Quantifying the future impact of disease on society: life table—based measures of potential life lost

Quantifying the

Future

Impact

of

Disease

on

Society: Life

Table-Based

1Measures of Potential

Life

Lost

Wen-Chung Lee, MD, PhD

Introduction

Quantifying

health status in human

populations

has long been ofconsiderable

interest

to

epidemiologists

and

publc

health workers.For this purpose, mortal-ityrates, including age-specific and age-adjustedones, arefrequentlyused. How-ever, the

mortaity

rate does not fully address the issue of premature mortality, theimpact of diseaseordeath, and its cost to society. In recent years, attention has expanded to include such indices as

"years

of

potential

life lost"

(YPLL).2

The statisticmeasures the total number of lifeyearslostowingtopremature

death

in a population from a certain cause. The definition ofprematuredeath is somewhat arbitrary and varies; for example, deathat theageof lessthan65, 70,or75 years,or

>irfls.<

less than the average life

expectacy.

Gardner and

Sanbom2

proposed another approach: estimating the impact of

death

W;''''2.'/

by dividing

the lifetime into three seg-ments-investment,production, and con-sumption.Theresultingindex ofpotential 3

life

lost is termed

"valued

years of

potential

life lost"

(VYPLL).

Tobroaden thescopeof

potential

life losttoreflectthe full impact and the loss to society from

impairment

or

disability,

Linn and

Sheps3

recently suggested a modification using the overall

percentage

of

permanent

dis-abiity

to obtain estimates of "years of

potential

productivity

lost"

(YPPL).

How-evermanyforms theconceptof

potential

life lost may

take,

indices of this kind have an intuitive

appeal

and are well-suitedtocompare therelative

importance

of differentcausesofdeathfora

particular

population.

It must be

remembered, however,

that theaforementioned indices of

poten-tial life lostarecross-sectionalin

nature-they

quantify,

fora

particular

disease,

the

current losses to the

society.

In other

words, they are indices for a specific populationat aspecificpoint in time. It is true that the

current

losses appropriately reflectthedisease burdenin apopulation. Yet theeventsof deathordisability tallied in such cross-sectional indices have al-ready takenplace and thus are nolonger preventable.Whensetting health goals for preventingandcontrollingdiseases, what

really

counts,therefore, liesin thesocietal impacts of the various diseases in the future but not in the present. In this respect, a prospective index ofpotential life lost isasimportantas across-sectional one,ifnotmoreso.

Inconstructinganindex ofpotential life lost that embraces the prospective sense, along-ignored problem has to be takenon

properly,

thatis, theproblem of competing risk. In a population, deaths occur notalways from thecauseofdeath under

concern.

Rather, alarge number of causesarein competition totake human

lives.4

It

is

conceivablethat themagnitude ofimpactaparticular causeof deathcan

exert onthesocietydepends also onthis

competition.

In a

population

where the

mortality

rate from competing causes is very high, the societal impact of the

particular

cause may be

diminished

be-cause a vast number of

subjects

in this

population

will die from other causes

(competing

deaths) and thereforehaveno

chance to die from the cause under

concern.

Inasimilar

vein,

the

impact

ofa

The author is with the Graduate Institute of

Epidemiology, College of Public Health, Na-tional Taiwan University, and the National Defense MedicalCenter,Taipei,Taiwan.

Requests for reprints should be sent to Wen-Chung Lee,MD,PhD,Graduate Institute of

Epidemiology, National TaiwanUniversity,No.

1,Jen-AiRd,1st Sec,Taipei, Taiwan,Republicof

China.

This paper was accepted November 8,

1996.

particular cause may be higher in a populationwith low competition. Unfortu-nately,theaforementionedcross-sectional indicescannot reflect this simple fact.

Inthis paper I propose new indices ofpotential life lost that are prospective in nature andcanproperlyreflectthe effects of competing risks. The computation of thenewindices isas simple as that of the old ones, requiring no more than a standard life-table calculation. I will illustratethe methodologywith real-world aswell as hypothetical data.

Life

Table-Based

Measures

ofPotential

Life Lost

We begin by introducing "lifetime yearsofpotential life lost" (LYPLL) as a new measureofhealth status in a popula-tion. LYPLL is defined as the expected years ofpotential life lost owing to the particular cause under concern during a subject's lifetime.Asubject loses nothing if heorshelives long enoughto passthe upper cutoff age in the definition of premature mortality. Alternatively, the subject may die young, and therefore someyearsof potentiallifearelost.If the causeof thisprematuredeath happensto be the one underconcern, thelostyears naturally should be counted. If not, the loss is not attributed to the particular cause. The best way to calculate the expected value ofyears lost under these various

possibilities

is to resort to a life-table

methodology.5

In this case a hypothetical cohort of 100 000 individu-als is defined at age0. Subsequently, the numberofperson-years canbecalculated in each5-yearage groupof the hypotheti-cal cohort. Theage groups are

0-4, 5-9,

...

80-84,

85+ and are indexed

by

i

(i= 1,

2, ...,

18). The number of person-yearsin eachagegroupcalculated from the life table is denoted by

yi.

LYPLL for a particular cause can then be esti-mated with thefollowing

simple

formula: LYPLL

= Yi mi (75

-(Si-

2.5))]/100 000,

where

mi

is the

age-specific

mortality

rate

of the

particular

cause under concern. Notethatherethecutoffageofpremature

mortality

isdefinedas75years;

however,

the formula can

easily

be modified for other definitions ofpremature

mortality.

The life-table

methodology

can also be

applied

toestimate lifetime VYPLL and YPPL. Thecalculations

presented

inthis

paper rely on an abridged life table (5-year age groups); for a more refined estimation, one can resort to a complete life table.

Itis of interesttofollowa hypotheti-cal cohortbeginningat an ageother than 0,say25, andcalculate the expected value of lost years, using the same principle outlined above. The result can be inter-pretedas the expected years of potential life lost (EYPLL) during the remaining lifetime (or simply, in the future) of a subject now aged 25. Such an index is denoted

EYPLL25

(EYPLLX forage x, in general). Note that the previously dis-cussed LYPLL isjust the

EYPLLO

now. Just as a table with life expectancies at various agesis frequentlyused as a basis for the computation of life insurance premiums, annuities, and other life contin-gencies,atable ofEYPLLXatvariousages x may then have much to tell. For one thing, it helpsto

identify

whowillbenefit moreif thecauseof death underconcern iseliminated from the population.

The above proposition discusses expected years lost in the future for a single subject. Now we can consider expected years lost in the future for an entire

population.

A

population

is com-posed of

subjects

of varied ages. Let

qi(i

= 1,

2,

..., 18) denote its age structure, that is,

qi

is the proportion of

subjects

in the i'th age group. The expected

(future)

years of

potential

life lostofa

representative

sample of 100 000

subjects

from the

population (denoted

as EYPLLP) can then be approximated by the

following

formula:

EYPLLP

=| qi

EYPLL5i-5]

100 000.

Mathematically,

theabove

expression

for EYPLLPis similarto thatof YPLLper 100000

population

(YPLL per 100000=

[i1qi*mi.

*(75-(5i-2.5))]

.100

000),

both

being

weighted

measures

basedontheage structureof the

popula-tion.

HoWever,

the traditional YPLL is cross-sectional in nature,

measuring

the current lost years

owing

to the

cause-specific

death in the

population,

whereas the EYPLLP embraces the

prospective

sense,

quantifying

the cumulative lost years from now on for the

subjects

presently

alivein the

population.

Itshould benoted that thenewindicesof

potential

life lost

(LYPLL,

EYPLL,

and

EYPLLP),

although they

havea

prospective

interpre-tation,

are

actually

based on a

cross-sectional life table.Thecredibilityof such anapproachwill be discussedlater.

Besides having the desirable feature ofbeing prospective (futuristic) in nature, the newly proposed indices have also properly taken into account theeffectof competing causes of death. The key hinges on the use of life table-derived person-years. Everything else being the same, apopulation withahigher mortality rate from competing causes will have fewerperson-years left in the successive ageintervalsduring thefollow-up of the life-table cohort and therefore will be associated with lower values of LYPLL, EYPLL, and EYPLLP. Conversely, a population withalower competing death ratewillhavemore person-yearsleft and thus be associated withhigher values of these indices. In other words, the life table-derived indices ofpotential life lost doaccurately reflectourbelief that, ina population where deaths from othercauses are dominant, the cause of death under concern shouldnaturally playarelatively minorrole, and inapopulation where the competing deathrateislower, the particu-larcause mayhaveachancetofullyexert itsimpact.

Examples

Table 1 presentsthe

population

size and structure and mortality rates for all causes and for diabetes mellitus in Tai-wan, 1990, extracted from the official vital statistics. The purpose here is to characterize the

impact

of death from diabetesin theTaiwanese

population.

The impactmay differ between the male and female

populations;

for ease of

illustra-tion,

an

analysis by

sex isnot

presented.

Using 5-year

agegroup

age-specific

total

mortality

rates,we

begin by

applying

the standard life-table

technique

(Chiang's

method5)

to derive the person-years in each

5-year

age groupafter the

follow-up

of

hypothetical

cohorts. Thecohortsstart

fromages

0, 5,..

.,

70,

respectively.

Next we calculate,

using

the aforementioned

formula,

the EYPLLX at various ages x

(for

x=

0,

5,

...,

70)

and the EYPLLP. The resultsareshown in Table 2. Forease

of

interpretation,

the results of

EYPLLx

are

presented

in

days,

notyears. Note that LYPLL is

EYPLLO

(64.6

days)

for theage group 0-4 years. For

comparison,

the table also shows the

traditionally

defined YPLL

(owing

todiabetes

mellitus)

for the entire

population

aswell as per 100 000

population.

The EYPLL and LYPLL are

TABLE

1-Population

Size andStructure and

Mortality

Ratesfor AllCauses and for Diabetes Mellitus In Taiwan, 1990

Mortality from Mortality from Population AllCauses Diabetes Mellitus

Age, y Number % Number Ratea Number Ratea

0-4 1605 602 7.94 2 748 171.2 0 0.0 5-9 1 918 897 9.49 670 34.9 0 0.0 10-14 1993725 9.86 734 36.8 3 0.2 15-19 1802480 8.91 1 733 96.1 4 0.2 20-24 1907466 9.43 1 996 104.6 6 0.3 25-29 1971 888 9.75 2 388 121.1 8 0.4 30-34 1855475 9.17 2 692 145.1 21 1.1 35-39 1642 644 8.12 3268 198.9 45 2.7 40-44 1081 528 5.35 3 001 277.5 46 4.3 45-49 899432 4.45 3702 411.6 91 10.1 50-54 837303 4.14 5153 615.4 152 18.2 55-59 765 934 3.79 7269 949.0 303 39.6 60-64 717109 3.54 10543 1470.2 570 79.5 65-69 529 359 2.62 12 740 2 406.7 745 140.7 70-74 336618 1.66 13 725 4 077.3 758 225.2 75-79 217 640 1.08 14 545 6 683.1 736 338.2 80-84 100 413 0.50 9 605 9565.5 331 329.6 85+ 46691 0.23 7577 16 228.0 141 302.0 Total or average 20 230 204 100.00 104 089 514.5 3 960 19.6 aRate per 100 000population.

TABLE 2-LifeTable-DerivedIndices of PotentialLifeLostowing to Diabetes MellitusIn Taiwan,1990

Person-Years from Follow-upof100000Subjects,

Startingfrom EYPLLa Age, y Age0 Age 5 ... Age65 Age 70 (inDays)

0-4 497869.7 ... ... ... ... 64.6b 5-9 495307.1 499563.9 ... ... ... 65.1 10-14 494419.7 498668.9 ... ... ... 65.3 15-19 492780.2 497015.3 ... ... ... 65.2 20-24 490313.0 494526.9 ... ... ... 65.3 25-29 487554.3 491744.5 ... ... ... 65.3 30-34 484321.5 488483.9 ... ... ... 65.4 35-39 480176.6 484303.3 ... ... ... 65.0 40-44 474496.7 478574.7 ... ... ... 63.7 45-49 466405.9 470414.4 ... ... ... 62.1 50-54 454612.2 458519.3 ... ... ... 58.2 55-59 437243.6 441001.4 ... ... ... 52.5 60-64 411736.2 415274.8 ... ... ... 42.1 65-69 374094.5 377309.6 ... 471623.8 ... 26.5 70-74 319063.3 321805.4 ... 402245.4 453748.1 9.3 75-79 245519.6 247629.7 ... 309528.4 349159.8 0.0 80-84 165033.4 166451.8 ... 208058.9 234698.3 0.0 85+ 154754.8 156084.8 ... 195100.5 220080.8 0.0 EYPLLP 16494.0 years

YPLLfor theentire 31020.0years

population

YPLL per 100 000 153.3years

population

interpreted accordingly. We see that the

LYPLLindex isequalto64.6. Thismeans

that a Taiwanese will, on average, lose 64.6daysofpotentiallifeduringhisorher

lifetimeowingtodiabetesmellitus.From the EYPLLindices, onealso notices that

the impact of diabetes is different for subjects of different ages. For all age

groups younger than 45 years, the

ex-pectedloss in thefutureowingtodiabetes is approximately equal, whereas the

ex-pected future loss declines sharply for

every yearasubjectmanagestostayalive

past45. Onecanalsoconsiderthe "what if" scenario. It can be seen that those

subjects aged 30-34 years in Taiwan would receive the most benefit (i.e., EYPLL attains maximum) if diabetes mellituswere nolongerathreattohuman

lives. Without theproposednew indices,

all thesefindingsarenoteasilydiscernible from a simple inspection of a table of

age-specific mortalityrates.

Itisof interesttocompareEYPLLP with YPLL, inasmuch as they are both

population-level

indices.When the

popu-lation size is standardized to 100000, EYPLLP is considerably larger than YPLL(16494.0vs153.3).This isbecause EYPLLP,asexplained earlier,isa

cumula-tive indexcapturingthe presentaswellas

futureloss,whilethe YPLL index reflects

onlythe loss in the currentyear.

Next, let us consider the effect of

competing deaths. Table 3 presents two

hypothetical populations, A and B. The

populationsizes andstructuresaswellas

themortalityratesfrom diabetes mellitus

ofthesetwopopulationsarethesame as

those of the Taiwanese population, but

competingcauses of death playdifferent

roles. Population A has a

highet

total

mortalityratethan that of the Taiwanese

population, while population B has a

lower one.The EYPLLindices differ in thesepopulations, especiallyforthe

youn-gersubjects.Compared with the

Taiwan-ese population, the EYPLL indices are

lower for allagesforpopulation A,while

thereverseistrueforpopulationB. These

findings make sense because the

impor-tanceof death from diabetesmellitus fora

subjectinagivenpopulationisbasednot

only onthe magnitudeofmortalityfrom

diabetesper se buton themagnitude of

competingdeathsaswell.The maximum

value of EYPLL occurs at age 50 in

populationA(vsage30 in the Taiwanese

population)andatage10inpopulationB. These findings imply that if diabetes mellitus were eliminated, the benefit a

subject would enjoy depends on which populationhe or shebelongsto, and that

Note. EYPLL=expected yearsofpotentiallifelost; EYPLLP = EYPLL ofa

representative

sampleof 100 000subjectsfrom thepopulation;YPLL=years ofpotentiallifelost. aForx=0,5,10,...,70.

the group of subjects (young,

middle-aged, or old) who would benefit most

differsfrompopulationtopopulation. As forthepopulation-levelindex of EYPLLP, its value is lower (9238.0) in population A and higher (18034.9) in population B than in the Taiwanese population (16494.0). Thus we see that

although the current burden of deaths from diabetes is the same in these three

populations(YPLLper100000= 153.3),

futureimpactsarenot(ifcurrentmortality prevails). Froma public health point of

view, the prevention and control of diabetes mellitus should be given ahigh

priority in population B, while it is comparatively lessurgentin population A.

Discussion

In this paper Ipropose newindices

of potential life lost to quantify future impacts of specific causes of death on

society. Similar approaches that also rely

on life-table methodology have been

reported.6'7 In those studies, the contribu-tionofaspecificcauseofdeathtogeneral mortality is measured by the "potential gain in life expectancy," defined as the differencebetweentheexpectation of life before and after the complete or partial

elimination of that cause. While the

potential gain in life expectancy also

answersthe "whatif"question, I believe

themethod described here, which modi-fiestheexisting indices of YPLL, VYPLL,

and YPPL, better and more succinctly

reflectsthesocietal and economic impacts ofaspecific disease inapopulation.

It should be pointed out, however, that the proposed new indices, though

claimed to be prospective in nature, are

actually basedon a"current" rather thana

"cohort" life table. A current life table projects the lifespanofeachindividual in a hypothetical cohorton the basisofthe

cross-sectional death rates. The assump-tionanderlying theprocedureisthat each

subjectin thepopulation will be subject throughout his or her life to the same

age-specific mortality rates prevailing in

the current year. Clearly, this is a bold

assumption. To avoid the problem, one

couldrecord the actual mortality

experi-enceofaparticulargroupof individualsin

thegiven populationfromthe first birthto

the last death, construct the cohort life

table, and then calculate the

cohort-specific indices of potential life lost.

However, this is an all but impossible task.Recently,theage-period-cohort mod-eling technique has been adopted to overcome this kind of difficulty. This

technique has successfully obtained,

with-out actual follow-up, the cohort-specific lifetime risks of breastcancerin Connecti-cut8 and the cohort life expectancies in

Taiwan.9 Thesametechniquecanalsobe

appliedtothe present context. However, suchamodeling technique is beyond the scopeofthispaper.

It is of interest to note that the individual-level indices of LYPLL and

EYPLL are defined only through the

age-specificmortalityrates(forthecause

under concern and for all causes) and

therefore are invariant with respect to

changes in population sizes and struc-tures. Thisproperty maybe useful when

onewishestomake acomparisonof the

impacts of a particular disease between different populations or across different

districthealth authorities.By contrast,the

traditional YPLL index, being an index

lacking a denominator, can confound a

valid between-population comparison.'0 Another application for the

individual-levelindicesmaybetotheproblemofage

adjustment. LYPLL, for example,canbe

viewed as a summary condensing the

whole table of age-specific rates into a

single value. Such a summarization pro-cess is what characterizes the dozen

different indices of age adjustment, of

which the"comparativemortalityfigure" (direct adjustment) and the "standard

mortality ratio" (indirect adjustment) are

themostfrequently used.1' Both of these

indices, however, call for an external

"standardpopulation"onwhich compari-sonsof the mortalityratesoftwoor more

populations canbe based. The choice of

this external standardpopulationisnot at

allstandardized but oftenquite arbitrary, leadingto opendebates. In contrast, one can see that, as demonstrated here, the

calculationofLYPLL doesnotneedany

"standard"-neither in the sense of a

standard population structure, as in the

direct age-adjustment methodology, nor

in thesenseofstandardmortality rates,as

in theindirect one-because the LYPLL

index quantifies a certain aspect of the

TABLE

3-Indices

ofPotential Life Lost in Two Hypothetical Populations, ShowingtheEffect of Competing Causes of Death

Population A Population B

Mortality Mortality

from All Causes EYPLLXa fromAllCauses EYPLLXa

Age,y (per100000) (in days) (per 100 000) (in days)

0-4 300.0 33.1 50.0 71.6 5-9 100.0 33.6 10.0 71.8 10-14 150.0 33.8 15.0 71.9 15-19 200.0 33.9 30.0 71.7 20-24 300.0 34.0 40.0 71.6 25-29 500.0 34.2 60.0 71.5 30-34 1000.0 34.7 80.0 71.3 35-39 2000.0 35.6 100.0 70.7 40-44 2500.0 37.4 150.0 69.2 45-49 3000.0 39.7 200.0 67.2 50-54 3500.0 40.6 300.0 62.8 55-59 4000.0 40.2 500.0 56.2 60-64 4500.0 35.1 800.0 44.8 65-69 5000.0 23.5 1000.0 28.1 70-74 10000.0 8.2 2000.0 9.8 75-79 15000.0 0.0 3000.0 0.0 80-84 20000.0 0.0 5000.0 0.0 85+ 30000.0 0.0 10000.0 0.0

EYPLLP 9238.0 years 18034.9 years

YPLLfor the entire population 31020.0 years

31020.0years YPLLper100000population 153.3years 153.3years Note.Thepopulationsizes and structures as well as the mortality rates from diabetes mellitus

arethesame asthoseofthe Taiwanesepopulation,but thecompetingcausesofdeath play

different roles. PopulationAhas a higher total mortality rate than that of the Taiwanese

population,whilepopulationB has a lower one. EYPLL=expected years of potential life

lost;EYPLLP=EYPLLofarepresentative sample of 100 000 subjects from thepopulation; YPLL=yearsof potential life lost.

health status of the subjects in a given population. Such information (expected loss during lifetime)represents an inher-ent characteristic of the population in question and naturally does not concern anyotherpopulations. With this desirable property of indifference to thechoice of standard, the application of the LYPLL index as an alternative method of age adjustment deserves further study. E

References

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life lost (YPLL)-what does itmeasure? Epidemiology. 1990; 1:322-329.

3. Linn S, Sheps S.Disability and the years of

potential productivity lost: modifying the yearsofpotentiallife lost and the invest-ment-production-consumer model by dis-ability level. Epidemiology. 1993;4:449-454.

4. Chiang CL. Competing risks in mortality analysis. Annu Rev Public Health. 1991;12: 281-307.

5. Chiang CL. The Life Table and Its Applica-tions. Melbourne, Fla: Krieger Publishing

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6. Tsai SP, Lee ES, Hardy RJ. The effect ofa

reduction in leading causes of death: potential gains in life expectancy. Am J Public Health. 1978;68:966-971. 7. TsaiSP, Lee ES, Kautz JA. Changes in life

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