YPLL 只針對早逝所造成的社會和經濟損失的影響，而不涉及死亡的成本、死亡的可預防性或與特定死亡原因相關的疾病負擔。與特定死亡原因相關的醫療及其他經濟成本不包括在任何 YPLL 指標中，也不包括任何生活品質的價值。全面的經濟分析必須解決所有這些問題，以評估特定死亡原因的全面經濟影響（16）。例如，45 歲因意外或心臟病突發而死亡的經濟影響，可能與同一個體因長期癌症或器官疾病在同年齡去世的影響大相徑庭。終末期護理、殘疾及其他生活品質問題所涉及的醫療成本，將根據死亡的原因和情況而有很大不同。

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  1. Department of Preventive Medicine and Biometrics, F. Edward Hébert School of Medicine, Uniformed Services University of the Health Sciences, 4301 Jones Bridge Road, Bethesda, MD 20814-4799 (address reprint requests to Dr Gardner).
    預防醫學與生物統計學系，F. Edward Hébert 醫學院，統一服務健康科學大學，4301 Jones Bridge Road，Bethesda, MD 20814-4799（請將重印請求寄給 Gardner 博士）。
    © 1990 Epidemiology Resources Inc.
    © 1990 流行病學資源公司
    • Variables: i = i = i=i= age at death, L t = L t = L_(t)=L_{t}= life expectancy at age i , N = i , N = i,N=i, N= upper cutoff age, W = W = W=W= lower cutoff age, I ( j ) = I ( j ) = I(j)=I(j)= value at age j , d 1 = j , d 1 = j,d_(1)=j, d_{1}= number of deaths at age i , n 1 = i , n 1 = i,n_(1)=i, n_{1}= population at age i 1 r 1 = i 1 r 1 = i_(1)r_(1)=i_{1} r_{1}= death rate at age i ( = d / n 1 ) , w 1 = i = d / n 1 , w 1 = i(=d//n_(1)),w_(1)=i\left(=d / n_{1}\right), w_{1}= weight for age i i ii.
      變數： i = i = i=i= 死亡年齡， L t = L t = L_(t)=L_{t}= i , N = i , N = i,N=i, N= 歲的預期壽命， W = W = W=W= 上限年齡， I ( j ) = I ( j ) = I(j)=I(j)= 下限年齡， j , d 1 = j , d 1 = j,d_(1)=j, d_{1}= 歲的數值， i , n 1 = i , n 1 = i,n_(1)=i, n_{1}= 歲的死亡人數， i 1 r 1 = i 1 r 1 = i_(1)r_(1)=i_{1} r_{1}= 歲的人口， i ( = d / n 1 ) , w 1 = i = d / n 1 , w 1 = i(=d//n_(1)),w_(1)=i\left(=d / n_{1}\right), w_{1}= 歲的死亡率， i i ii 歲的權重。
      † † †\dagger Numbers in parentheses refer to referenced articles that use that method.
      † † †\dagger 括號中的數字指的是使用該方法的參考文章。
      ‡ ‡ ‡\ddagger Excluding infant deaths.
      ‡ ‡ ‡\ddagger 排除嬰兒死亡。