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

). 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

）。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})

.
（該年齡的體重）

] = Σ (d_{i}) (w_{i})

。
This calculation is similar to that of an age-adjusted rate (which uses

r_{i}

rather than

d_{i}

). It is of interest to explore the weights (

w_{i}

) used in the various YPLL calculations. First of all, these measures use the number of deaths at each age

(d_{i})

, rather than mortality risk (or rate,

r_{i}

) at each age. The fundamental health characteristic of a population is its specific mortality rates (

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})]

. This inherent inclusion of age-specific populations

(n_{i})

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}

而不是

d_{i}

）。探索在各種 YPLL 計算中使用的權重（

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})

，而不是每個年齡的死亡風險（或比率，

r_{i}

）。一個人口的基本健康特徵是其特定的死亡率（

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})]

。這種在 YPLL 計算中固有的年齡特定人口

(n_{i})

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}

). 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 %

of males and females died, respectively, according to the 1952 life tables (PYPLL, with

N = 85

for males and

N = 88

for females). They also calculated the years of life lost during “the working age period” (WYPLL, with

W = 15

and

N = 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) =

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

). Perloff et al (9) included deaths occurring under age 1 , but calculated only “potentially productive years of life lost” (WYPLL, with

W = 15

and

N = 70

). The CDC, in its MMWR tables introduced in 1982 (3), calculated years of life lost from age 1 to 65 (PYPLL* with

N =

65), but changed in 1986 (10) to include infant deaths (PYPLL with

N = 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}

）。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 %

歲時的生命損失年數（PYPLL，男性為

N = 85

，女性為

N = 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

和

N = 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) =

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

）。 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

和

N = 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 =

65），但在 1986 年（10）改為包括嬰兒死亡（PYPLL 參見

N = 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)

. For example, the YPLL formula uses

I (j) = 1

for all

j

; PYPLL uses

I (j) = 1

for

j < N

and

I (j) = 0

for

j ⩾ N

; PYPLL* is the same as PYPLL except that it uses

I (j) = 0

for all

j

when

i = 0

; WYPLL uses

I (j) = 1

for

w ⩽ j < N

and

I (j) = 0

otherwise; and the crude total deaths use this formula with

I (j) = 1

when

j = i

and

I (j)

= 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)

值。例如，YPLL 公式對所有

j

使用

I (j) = 1

；PYPLL 對

j < N

使用

I (j) = 1

，對

j ⩾ N

使用

I (j) = 0

；PYPLL*與 PYPLL 相同，只是當

i = 0

時對所有

j

使用

I (j) = 0

；WYPLL 對

w ⩽ j < N

使用

I (j) = 1

，對

I (j) = 0

則使用其他值；而粗略總死亡人數在

j = i

時使用此公式，當

I (j)

= 0

時則使用

I (j) = 1

。因此，每個計算中使用的權重為

{weight}_{i} = n_{i} (\sum_{j = i}^{i + L_{1}} I (j))

and the differences between methods are due solely to the different values of

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

, 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)

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

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}

) for

N

(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)

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}

）作為

N

（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)

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

†

縮寫

†

Name 名稱

Formula 公式

YPLL (6, 2)

Years of potential life lost
潛在生命損失年數

\sum_{i = 0}^{\infty} d_{i} (L_{i})

PYPLL

(5, 7, 10)

Premature (to

N

) years of potential life lost
過早（至

N

）年潛在生命損失

\sum_{i = 0}^{N} d_{i} (N - i)

PYPLL

(8, 3)

Premature (to

N

) years of potential life lost

‡

過早（至

N

）年潛在生命損失

‡

\sum_{i = 1}^{N} d_{i} (N - i)

WYPLL

(7, 9)

Working (

W

N

) years of potential life lost
工作（

W

到

N

年）潛在生命損失

\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

\sum_{i = 0}^{\infty} d_{i} [\sum_{j = i}^{i + L} I (j)]

CRUDE (14) 原油 (14)

Crude death rate 粗死亡率

\frac{\sum d_{1}}{\sum n_{1}} = \frac{\sum (r_{i}) (n_{1})}{\sum n_{i}}

ADJ (14)

Adjusted death rate 調整後死亡率

\frac{Σ (r_{i}) (w_{i})}{Σ w_{i}}

{CI}_{L}

(14)

Lifetime cumulative incidence rate
終生累積發生率

1 - \exp (- \sum_{i = 0}^{L} r_{i})

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)

.
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)

中世紀 (2)

Mid-

Age

(2)

生活期待

^{\circ}

(3)

Life

Expectancy

^{\circ}

(3)

0-19

20-64

65 +

網絡投資

^{†}

(10)

Net

Investment

^{†}

(10)

潛在損失† (11)

Potential

Loss†

(11)

收到 (4)

Received

(4)

未收到 (5)

Didn't

Receive

(5)

生產 (6)

Produced

(6)

未生產 (7)

Didn't

Produce

(7)

消耗 (8)

Consumed

(8)

未消耗 (9)

Didn't

Consume

(9)

0.5

19.5

0.0

45.0

0.0

10.5

0.5

15.5

1-4

3.0

17.0

0.0

45.0

0.0

11.0

3.0

20.0

5-14

10.0

0.0

45.0

0.0

11.0

10.0

34.0

15-24

20.0

0.0

45.0

0.0

11.0

20.0

54.0

25-34

30.0

20.0

0.0

10.0

35.0

0.0

12.0

10.0

33.0

35-44

40.0

20.0

0.0

20.0

25.0

0.0

12.0

0.0

13.0

45-54

50.0

20.0

0.0

30.0

15.0

0.0

14.0

-10.0

-9.0

55-64

60.0

20.0

0.0

40.0

5.0

0.0

15.0

-20.0

-30.0

65-74

70.0

20.0

0.0

45.0

0.0

5.0

14.0

-20.0

-34.0

75-84

80.0

20.0

0.0

45.0

0.0

15.0

8.0

-10.0

- 18.0

85 +

88.0

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。
$†$ Net investment $(10) = [$ received $] + [$ consumed $] - [$ produced] $= (4) + (8) - (6)$ .
$†$ 淨投資 $(10) = [$ 收到 $] + [$ 消耗 $] - [$ 生產] $= (4) + (8) - (6)$ .
Potential loss (11) = [net investment] + [didn’t produce] - [didn’t receive] - [didn’t consume] $= (10) + (7) - (5) - (9) = Σ I (j)$ .
潛在損失 (11) = [淨投資] + [未生產] - [未收到] - [未消耗] $= (10) + (7) - (5) - (9) = Σ I (j)$ 。
(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)

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)

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

), Producer years (ages 20-64), and Consumer years (ages

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

and

65 +

, less the amount produced during age

20 - 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

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)

, and at age 50 a net gain of 9 years

(+ 20 - 30 + 15 - 14 = - 9)

, while dying at age 65 gives a net gain of 42 years

(+ 20 - 45 - 17 =

-42 ), and at 80 a net gain of 18 years (

+ 20 - 45 + 15

- 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

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

Abstract 摘要

What Does YPLL Measure? YPLL 測量什麼？

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

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

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