Summary Measures of Population Health:

Methods for Calculating Healthy Life Expectancy

Michael T. Molla, Ph.D.; Diane K. Wagener, Ph.D.; and Jennifer H. Madans, Ph.D.

Abstract

This report is one of several appearing as Healthy

People Statistical Notes that evaluate methodological

issues pertaining to summary measures. Summary

measures of population health are statistics that

combine mortality and morbidity to represent overall

population health in a single number—in this report,

health expectancy measures. This report presents a

comprehensive discussion of the methods for

calculation and methodologic issues related to the

interpretation of healthy life expectancy. These

measures combine both mortality and morbidity using

an abridged life-table procedure. Data from the

National Center for Health Statistics and other sources

will be used to illustrate the calculation of the statistics

and the associated statistical tests.

Key words: summary measures c compression of

morbidity c life table c life expectancy c healthy life

expectancy c healthy years.

Introduction

For the populations of the industrialized nations of the

world, the 20th century has been a period of both

demographic and epidemiologic transitions. In addition to

the substantial decrease in fertility during this period, all

industrialized countries experienced huge declines in crude

death rates and infant mortality rates. This resulted in an

impressive rise in the average life expectancy. For example,

in the United States during the first half of the century, the

average expectation of life at birth for the total population

increased by nearly 45 percent—from 47.3 years in 1900 to

68.2 years by 1950 (1), a gain of nearly 21 years. In the

second half of the century, mortality in the United States

continued to decline, though at a much slower rate compared

with the first half of the century. For example, from

1950–98 the average expectation of life at birth increased

from 68.2 to 76.7 years, a gain of only 8.5 years.

The substantial gain in life expectancy during the first

half of the century caused a dramatic change in the age

structures of the populations of these industrialized countries

in the second half of the century. The longer average life

span meant a sharp rise in the percent of the elderly

population. There was also a sharp rise in noncommunicable

Number 21 August 2001
chronic and degenerative diseases primarily affecting the 

older population. In the United States, the combined effect 

of these changes has encouraged a shift in focus from 

longevity to preventing disability, improving functioning, 

and relieving physical pain and emotional distress (2). This 

also meant that population health measures were needed to 

account for morbidity as well as longevity (3). One group 

of measures that included both of these components 

are health measures broadly known as ‘‘healthy life 

expectancy’’ (HLE). 

Healthy Life Expectancy

The development of health measures that include both 

mortality and morbidity conditions of the population has 

been a focus of study since the 1960’s. After Sanders 

published the results of his research on measuring 

community health levels (4), HLE estimates were published 

by the U.S. Department Health, Education, and Welfare for 

the first time in 1969 (5). Sullivan (6) later published the 

methods for calculating these estimates. At that time, the 

World Health Organization (WHO) noted that the 

fundamental objective of human activity should include both 

long life as well as good health. They expanded the 

definition of health as ‘‘a state of complete physical, mental 

and social well-being.’’ Both WHO and the Organization for 

Economic Cooperation and Development reported on healthy 

life (7). In 1974, WHO recommended that ‘‘person-years of 

life in health’’ be calculated and be compared with the total 

person-years of life (8). 

In the 1980’s, two new concerns became important, the 

relationship between changes in mortality and morbidity and 

the relatively greater burden of morbidity in the older ages. 

Debate centered on whether the factors responsible for the 

reductions in mortality would have a similar effect on 

morbidity. Some argued that most of the years of life that 

the elderly gained due to the decline of mortality were 

‘‘healthy years’’ because morbidity was being pushed to the 

last few years of life, the compression of morbidity (9, 10). 

Others argued that the mortality decline observed over the 

past several decades was more likely to be the result of 

improvements in health care that saved more lives rather 

than either disease prevention that maintains healthy states 

or medical care that delays functional consequences of 

disease (11). 

At the same time, Manton (12) introduced the concept 

of dynamic equilibrium. The theory of dynamic equilibrium 

is that chronic diseases have become less of a problem 

because deterioration in health due to disease has slowed 

down. The argument further suggested that while the 

decrease in mortality might have contributed to an increase 

in the prevalence of chronic diseases, these diseases would 

be of milder character leading to an overall better quality of 

life. Clearly, the issues related to the compression of 

morbidity further made clear that health status was a 

consequence of an interaction between mortality and 

morbidity, both at the micro and macro levels. 

-2-

Mortality component: 

Age-specific death rates 

Summary measure of population health: 

Healthy life expectancy or healthy 

life years 

-

Morbidity component: 

Population morbidity, 

disability, or healthrelated quality of life 

SOURCE: Adapted from a model by the Institute of Medicine, National Academy of 

Sciences (2). 

Life table technique 

Figure 1. A schematic presentation of the model

Encouraged by the basic idea of developing health 

measures that incorporate mortality and morbidity and 

motivated by the concept of compressing morbidity, health 

researchers continued to study empirical and methodologic 

issues throughout the 1990’s (see appendix). Empirical 

studies estimated healthy life expectancy indexes based on a 

variety of health attributes. The name given the various HLE 

indexes depends on methods by which different health states 

are measured (13). When health states are measured based 

on broadly defined chronic or acute morbid conditions, the 

more general name ‘‘healthy years’’ or ‘‘healthy life 

expectancy’’ is used . However, when health states are 

defined based on social or functional limitation, the 

estimated index is called ‘‘disability-free life expectancy.’’ 

When health states are measured by activity limitation, the 

index is often called ‘‘active life expectancy.’’ 

Components of Healthy Life Years

The estimation of healthy life expectancy is based on 

the concept of a closed population within a given period of 

time, that is, a population with no immigration or 

emigration. The period of time may be of any length, but the 

most commonly used period is one year. At the end of the 

year, the population can be partitioned into those who died 

within the period and those who are still alive. Of those still 

alive, the majority are expected to be healthy, and some are 

expected to be unhealthy. Hence, a model can be built that 

measures the health status of persons who are alive at the 

same time it accounts for those who die in the period of 

time. Such a model is schematically presented in figure 1. 

According to this model, healthy life expectancy is a 

summary measure of a population composed of two sets of 

partial measures. The first set of measures, the age-specific 

death rates, accounts for the mortality component. The 

second set of measures, the age-specific rates of population 
Mortality data 

Midyear 

population 

estimates 

Health data 

Age-specific death 

rates 

Life table 

technique 

U.S. Bureau 

of the Census 

Self-assessed health 

(poor or fair) 

( 

(D) 5

5

5

x

x

(1- x) 

Self-assessed health 

(good or better) 

Healthy life 

expectancy 

NCHS 

NCHS 

Data sources Data Calculation Index 

NOTES: NCHS is the National Center for Health Statistics. Variables are defined in tables 1-5. 

) 

Figure 2. A schematic framework for estimating healthy life expectancy at the national level using respondent-assessed health status as

an example

morbidity, disability, or health-related quality of life,1 

accounts for the morbidity component. These two 

components are combined using a mathematical function that 

transforms the two sets of partial measures into a single 

composite measure using a life table methodology. Figure 2 

displays the framework of this calculation, including the type 

of data needed and the techniques used to estimate the two 

components of the measure at the national level. 

At the national level, the mortality data are obtained 

from the National Vital Statistics System of the National 

Center for Health Statistics (NCHS), Centers for Disease 

Control and Prevention. Mortality data are collected by each 

state and the District of Columbia and compiled at the 

national level by NCHS. Midyear population estimates are 

from the U.S. Bureau of the Census. 

Health data can come from a number of different 

sources depending on the type of health measure and the 

population being considered. Boyle and Torrance (14) 

developed a ‘‘health state classification system’’ (displayed 

in part in figure 3). Only some health attributes are 

interrelated. Hence, attributes can be classified to show 

similarities and differences. The classification system of 

Boyle and Torrance conceptualizes the interrelationship of 

health attributes as hierarchal, based on breadth and on 

coverage of different aspects of health. For example, 

physical function, which is one of the primary-level health 

1

Health related quality of life (HRQOL) refers to the effect of health 

conditions on function. It focuses on the qualitative dimension of 

functioning and incorporates duration of stay in various health states 

(Kaplan and Anderson (15)). 

attributes, has four secondary-level attributes, one of which 

is self-care. Self-care may, in turn, be disaggregated into 

more specific health attributes, shown as the third level of 

classification in figure 3. The interpretation of the HLE 

depends on the health data used to estimate the statistic. 

Because national data for respondent-assessed health are 

evaluated in the example presented here, the National Health 

Interview Survey (NHIS) conducted by NCHS is used. To 

calculate the age-specific prevalence rates of being healthy, 

HEALTH 

Emotional 

function 

Depth of 

coverage 

Physical 

function 

Sensory 

function 

Pain Cognitive 

ability 

Physical Mobility 

activity 

Self-care Role 

performance 

Dressing Bathing Continence Eating 

Breadth of coverage 

SOURCE: Adapted from Boyle and Torrance (14). 

Figure 3. An example of a classification system for health

attributes

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first calculate the rates of reporting ‘‘fair or poor’’ health 

(nπx). The rates of being healthy, that is, reporting ‘‘good or 

better’’ health is then (1−nπx). Then for each age interval 

(x, x+n), the rates of being healthy (1−nπx) are multiplied 

with the total number of years lived within the same age 

interval (nLx) to estimate the total number of years a group 

of persons is expected to live in a healthy state during the 

interval. The age interval (x, x+n) is equal to 1 if data used 

are in single-year age groups, or 5 or 10 if data used are in 

5- or 10-year age groups. 

The model used to estimate healthy life expectancy (i.e., 

the expected number of years in good or better health) is: 

w 1 

e′ x = ∑ (1−nπx) nLi lx i=x (1) 

where 

ex ′	 is healthy life expectancy at age x, or the number of 

remaining years of healthy life for persons who 

have reached age x 

lx is the number of survivors at age x 

(1−nπx) represents the age-specific rate of being healthy 

nLx	 is the total number of years lived by a cohort in the 

age interval (x, x+n) 

w is the oldest age category 

HLE could be estimated using a variety of health 

attributes. For example, the model may be used to estimate 

disability-free life expectancy or life without activity 

limitation, also referred to as expected years of active life. 

Regardless of the health attribute chosen, however, the 

model uses two separate and independent partial health 

measures: (1−nπx) for the morbidity component and lx and 

nLx for the mortality component. 

Life Table Technique

The life table, also known as the mortality table, is 

used to present the most complete statistical description 

of mortality (16). The life table has also been an 

important tool of demographers who are interested in 

estimating the probability of marriage and remarriage, 

widowhood, becoming an orphan, and migration and 

population projections (17). In addition to the analyses of 

mortality and other demographic characteristics of human 

populations, the life table technique has been used to 

measure decrements in nonhuman groups or aggregates, 

including animals, insects, cases of illness, or even items 

of industrial equipment (18). The technique has been used 

to estimate risks and insurance benefits and school 

life (19), and even used to analyze prime time programs 

on a television network (20). 

The method of calculating HLE is presented in this 

report in four parts. Healthy life expectancy is a modified 

life expectancy calculation. Therefore, the method is best 

presented by showing the calculations of life expectancy and 

discussing the modifications. Part I addresses the estimation 

of life table values. Part II presents the estimation of 

age-specific prevalence rates of health states and how the 

two partial measures of the mortality and morbidity 

components are combined to estimate the final age-specific 

composite health measure. Part III covers the estimation of 

the standard errors of healthy life expectancy. Part IV 

explains the application of the estimated healthy life 

expectancy and the associated standard errors in the 

statistical testing of health disparity between population 

subgroups. 

Estimating Average Life Expectancy

The objective of the life table is to calculate the 

expected life expectancy of groups of people currently at 

specified ages if they lived the rest of their lives 

experiencing the age-specific mortality rates observed for 

the population at a specific time. The technique, therefore, 

uses the age-specific mortality to calculate the proportion 

of people alive at the beginning of an age interval who 

die before reaching the next age group. The average 

number of person-years lost because of those deaths is 

then subtracted from the total possible person-years for 

the age group of the cohort. These person-years are then 

added for all the age groups being considered to yield the 

expected number of years remaining. The method for 

constructing a complete annual life table is discussed in 

another NCHS publication (21). 

The estimation of life table values, such as the 

expectation of life, begins with the computation of 

age-specific death rates. An illustrative example is presented 

in table 1 using 1995 data for white females in the United 

States. The two sets of data required to construct a life table 

are the midyear population and the number of deaths in that 

year. These data could be analyzed in single years of age or 

5- or 10-year age groups. The process could be applied to 

the construction of a life table for national, state, or local 

populations. 

In the first column, the age groups are listed. In the 

example shown in table 1, the initial 5-year age group 

is 0–4 years2 and the final age groups is 85 years and over. 

The determining factor for the age grouping is the 

availability and quality of data. It should be noted that the 

age that begins the final age group (also known as the open 

age interval) does not have any effect on the life table being 

constructed. 

The next two columns of the table give counts for the 

population nPx and deaths nDx for each age group. The 

population counts are based on midyear estimates. The 

deaths are for the entire year. These are used to compute 

the average death rate of each age-group for the year 

(nMx, where n, the number of years in the age groups is 5 in 

table 1), as 

nMx = nDx / nPx (2) 

2

Mortality rates for age 0 and age group 1–4 are calculated separately when 

knowing ‘‘their pattern in more detail’’ is preferred (22). 

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Table 1. Life table for white females: United States, 1995

Proportion Probability Total Number of Life 

Age- of years lived of dying Number number of years lived expectancy 

Number specific by those who during age alive at the years lived in this and at beginning 

Age Mid-year of deaths die in age interval beginning of in age subsequent of age 

interval1 population deaths per 1,000 interval2 age interval interval age intervals interval 

x to x+5 5Px 5Dx 5Mx ax 5qx lx 5Lx Tx ex

0–4 years ................. 7,530,865 10,277 1.3647 0.178 0.0068 100,000 497,211 7,945,930 79.5 

5–9 years ................. 7,375,960 1,112 0.1508 0.477 0.0008 99,321 496,412 7,448,720 75.0 

10–14 years ............... 7,294,788 1,335 0.1830 0.530 0.0009 99,247 496,020 6,952,308 70.1 

15–19 years ............... 7,010,351 3,084 0.4400 0.555 0.0022 99,156 495,294 6,456,288 65.1 

20–24 years ............... 7,020,389 3,102 0.4419 0.517 0.0022 98,938 494,163 5,960,994 60.3 

25–29 years ............... 7,583,792 4,067 0.5363 0.519 0.0027 98,720 492,962 5,466,831 55.4 

30–34 years ............... 8,918,195 6,554 0.7349 0.538 0.0037 98,455 491,441 4,973,870 50.5 

35–39 years ............... 9,190,371 9,651 1.0501 0.524 0.0052 98,094 489,247 4,482,429 45.7 

40–44 years ............... 8,478,260 12,541 1.4792 0.524 0.0074 97,580 486,191 3,993,182 40.9 

45–49 years ............... 7,485,773 17,056 2.2784 0.528 0.0113 96,861 481,715 3,506,991 36.2 

50–54 years ............... 5,969,413 22,572 3.7813 0.531 0.0187 95,764 474,612 3,025,276 31.6 

55–59 years ............... 4,913,335 29,877 6.0808 0.534 0.0300 93,969 463,278 2,550,664 27.1 

60–64 years ............... 4,570,327 44,926 9.8300 0.534 0.0480 91,152 445,546 2,087,386 22.9 

65–69 years ............... 4,728,330 71,430 15.1068 0.534 0.0730 86,772 419,113 1,641,841 18.9 

70–74 years ............... 4,451,633 105,434 23.6844 0.539 0.1123 80,441 381,366 1,222,727 15.2 

75–79 years ............... 3,573,206 134,299 37.5850 0.543 0.1730 71,408 328,775 841,361 11.8 

80–84 years ............... 2,603,800 163,724 62.8788 0.529 0.2739 59,051 257,187 512,586 8.7 

85 years and over ............ 2,405,023 349,118 145.1620 0.596 1.0000 42,880 255,399 255,399 6.0 

1Mortality rates for those less than 1 year and age group 1–4 years are calculated separately when knowing ‘‘their pattern in more detail’’ is preferred (22). 2For a more detailed discussion of ax, see DHEW (24) and Keyfitz (27). 

The computed age-specific death rates need to be checked 

for stability. Age-specific death rates are considered to be 

stable if they are based on 20 or more deaths. Rates based 

on fewer than 20 deaths have a relative standard error of 

23 percent or more and therefore are considered highly 

variable (23). 

The conditional probability of dying within a given age 

group nqx is given in column 6. This is the proportion of 

people in the age group alive at the beginning of the age 

interval who die before reaching the next age group. 

Whereas nMx is an annual death rate, nqx is a conditional 

probability of dying. This probability is estimated as: 

nqx = [n c nMx ] / [1+n(1−ax) nMx] (3) 

where ax is average proportion of years lived by those who 

died in this age interval (given in column 5). The conditional 

probability of dying is assumed to be 1.0 for the open, 

oldest age interval. In the example presented here, n is 5 

years, so the probability becomes: 

5qx = [5 c 5Mx] / [1+5(1−ax) 5Mx ] 

The values for ax are constants derived from the complete 

U.S. life tables of 1949–51 (24). For single-year life table 

value calculations, ax may be assumed to be 1⁄2. 

Having calculated the conditional probability of dying, 

one can now calculate the probability of surviving to an 

exact age marking the beginning of an interval. In the life 

table, this is expressed as the number of persons surviving to 

an exact age (or the exact age at the beginning of an age 

interval when group data are used), starting with an assumed 

cohort population (l0) frequently expressed as 100,000 at 

birth (column 7). For any other specific age, the number of 

survivors at that age, (lx) can be calculated. Hence, the 

number alive at exact age x+n (lx+n) is calculated by 

multiplying the number of survivors at exact age x (lx) by 

the probability of surviving from age x to age x+n (1−nqx) 

or: 

lx+n = lx (1−nqx ) (4) 

The total number of person-years lived for those people who 

began the age interval x to x+n (column 8) is then the sum 

of the total number of years lived by individuals surviving to 

the end of the age interval plus the total number of years 

lived by those who die in the age interval. This becomes: 

nLx =n [lx+n + ax (lx − lx+n)] (5) 

In the example presented here, n = 5 so, 

5Lx =5 [lx+5 + ax (lx − lx+5)] 

Column 9, the person-years remaining for the 

population, that is, Tx, is the total of all the person-years for 

age x and all subsequent age groups, or: 

Tx = ∑ Li i=x 

for i = x, x+n, ... , oldest age group (6) 

The average per person expected years (column 10) is the 

total person-years divided by the number of persons 

surviving to the beginning of the age interval x, or: 

ex = Tx / lx (7) 

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Table 2. Calculation of healthy life expectancy for white females by Sullivan’s method using abridged life table: United States, 1995

Number of Average number 

Proportion of years lived in of years in 

Number alive Number of persons in age Proportion of Number of healthy state in healthy state 

at the years interval in state persons in age healthy years this and all remaining at 

beginning of lived in considered interval in lived in subsequent age beginning of 

Age interval each interval age interval unhealthy healthy state age intervals intervals age interval 

x to x+5 lx 5Lx 5πx (1−5πx ) ′ 5Lx ′ T x ′ ex

0–4 years ................. 100,000 497,211 0.0185 0.9815 488,012 6,981,686 69.8 

5–9 years ................. 99,321 496,412 0.0196 0.9804 486,682 6,493,674 65.4 

10–14 years ............... 99,247 496,020 0.0189 0.9811 486,645 6,006,992 60.5 

15–19 years ............... 99,156 495,294 0.0435 0.9565 473,749 5,520,347 55.7 

20–24 years ............... 98,938 494,163 0.0490 0.9510 469,949 5,046,598 51.0 

25–29 years ............... 98,720 492,962 0.0617 0.9383 462,546 4,576,649 46.4 

30–34 years ............... 98,455 491,441 0.0614 0.9386 461,266 4,114,103 41.8 

35 –39 years ............... 98,094 489,247 0.0773 0.9227 451,428 3,652,837 37.2 

40–44 years ............... 97,580 486,191 0.0890 0.9110 442,920 3,201,409 32.8 

45–49 years ............... 96,861 481,715 0.1094 0.8906 429,015 2,758,489 28.5 

50–54 years ............... 95,764 474,612 0.1506 0.8494 403,136 2,329,473 24.3 

55–59 years ............... 93,969 463,278 0.1919 0.8081 374,375 1,926,338 20.5 

60–64 years ............... 91,152 445,546 0.2031 0.7969 355,055 1,551,963 17.0 

65–69 years ............... 86,772 419,113 0.2257 0.7743 324,520 1,196,908 13.8 

70–74 years ............... 80,441 381,366 0.2364 0.7636 291,211 872,388 10.8 

75–79 years ............... 71,408 328,775 0.2782 0.7218 237,310 581,177 8.1 

80–84 years ............... 59,051 257,187 0.3298 0.6702 172,367 343,867 5.8 

85 years and over ............ 42,880 255,399 0.3285 0.6715 171,501 171,501 4.0 

Therefore, in the example presented in table 1, the expected 

number of years of life at birth (e0) is 79.5 years, the 

expected number of years of life at age 20 years (e20) is 

60.3 years, and the expected number of years of life at age 

65 years (e65) is 18.9 years. 

Estimating Average Years of Healthy Life

The life table technique is a powerful tool for estimating 

the remaining years of life that a group of persons can 

expect to live once they had reached a certain age. 

Regardless of their age, the remaining years of life might be 

lived in good health, in less optimal health status, or some 

combination of both. The traditional life table technique does 

not distinguish between remaining healthy years and 

unhealthy years. Additional data are needed to disaggregate 

the total number of years into expected years of healthy and 

of unhealthy life. 

Using health data, the total number of expected years of 

life are separated into healthy and unhealthy years (see 

figure 2). In general, health data, collected through health 

surveys or from clinical observations, are used to estimate 

the prevalence of different levels of health status. The 

population is then partitioned into proportions that are 

experiencing varying levels of health status. The separation 

may be as simple as dividing the population into those who 

are healthy or unhealthy. Or the population may be separated 

into more than two population subgroups according to 

varying levels of health status using multidimensional 

scaling to describe health status. 

To calculate the HLE, the population of each age 

interval in the life table is separated into the proportion 

-6-

experiencing an unhealthy condition (nπx) and those 

considered as healthy (1−nπx). An example is shown in 

columns 4 and 5 of table 2. Because nLx is the total number 

of person-years lived for the population in age interval x to 

x+n (equation 5), the proportion of these years lived in a 

′ healthy state ( nLx) is then: 

′ 

nLx = (1−nπx) nLx (8) 

This is shown in column 6 of table 2. Equations (6) and (7) 

can then be used to obtain the healthy life expectancy (see 

column 8 of table 2) from the number of healthy 

person-years determined in (8) or 

w 1 ′ ′ 

ex = ∑ nLi lx i=x (9) 

′ The expected years of unhealthy life are ex− ex . However, if 

multiple states of health status are described, the prevalence 

for each of those states for each age interval must be 

calculated and equations similar to (8) and (9) are used to 

estimate separately the expected years of life in those health 

states. 

In table 2, the health states have been defined using 

respondent-assessed health, which is obtained from health 

interview surveys using the question, ‘‘Would you say your 

health in general is excellent, very good, good, fair or poor’’ 

with five response categories: excellent, very good, good, 

fair, and poor. Health states are then defined as two mutually 

exclusive states: self-assessed health as poor or fair (column 

4) and self-assessed health as good or better (column 5). The 

number of survivors at exact age x (lx) and number of 
Table 3. The variance and standard error of healthy life expectancy for white females assuming simple random sampling: United States,

1995

Average 

number of years Proportion of 

of healthy life Number of persons in Variance of Variance of Standard error 

Number of remaining at persons in age interval the prevalence healthy life of healthy life 

years lived in beginning of survey in in healthy rates in expectancy in expectancy in 

Age interval age interval age interval age interval state age interval age interval age interval 

′ ′ x to x+5 5Lx ex 5Nx (1−5πx ) S2

( 5πx ) VAR (ex ) s (e′ 

x ) 

0–4 years ................. 497,211 69.8 3,170 0.9815 0.000006 0.01812 0.135 

5–9 years ................. 496,412 65.4 3,282 0.9804 0.000006 0.01823 0.135 

10–14 years ............... 496,020 60.5 3,221 0.9811 0.000006 0.01811 0.135 

15–19 years ............... 495,294 55.7 2,840 0.9565 0.000015 0.01800 0.134 

20–24 years ............... 494,163 51.0 2,685 0.9510 0.000017 0.01771 0.133 

25–29 years ............... 492,962 46.4 3,033 0.9383 0.000019 0.01735 0.132 

30–34 years ............... 491,441 41.8 3,411 0.9386 0.000017 0.01697 0.130 

35–39 years ............... 489,247 37.2 3,648 0.9227 0.000020 0.01667 0.129 

40–44 years ............... 486,191 32.8 3,365 0.9110 0.000024 0.01635 0.128 

45–49 years ............... 481,715 28.5 2,848 0.8906 0.000034 0.01599 0.126 

50–54 years ............... 474,612 24.3 2,246 0.8494 0.000057 0.01549 0.124 

55–59 years ............... 463,278 20.5 1,828 0.8081 0.000085 0.01464 0.121 

60–64 years ............... 445,546 17.0 1,730 0.7969 0.000094 0.01336 0.116 

65–69 years ............... 419,113 13.8 1,764 0.7743 0.000099 0.01228 0.111 

70–74 years ............... 381,366 10.8 1,634 0.7636 0.000110 0.01160 0.108 

75–79 years ............... 328,775 8.1 1,207 0.7218 0.000166 0.01157 0.108 

80–84 years ............... 257,187 5.8 813 0.6702 0.000272 0.01176 0.108 

85 years and over ............ 255,399 4.0 625 0.6715 0.000353 0.01252 0.112 

person-years (nLx) have been copied from table 1 into the 

second and third columns of table 2. The healthy 

person-years for each age group (column 6) is the multiple 

of columns 5 and 3. Using the equations above, the expected 

′ years of healthy life at age x (ex) can be calculated (column 

8). Therefore, whereas the total expected life at birth (e0) 

from table 1 is 79.5 years, the expected life lived in good or ′ ′ better health (e0) from table 2 is 69.8 years. The e0 may be 

interpreted as the number of years a newborn white female 

is expected to live in a healthy state provided that she 

experiences the 1995 age-sex-specific mortality and 

survey-measured age-sex-specific prevalence rates of good 

or better health that are given in table 2. Similarly, at age 65, 

the total expected life (e65) is 18.9 years (table 1) and 

′ expected healthy life (e65) is 13.8 years (table 2), that is, 

whereas a female age 65 years is expected to live about 19 

more years, only 14 of those years are expected to be in 

good or better health. 

Statistical Test for HLE

The estimates for age-specific prevalence of healthy and 

unhealthy states are derived from surveys or samples. 

Consequently, these estimates have associated sampling 

error. Calculating the standard error of the resulting 

estimated HLE is especially important when comparing 

population subgroups. This section discusses the method of 

estimating the standard errors of HLE with and without 

information on the survey sample design. Standard errors of 

each of the other life table values can be calculated 

separately when needed. See Chiang (25) and Keyfitz (26) 

for details. 

The variance estimation method will be illustrated with 

and without taking into account the sample survey design. 

The method that takes the sample survey design into account 

will be illustrated using the 1995 NHIS data in conjunction 

with the SUDAAN statistical software. The alternative 

method that assumes a simple nonstratified sample survey is 

presented to illustrate the application of the method when 

complete information on sample survey design is not 

available. 

Standard Errors of HLE

Each age-specific value of the prevalence of the 

population experiencing healthy life (1−nπx) is an estimated 

proportion with an associated variance and standard error. 

Because the distribution of these proportions is binomial, the 

variance (S2

) is given by: 

S2

(nπx)= [nπx c (1−nπx)] / nNx (10) 

where nNx is the number of persons in the age interval 

(x, x+n) of the sample from which the prevalence rates were 

computed. 

The variances of the prevalence rates from equation (10) 

′ can be used to estimate the overall variance of ex by: 

w 1 ′ 2 VAR(ex)= 2 ∑[xLi c S2

(1−nπx)] lx i=x (11) 

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Table 4. Estimated variance and standard error of healthy life expectancy for white females taking the sample design of the health

survey into account: United States, 1995

Average number Variance of Variance of Variance of Standard error 

Average number of years of the prevalence the prevalence healthy life of healthy life 

of years of life healthy life Proportion of rates in rates in expectancy expectancy in 

remaining at remaining at the persons in age interval age interval in age interval age interval 

beginning of beginning of age interval in estimated estimated using estimated using estimated using 

Age interval age interval age interval healthy state without SUDAAN SUDAAN SUDAAN SUDAAN 

x to x+5 ex ′ ex (1−5πx ) s2

(1−5πx ) s2(1−5πx ) ′ VAR (ex ) ′ s (ex ) 

0–4 years ................. 79.5 69.8 0.9815 0.000006 0.000007 0.02050 0.143 

5–9 years ................. 75.0 65.4 0.9804 0.000006 0.000006 0.02061 0.144 

10–14 years ............... 70.1 60.5 0.9811 0.000006 0.000006 0.02048 0.143 

15–19 years ............... 65.1 55.7 0.9565 0.000015 0.000019 0.02036 0.143 

20–24 years ............... 60.3 51.0 0.9510 0.000017 0.000020 0.01997 0.141 

25–29 years ............... 55.4 46.4 0.9383 0.000019 0.000022 0.01955 0.140 

30–34 years ............... 50.5 41.8 0.9386 0.000017 0.000018 0.01910 0.138 

35–39 years ............... 45.7 37.2 0.9227 0.000020 0.000019 0.01878 0.137 

40–44 years ............... 40.9 32.8 0.9110 0.000024 0.000026 0.01849 0.136 

45–49 years ............... 36.2 28.5 0.8906 0.000034 0.000037 0.01811 0.135 

50–54 years ............... 31.6 24.3 0.8494 0.000057 0.000064 0.01759 0.133 

55–59 years ............... 27.1 20.5 0.8081 0.000085 0.000104 0.01663 0.129 

60–64 years ............... 22.9 17.0 0.7969 0.000094 0.000119 0.01499 0.122 

65–69 years ............... 18.9 13.8 0.7743 0.000099 0.000104 0.01341 0.116 

70–74 years ............... 15.2 10.8 0.7636 0.000110 0.000125 0.01278 0.113 

75–79 years ............... 11.8 8.1 0.7218 0.000166 0.000182 0.01263 0.112 

80–84 years ............... 8.7 5.8 0.6702 0.000272 0.000266 0.01282 0.113 

85 years and over ............ 6.0 4.0 0.6715 0.000353 0.000416 0.01476 0.122 

This variance estimation method assumes that the health data 

were collected through a simple, nonstratified sample survey, 

also referred to as simple random sample survey (27). 

Table 3 displays the results from table 2. The prevalence data 

in table 2 were derived from a survey of 43,350 white 

females who participated in the 1995 National Health 

Interview Survey (28). In table 3, the variance of these data 

are assumed to be the result of simple random sampling. 

Column 4 of table 3 gives the number of persons in the 

survey who were in the specific age intervals (nNx). The 

proportion of each age-specific population reporting good or 

better health (1−nπx) (column 5) are the same values shown 

in table 2. Equation 10 can be used to calculate the 

age-specific variances shown in column 6. The total variance 

′ of ex using equation 11 is shown in column 7. The standard ′ ′ error (s(ex)) of ex is given in column 8. 

Many surveys, including NHIS, do not use simple 

random sampling to identify respondents. For surveys that 

use a complex multistage sample design, the sample design 

must be taken into account in the estimation of the variance 

and standard error (29). Computer programs exist that can 

compute the variance and standard errors using sample 

design variables to approximate the true variance and 

standard errors. One such program is SUDAAN (30). In 

table 4, the data presented previously have been reanalyzed 

using SUDAAN to develop estimates of the variance for 

age-specific prevalence (column 6). The binomial variance 

estimate of table 3 is also shown for comparison in column 

5. Using equation 11, the variance and standard errors of 

healthy life expectancy were calculated. Estimates that 

incorporate information from the complex sample design 

-8-

may differ from those calculated using the simple random 

sampling assumption. In this example, the standard errors of 

the prevalence rates estimated using the SUDAAN procedure 

were 5–10 percent larger than those estimated using the 

binomial estimation. 

Test for Difference Between Two Populations

Health disparity between two population subgroups can 

be tested using statistical methods usually used for testing 

the difference between two means. The estimated HLE 

within each age group is a mean of random variables 

assumed to be independent of each other and with normal 

distribution (31). Hence, a z-score3 test can be constructed 

using the estimated HLE and the corresponding variance to ′ ′ compare the HLE’s (ex,1 and ex,2) of two population 

subgroups at a specified age. Note that the specified age is 

′ the same for each HLE. Assuming ex,1 stands for healthy life 

′ expectancy of white females at a specific age and ex,2 is 

healthy life expectancy at the same age for white males, a 

score for testing a hypothesis about the equality of healthy 

life at that specified age can be stated as 

′ ′ 

ex,1 − ex,2 

z = ′ ′

√S2

(ex,1 − ex,2) (12) 

3

The z-score is a standard normal variable estimated by transforming a


nonstandard normal variable x based on the statistical formula


z = (x − μx)/ σx, where μx is the mean of the x-values and σx is the standard


error (32, 33).

Table 5. Statistical test for disparity in healthy life expectancies at specific ages for the white population: United States, 1995

Female Male Approximate 

standard error 

Standard error Standard error Difference in of difference in 

Healthy life of healthy life Healthy life of healthy life healthy life healthy life p-value 

Age interval expectancy expectancy expectancy expectancy expectancy expectancy z-statistic Pr(Z>=z) 

′ ′ ′ ′ x to x+5 ex,1 s (ex,1) ex,2 s (ex,2) (2) − (4) (3) + (5) z p

0–4 years ................. 69.8 0.143 65.7 0.130 4.078 0.273 14.93 <0.001 

5–9 years ................. 65.4 0.144 61.5 0.130 3.931 0.274 14.37 <0.001 

10–14 years ............... 60.5 0.143 56.6 0.129 3.907 0.273 14.34 <0.001 

15–19 years ............... 55.7 0.143 51.8 0.129 3.878 0.272 14.28 <0.001 

20–24 years ............... 51.0 0.141 47.2 0.129 3.822 0.270 14.16 <0.001 

25–29 years ............... 46.4 0.140 42.6 0.128 3.730 0.268 13.91 <0.001 

30–34 years ............... 41.8 0.138 38.1 0.128 3.655 0.266 13.72 <0.001 

35–39 years ............... 37.2 0.137 33.7 0.128 3.495 0.265 13.19 <0.001 

40–44 years ............... 32.8 0.136 29.4 0.128 3.366 0.264 12.77 <0.001 

45–49 years ............... 28.5 0.135 25.2 0.128 3.242 0.262 12.36 <0.001 

50–54 years ............... 24.3 0.133 21.2 0.127 3.098 0.260 11.92 <0.001 

55–59 years ............... 20.5 0.129 17.6 0.125 2.918 0.254 11.49 <0.001 

60–64 years ............... 17.0 0.122 14.3 0.121 2.746 0.243 11.28 <0.001 

65–69 years ............... 13.8 0.116 11.4 0.119 2.379 0.234 10.15 <0.001 

70–74 years ............... 10.8 0.113 9.0 0.118 1.895 0.231 8.19 <0.001 

75–79 years ............... 8.1 0.112 6.8 0.121 1.354 0.234 5.79 <0.001 

80–84 years ............... 5.8 0.113 5.0 0.133 0.796 0.246 3.23 <0.002 

85 years and over ............ 4.0 0.122 3.7 0.168 0.271 0.289 0.94 <0.200 

′ ′ ′ ′ Because S2

[ex,1 − ex,2] ≤ [S(ex,1)+ S(ex,2)]2, the z-score value 

may be conservatively approximated (34) using: 

′ ′ 

z � ex,1 − ex,2 

′ ′ S (ex,1)+ S (ex,2) (13) 

Table 5 presents 1995 data comparing white males and white 

females. The health expectancies and corresponding standard 

errors are given in columns 2–5. (The SUDAAN estimates 

of the standard errors of the age-specific prevalence rates are 

used in this table.) The difference between health 

expectancies is given in column 6, and the approximate 

standard error is given in column 7. The z statistics, shown 

in column 8, range from 14.93 for age group 0–4 years to 

0.94 for ages 85 years and over. The critical value of the 

z-score for a two-tailed test at the 95 percent level of 

significance is 1.96 (table 6). Because the computed 

z-statistics are larger than the observed z-score at all ages 

except at ages 85 years and over, the hypothesis that the 

HLE’s of white males and white females are equal is not 

accepted for all age groups except at age 85 years and over. 

Thus, the test shows that a significant difference exists 

between healthy life expectancies of white males and white 

females at all ages except 85 years and over. The z-statistics 

were also calculated using the binomial estimate of the 

standard error (data not shown). In this example, the same 

conclusions resulted from the statistical tests using either 

method of estimating the standard error. 

Table 6. Critical values of the standardized normal variable z

Level of significance Level of significance z-critical 

for a two-tail test for a one-tail test values 

0.200 .................... 0.100 1.28 

0.100 .................... 0.050 1.645 

0.050 .................... 0.025 1.96 

0.020 .................... 0.099 2.33 

0.010 .................... 0.005 2.58 

0.002 .................... 0.001 3.09 

0.001 .................... 0.0005 3.29 

SOURCE: Murdoch and Barnes (34). 

Appendix

Selected publications related to healthy life expectancy: 

I. Publications on methodology

A. Theoretical publications 

1. Mathematical modeling (35) 

2. Validity tests (36) 

3. Choosing the appropriate measures (37) 

4. Global disability indicators (38) 

5. Mental health indicators (39) 

6. New methods (40) 

B. Theoretical background and policy implications 

1. Quality of life (41, 42) 

2. Life tables and Sullivan’s method (43) 

-9-
3. Population health leading indicators (44) 

4. Issues related to health measures (45, 46) 

5. Policy implications of measures (47) 

6. Measures of health in the 1990s (48) 

II. Empirical publications

A. Healthy life 

1. Years of healthy life (49) 

2. Healthy life expectancy (50) 

3. Healthy aging (51) 

B. Life without disability 

1. Disability-free life expectancy (52) 

2. DFLE among the elderly (53) 

3. Disability-adjusted life expectancy (54) 

C. Active life 

1. Active life expectancy (55) 

2. Educational status and active life expectancy (56) 

3. Active life expectancy in older populations (57, 58) 

4. Causes of death and active life expectancy (59) 

D. Health status, morbidity, and life expectancy 

1. Health status and life expectancy (60) 

2. Longevity and expansion of morbidity (61). 

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Number Title Date of Issue 

Healthy People 2000

2 Infant Mortality Winter 1991 

6 Direct Standardization (Age-Adjusted Death Rates) March 1995 

7 Years of Healthy Life April 1995 

19 Healthy People 2000: An Assessment Based on the Health Status November 2000 

Indicators for the United States and Each State 

Healthy People 2010

20 Age Adjustment Using the 2000 Projected U.S. Population January 2001 

NOTE: These issues of Healthy People Statistical Notes deal with statistical issues affecting the tracking of Healthy People 2010. 

- 11 -
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Suggested citation

Molla MT, Wagener DK, Madans JH. Summary 

measures of population health: Methods for 

calculating healthy life expectancy. Healthy People 

Statistical Notes, no. 21. Hyattsville, Maryland: 

National Center for Health Statistics. August 2001. 

DHHS Publication No. (PHS) 2001-1237 

1-0472 (8/01)