Methodological Issues

in Measuring Health

Disparities

Series 2,Number 141 July 2005
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Keppel K, Pamuk E, Lynch J, et al. Methodological issues in measuring health

disparities. National Center for Health Statistics. Vital Health Stat 2(141). 2005.

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Methodological issues in measuring health disparities.

p. ; cm. -- (DHHS publication ; no. (PHS) 2005-1341) (Vital and health

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Authors, Kenneth Keppel, et al.

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1. Health status indicators--United States--Measurement. 2. Social indicators-­

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National Center for Health Statistics

Edward J. Sondik, Ph.D., Director

Jennifer H. Madans, Ph.D., Acting Co-Deputy Director

Michael H. Sadagursky, Acting Co-Deputy Director

Jennifer H. Madans, Ph.D., Associate Director for Science

Edward L. Hunter, Associate Director for Planning, Budget,

and Legislation

Michael H. Sadagursky, Associate Director for

Management and Operations

Lawrence H. Cox, Ph.D., Associate Director for Research

and Methodology

Margot A. Palmer, Director for Information Technology

Margot A. Palmer, Acting Director for Information Services

Linda T. Bilheimer, Ph.D., Associate Director for Analysis

Epidemiology, and Health Promotion

Charles J. Rothwell, Director for Vital Statistics

Jane E. Sisk, Ph.D., Director for Health Care Statistics

Jane F. Gentleman, Ph.D., Director for Health Interview

Statistics

Clifford L. Johnson, Director for Health and Nutrition

Examination Surveys

Office of Analysis and Epidemiology

Diane M. Makuc, Dr.P.H., Acting Associate Director

Richard J. Klein, M.P.H., Acting Chief, Health Promotion

Statistics Branch
Contents

Abstract ................................................................................................. 1

Introduction ............................................................................................. 1

Measuring Disparity ..................................................................................... 1

Issues and Choices ...................................................................................... 2

Discussion ............................................................................................... 14

Conclusions ............................................................................................. 15

References .............................................................................................. 15

Text Tables

A. Differences between infant mortality rates by race and Hispanic origin of mother and selected reference points:

United States, 2000 ................................................................................. 3

B. Absolute and relative measures of disparity between the mortality rate for infants of mothers in four race and Hispanic

origin groups and the rate for infants of Asian or Pacific Islander mothers (the best group rate): United States, 2000 . . 4

C. Changes in the simple difference and the percentage difference between infant mortality rates for each of four race

and Hispanic origin groups and the rate for infants of Asian or Pacific Islander mothers (the best group rate):

United States, 1990 and 2000 ......................................................................... 4

D. Percentages of non-Hispanic white and Hispanic women aged 40 years and over by use of mammography within the

past 2 years: United States, 1990 and 1998 .............................................................. 6

E. Mean deviations from alternative reference points in the percentage of mothers without prenatal care during the first

trimester by race and Hispanic origin: Maine and Mississippi, 1997–99 ....................................... 8

F. Weighted mean deviations from alternative reference points in the percentage of mothers without prenatal care during

the first trimester by race and Hispanic origin: Maine and Mississippi, 1997–99 ................................ 9

G. Percentages of two hypothetical populations in fair or poor health by income level ............................. 10

H. Percentages in fair or poor health by income level and regression-based summary indices of disparity for three

hypothetical populations ............................................................................. 11

J. Summary indices of disparity for three hypothetical populations ............................................. 14

Figures

1. Percentages of non-Hispanic white and Hispanic women aged 40 years and over by use of mammography within the

past 2 years: United States, 2000 ...................................................................... 5

2. Percentages of mothers with no prenatal care in the first trimester by race and Hispanic origin: Maine and Mississippi,

1997–99 .......................................................................................... 8

3. Percentages of hypothetical population in fair or poor health by income level .................................. 11

4. Lorenz curve for a hypothetical population .............................................................. 12

5. Concentration curve for hypothetical population 1......................................................... 13

6. Concentration curve for hypothetical population 2......................................................... 13

iii
Objectives

This report discusses six issues that

affect the measurement of disparities in

health between groups in a population:

+ Selecting a reference point from

which to measure disparity

+ Measuring disparity in absolute or

in relative terms

+ Measuring in terms of favorable or

adverse events

+ Measuring in pair-wise or in

summary fashion

+ Choosing whether to weight

groups according to group size

+ Deciding whether to consider any

inherent ordering of the groups.

These issues represent choices that

are made when disparities are

measured.

Methods

Examples are used to highlight how

these choices affect specific measures

of disparity.

Results

These choices can affect the size

and direction of disparities measured at

a point in time and conclusions about

the size and direction of changes in

disparity over time. Eleven guidelines

for measuring disparities are presented.

Conclusions

Choices concerning the

measurement of disparity should be

made deliberately, recognizing that

each choice will affect the results.

When results are presented, the

choices on which the measurements

are based should be described clearly

and justified appropriately.

Keywords: Disparity c Statistics c

Race c Hispanic origin

Methodological Issues in

Measuring Health Disparities

By Kenneth Keppel, Ph.D., and Elsie Pamuk, Ph.D., National Center

for Health Statistics (NCHS); John Lynch, Ph.D., McGill University;

Olivia Carter-Pokras, Ph.D., University of Maryland School of

Medicine; Insun Kim, Dr.P.H., NCHS; Vickie Mays, Ph.D., M.S.P.H.,

University of California, Los Angeles; Jeffrey Pearcy, M.S., NCHS;

Victor Schoenbach, Ph.D., University of North Carolina School of

Public Health; and Joel S. Weissman, Ph.D., Harvard Medical School

Institute for Health Policy

Introduction

One of the goals of Healthy People

2010 is ‘‘to eliminate health disparities

among segments of the population,

including differences that occur by

gender, race or ethnicity, education or

income, disability, geographic location,

or sexual orientation’’(1). The U.S.

Department of Health and Human

Services Strategic Plan includes a goal

to eliminate disparities in health care (2)

and Congress mandated an annual

National Healthcare Disparities Report

(NHDR) (3). States have also adopted

the Healthy People 2010 goal to

eliminate disparities for selected

indicators of health (4). Each of these

initiatives entails an obligation to

measure disparities in health and to

monitor trends in disparities.

This report discusses six significant

issues that should be considered in

measuring disparities: first, the selection

of a reference point from which to

measure disparity (5); second,

measurement of disparity in absolute or

in relative terms (5); third, measurement

of disparity in terms of favorable or

adverse events (6,7); fourth,

measurement of disparity focusing on

individual groups in a pair-wise fashion

or focusing on a summary measure for

the domain that includes these groups

(8,9); fifth, choosing whether to weight

component groups when calculating

summary measures of disparity; and

sixth, choosing whether or not to

consider the order inherent in the

domains with ordered categories when

calculating summary measures of

disparity (6). These measurement

choices affect the way a disparity is

expressed, including the size and

direction of the disparity. Furthermore,

these choices have implications for

conclusions about changes in disparities

over time, as well as for conclusions

about differences in disparity across

different health indicators, geographic

areas, or populations. Different choices

can, and frequently do, lead to different

conclusions about disparities.

In addition to discussing these

issues, this report presents guidelines for

making measurement choices. These

guidelines provide a consistent

framework for describing the size and

direction of disparities; promote clear

communication about the nature of

disparities to policymakers and the

general public; and facilitate

comparisons of disparities over time and

across indicators, geographic areas, or

populations. There is no single, best

way to measure disparity that is

appropriate in all situations. The

strengths and limitations of different

choices are highlighted, and not all of

the guidelines presented here are

applicable in every situation.

Measuring Disparity

Indicators of health are measured in

terms of rates, percentages, proportions,

means, or other quantifiable measures

Page 1
Page 2 [ Series 2, No. 141

such as life expectancy. These measures

can be calculated for each group in a

domain of groups. A domain is a set of

groups defined in terms of a specific

characteristic of persons in a population.

Ideally, the set of groups is mutually

exclusive and exhaustive (that is, each

person in the population is assigned to

only one group, and all persons in the

population are assigned to a group). For

example, the domain of gender consists

of males and females.

Disparities become evident when

quantitative measures of health (rates,

percentages, etc.) are compared between

the groups in a domain. These measures

permit comparisons between groups

regardless of the number of persons in

the group. Disparities are frequently

measured between groups in a domain;

however, disparities can also be

measured from other reference points

such as the total population. The choice

of a reference point from which to

measure disparity is one of the critical

issues discussed below.

For the purposes of this discussion,

the following definition is proposed:

Disparity—The quantity that

separates a group from a specified

reference point on a particular

measure of health that is expressed

in terms of a rate, percentage,

mean, or some other quantitative

measure.

This definition provides the basis

for the direct measurement of disparities

in indicators of health between groups.

It also provides the basis for monitoring

changes in disparities over time, and for

making comparisons of disparities

across health-related indicators and

across geographic areas or populations.

In the interest of brevity the term ‘‘rate’’

is generally used in the discussion that

follows, but the principles discussed

apply to rates, proportions, percentages,

means, and other quantitative measures

of health.

This definition does not presume

that membership in a particular group is

necessarily the cause of any disparity

between groups. For example, the

disparity between males and females in

breast cancer death rates is largely due

to gender-specific genetic differences.

However, the gender disparity in

cigarette smoking might be due to a

variety of cultural, educational, and

economic factors related to gender.

Identification of the determinants of

disparity is beyond the scope of this

discussion.

Issues and Choices

Choosing a reference point

Disparities are measured from a

reference point.

Reference point—The specific

value of a rate, percentage,

proportion, mean, or other

quantitative measure from which a

disparity is measured.

Any one of the groups in a domain

could be chosen as a reference point

from which to measure disparity. The

group that represents the largest

proportion of the population might be

chosen (3). The rate for the largest

group is usually the most stable, but

there are frequently groups with rates

better than the rate for the largest group.

The most favorable group (hereinafter

referred to as the ‘‘best’’ group) rate

provides a convenient reference point

for comparing the disparity status of

other group rates because all differences

are in the same direction (7). Using the

group with the best rate as a reference

point has possible disadvantages. For

example, this group might change over

time or differ from place to place; or it

might be a very small population group,

thus making this group’s rate the least

stable. When there are only two groups

in a domain (gender, for example) or

only two groups of interest, the rate for

either group could be chosen as the

reference point. In these cases, the more

favorable group rate (the rate reflecting

better health status or less risk) is

usually chosen as the reference point.

Disparities also can be measured

relative to a reference point that is not a

specific group. The unweighted

arithmetic mean of the rates for the

groups in a domain could be employed

as a reference point. The mean is

employed in measures of variability

such as the mean deviation, the

variance, the standard deviation, and the

coefficient of variation. However, the

mean is influenced by outliers—group

rates that are substantially different from

the rates for most of the groups. Over

time, the mean of group rates is affected

by substantial changes in the rate for

any particular group.

Disparities can be measured relative

to the rate for the total population

represented by the domain of groups.

The rate for the total population is a

weighted average of the group rates in a

domain (the group rates are weighted by

the proportion of persons in each

group). The total population rate is also

the mean for all individuals in the

population. The total population rate is

more stable than the other reference

points above, and unlike the mean of

group rates, it will have the same value

across all domains that encompass the

same population. However, the total

population also has limitations as a

reference point when comparisons are

made over time or across geographic

areas or populations using summary

measures. Changes in the total

population rate over time are a function

of changes in group rates as well as

changes in the distribution of persons

among groups. It can, therefore, be

difficult to distinguish the effects of

changes in group rates from changes in

group composition.

Disparities can also be measured

relative to a standard such as a Healthy

People target (1). The target can be

fixed for an extended period of time and

it has no sampling or other sources of

random variation associated with it.

Unlike the other reference points

discussed above, a target is chosen

through a deliberative process that may

involve the application of specific

criteria. If the targets for health

indicators are established using different

criteria, this should be taken into

consideration when disparities are

compared across indicators.

In table A, simple differences

between infant mortality rates by race

and Hispanic origin of the mother and

each of five possible reference points

are shown. These rates are based on the

2000 period linked birth/infant death

data set (10). For each race/ethnic group

the size of the difference depends on the

reference point from which it is

measured. For infants of Asian or
2000

Series 2, No. 141 [ Page 3

Table A. Differences between infant mortality rates by race and Hispanic origin of mother and selected reference points: United States,

Reference point1

Number Number Infant

Another

group rate

(Non-Hispanic

white)

5.7

Best group

rate (Asian

or Pacific

Islander)

4.9

Mean

of group

rates

7.6

Total

population

rate

6.9

Healthy

People

2010

target

4.5

Race and Hispanic origin of mother

of infant

deaths

of live

births

mortality

rate1 Difference1

American Indian or Alaska Native ..... 346 41,668 8.3 2.6 3.4 0.7 1.4 3.8

Asian or Pacific Islander ........... 977 200,544 4.9 –0.8 0.0 –2.7 –2.0 0.4

Hispanic ..................... 4,564 815,883 5.6 –0.1 0.7 –2.0 –1.3 1.1

Non-Hispanic black .............. 8,212 604,367 13.6 7.9 8.7 6.0 6.7 9.1

Non-Hispanic white .............. 13,461 2,362,982 5.7 0.0 0.8 –1.9 –1.2 1.2

1

Infant deaths per 1,000 live births.

SOURCE: National Vital Statistics System, linked birth/infant death data file.

Pacific Islander, Hispanic, and

non-Hispanic white mothers, the

direction (sign) of the difference also

depends on the reference point from

which it is measured.

The advantages and disadvantages

of each reference point depend on the

context in which disparities are being

measured. The choice of a reference

point also has implications for other

issues addressed in this report, such as

the measurement of disparities in

absolute or relative terms. It is not

possible to recommend a single reference

point for use in all situations. It is

essential to recognize, however, that the

choice of a reference point will determine

the size and direction of the disparity.

Guidelines 1 and 2

1. When disparities are measured, the

reference point should be explicitly

identified and the rationale for

choosing a particular reference

point should be provided.

2. If comparisons are made between

two groups, the more favorable

group rate should be used as the

reference point. (This would be the

lowest rate assuming that rates are

expressed in terms of adverse

events—see the following text.)

The first guideline is needed because the

nature of disparities cannot be

understood unless the point relative to

which they are measured is clearly

identified. The second guideline is a

recommendation that will contribute to

consistency in the measurement of

disparities.

Measuring disparity in absolute

and in relative terms

An absolute measure of disparity is

a simple arithmetic difference between a

group rate and a specified reference

point. An absolute measure of disparity

is expressed in the same units as the

rates themselves.

Simple difference = rate of interest–

reference point = Ri – Rr

In table A the simple difference was

calculated between the infant mortality

rate for mothers in each of five race or

ethnic groups and each of five possible

reference points.

A relative measure of disparity

expresses the difference between rates in

terms of the chosen reference point. The

percentage difference expresses the

simple difference from the reference

point as a percentage of the reference

point.

Percentage difference =

rate of interest – reference point c 100 = reference point

Ri – Rr

c 100 Rr

In a relative measure of disparity,

the reference point becomes the unit of

measurement. As with absolute measures

of disparity, the size and direction (sign)

of the disparity depends on which

reference point is selected.

Measuring disparity at a single point

in time

In table B both the simple

difference and the percentage difference

between the infant mortality rate for

mothers in each of four race or ethnic

groups and the rate for infants of Asian

or Pacific Islander mothers (the best

group rate) is shown.

When disparity is measured from

the same reference point, the simple

difference and the percentage difference

are perfectly correlated. The essential

difference between the two is in terms

of how the disparity is expressed.

Absolute and relative measures of

disparity from the same reference point

lead to the same conclusions about

disparities between groups. Both the

simple difference and the percentage

difference indicate that the largest

disparity is for infants of non-Hispanic

black mothers, and both indicate that the

disparity from the reference point for

non-Hispanic black mothers is about 2.5

times the disparity for infants of

American Indian or Alaska Native

mothers.

Measuring change in disparity over

time

Absolute and relative measures of

disparity can provide contradictory

evidence concerning changes in

disparity over time. In the upper panel

of table C the simple difference between

the mortality rate for infants of

non-Hispanic black mothers and the

reference point declined from 10.3 to

8.7 infant deaths per 1,000 live births

between 1990 and 2000. In the lower

panel the percentage difference between

the mortality rate for infants of

non-Hispanic black mothers and the

reference point increased from 156.1 to
Page 4 [ Series 2, No. 141

Table B. Absolute and relative measures of disparity between the mortality rate for infants Guideline 3

of mothers in four race and Hispanic origin groups and the rate for infants of Asian or

Pacific Islander mothers (the best group rate): United States, 2000 3. Disparities should be measured in

Absolute Relative

Infant

mortality Simple Percent

Race or ethnic group rate1 difference1 difference

Asian or Pacific Islander2 ........ 4.9 (

2

) (

2

)

American Indian or Alaska Native . . . 8.3 3.4 69.4

Hispanic ................... 5.6 0.7 14.3

Non-Hispanic black ............ 13.6 8.7 177.6

Non-Hispanic white ............ 5.7 0.8 16.3

1

Infant deaths per 1,000 live births.

2

The best group rate was used as the reference point.

SOURCE: National Vital Statistics System, linked birth/infant death data file.

177.6 percent between 1990 and 2000.

Different conclusions about the direction

of change are often observed when

absolute and relative measures of

disparity are compared over time.

In the example in table C the

discrepancy occurs because the relative

comparison adjusts for the decline in

infant mortality rates that occurred for

both non-Hispanic black mothers and

Asian or Pacific Islander mothers (the

group used as the reference point).

Depending on how the underlying rates

change, conclusions about changes in

disparity over time based on absolute

and relative comparisons may differ. If

rates were increasing rather than

decreasing, a decrease in a relative

measure of disparity might correspond

to an increase in an absolute measure of

disparity.

Expressing a disparity using a

relative measure has both advantages

and disadvantages that need to be

considered when choosing a reference

point. On one hand, changes in the

underlying rates are automatically

adjusted for. On the other hand,

information about the size of the change

in the underlying rates is not retained in

a relative comparison. Based on a

relative measure of disparity, for

example, the difference between one and

four deaths per 100,000 population is

the same as the difference between 100

and 400 deaths per 100,000

population—in both cases the second

rate is 300 percent greater than the first.

In absolute terms, the simple difference

between one and four deaths per

100,000 population is the same as the

simple difference between 401 and 404

deaths per 100,000 population.

both absolute and relative terms in

order to understand their magnitude,

especially when making comparisons

over time or across geographic areas,

populations, or indicators.

This guideline promotes a more

complete understanding of the

magnitude of disparities.

Comparing disparities across

geographic areas or populations

The disparity between a group rate

and a reference point in one geographic

area or population can be compared

with the disparity between a comparable

group rate and a comparable reference

point in another geographic area or

population. The disparity between men

and women in rates of death caused by

diseases of the heart could be compared

across two or more States, for example.

In such applications, conclusions based

on absolute and relative comparisons

will also depend on the underlying rates.

Comparisons based on both absolute and

relative measures are, therefore,

indicated.

Comparing disparities across different

indicators

The disparity between a group rate

and a reference point for one health

indicator can also be compared with the

disparity between a comparable group

Table C. Changes in the simple difference and the percentage difference between infant mortality rates for each of four race and Hispanic

origin groups and the rate for infants of Asian or Pacific Islander mothers (the best group rate): United States, 1990 and 2000

1990 2000

Race or origin group

Infant

mortality

rate1

Simple

difference1

Infant

mortality

rate1

Simple

difference1

Change

2000–19901

Asian or Pacific Islander2 ............... 6.6 (

2

) 4.9 (

2

) (

2

)

American Indian or Alaska Native .......... 13.1 6.5 8.3 3.4 –3.1

Hispanic .......................... 7.5 0.9 5.6 0.7 –0.2

Non-Hispanic black ................... 16.9 10.3 13.6 8.7 –1.6

Non-Hispanic white ................... 7.2 0.6 5.7 0.8 0.2

Percent Percent Change

difference difference 2000–19903

American Indian or Alaska Native .......... 13.1 98.5 8.3 69.4 –29.1

Hispanic .......................... 7.5 13.6 5.6 14.3 0.7

Non-Hispanic black ................... 16.9 156.1 13.6 177.6 21.5

Non-Hispanic white ................... 7.2 9.1 5.7 16.3 7.2

1

Infant deaths per 1,000 live births.

2

The best group rate was used as the reference point.

3

Change in percentage points.

SOURCE: National Vital Statistics System, linked birth/infant death data file.
Series 2, No. 141 [ Page 5

rate and a comparable reference point

for another health indicator. For

example, the disparity between men and

women in the rate of cigarette smoking

could be compared with the disparity

between men and women in rates of

death caused by lung cancer. Once

again, comparisons based on both

absolute and relative measures are

indicated because conclusions will

depend on the underlying rates. When

comparisons are made across indicators,

however, it is not possible to take

advantage of both absolute and relative

measures of disparity in all situations.

Absolute measures of disparity cannot

be compared across indicators that are

based on different units of measurement

(or across indicators that cannot be

converted to a common unit of

measurement). Relative measures, on the

other hand, can be used to make

comparisons across all indicators

regardless of the unit of measurement.

Measuring disparity in terms of

adverse events

Most health-related indicators can

be expressed either in terms of favorable

events or in terms of adverse events. A

favorable event or characteristic is

considered desirable and is promoted

through public health action. An adverse

event or characteristic is considered

undesirable, and reduction or elimination

is promoted through public health

action.

The utilization of mammography,

for example, can be expressed as a

favorable event (the percentage of

women who had a mammogram within

the past 2 years) or as an adverse event

(the percentage of women who did not

have a mammogram within the past 2

years).

The size of an absolute disparity

between a group and a reference point is

the same whether the indicator is

expressed in terms of favorable or

adverse events (although the sign

differs). The magnitude of a relative

disparity depends on the magnitude of

the reference point from which the

disparity is measured. The magnitude of

the reference point depends on whether

events. Therefore, both the size and

direction (sign) of a relative measure of

disparity depend on whether the

indicator is expressed in terms of

favorable or adverse events (6,7).

A simple example illustrates the

effect of expressing an indicator in

terms of favorable or adverse events on

absolute and relative measures of

disparity. On the left side of figure 1,

the percentage of non-Hispanic white

and Hispanic women 40 years and over

who had a mammogram within the past

2 years is shown based on data from the

National Health Interview Survey in

2000 (11). On the right side, the

percentage of women who did not have

a mammogram within the past 2 years is

shown for the same groups. The simple

difference between the two groups is

10 percentage points, whether the

comparison is based on the percentage

with a mammogram or the percentage

without a mammogram. As long as the

same reference point is used, the sign of

the difference changes, but the

magnitude of the difference between the

percentage of women who had a

mammogram and the percentage who

did not have a mammogram remains the

same.

However, when a relative measure

of disparity is employed, the magnitude

of the measure differs. On the left side

of figure 1, the percentage of

non-Hispanic white women who had a

mammogram is 16.1 percent greater than

the percentage of Hispanic women who

had a mammogram [(72 – 62) / 62 c

100 = 16.1 percent]. On the right side of

figure 1, the percentage of non-Hispanic

white women who did not have a

mammogram is 26.3 percent less than

the percentage of Hispanic women who

did not have a mammogram [(28 – 38) /

38 c 100 = –26.3 percent]. Not only the

sign (positive or negative) but also the

magnitude of the percentage difference

depend on whether it is computed based

on the percentage of women who had a

mammogram or the percentage who did

not have a mammogram. This will be

true whenever the reference point differs

from the exact midpoint of possible

values.

Conclusions about changes in

disparity over time also depend on

whether an indicator is expressed in

terms of favorable or adverse events (6).

Table D shows the percentage of women

who had a mammogram during the past

2 years and the percentage of women

who did not have a mammogram during

the past 2 years for non-Hispanic white

and Hispanic women in 1990 and 1998

(10). The simple difference between the

the indicator is expressed in terms of Figure 1. Percentages of non-Hispanic white and Hispanic women aged 40 years and over

favorable events or in terms of adverse by use of mammography within the past 2 years: United States, 2000
Page 6 [ Series 2, No. 141

Table D. Percentages of non-Hispanic white and Hispanic women aged 40 years and over by use of mammography within the past 2

years: United States, 1990 and 1998

Mammogram No mammogram

Year

Non-Hispanic

white

(Nhw)

Hispanic

(H)

Simple

difference

(Nhw–H)

Percent

difference

(Nhw–H)/H

x 100

Non-Hispanic

white

(Nhw)

Hispanic

(H)

Simple

difference

(Nhw–H)

Percent

difference

(Nhw–H)/H

x 100

Percent Percent

1990 ..................... 52.7 45.2 7.5 16.6 47.3 54.8 –7.5 –13.7

1998 ..................... 68.0 60.2 7.8 13.0 32.0 39.8 –7.8 –19.6

Percent change .............. 1

29.0 133.2 24.0 3–21.7 1–32.3 1–27.4 24.0 343.1

1

The percent change in the percent is calculated as follows: ((percent in 1998 – percent in 1990)/percent in 1990 x 100).

2

The percent change in the simple difference is calculated as follows: ((simple difference in 1998 – simple difference in 1990)/simple difference in 1990 x 100).

3

The percent change in the percent difference is calculated as follows: ((percent difference in 1998 – percent difference in 1990)/percent difference in 1990 x 100).

SOURCE: National Center for Health Statistics. Health, United States, 2004 With Chartbook on Trends in the Health of Americans. Hyattsville, MD: 2004.

percentage of non-Hispanic white and

Hispanic women who had a

mammogram during the past 2 years

increased from 7.5 percentage points in

1990 to 7.8 percentage points in 1998.

The simple difference also increased

from –7.5 percentage points to

–7.8 percentage points for women who

did not have a mammogram during the

past 2 years. However, changes in the

relative differences between Hispanic

and non-Hispanic white women were

not the same for both favorable and

adverse events. The percentage

difference between non-Hispanic white

and Hispanic women who had a

mammogram within the past 2 years

decreased from 16.6 percent in 1990 to

13.0 percent in 1998. A decrease in

disparity is indicated because the

percentage difference moved closer to 0.

The percentage difference between

non-Hispanic white and Hispanic

women who did not have a

mammogram within the past 2 years

increased from –13.7 percent in 1990 to

–19.6 percent in 1998. The percentage

difference moved further from 0,

indicating an increase in disparity.

In this example, both the magnitude

and direction of change in the relative

measure of disparity depend on whether

the indicator is expressed in terms of

favorable or adverse events. The

percentage difference between Hispanic

and non-Hispanic white women who

had a mammogram moved closer to 0

by 21.7 percent, and the percentage

difference between Hispanic and

non-Hispanic white women who did not

have a mammogram moved further from

0 by 43.1 percent. Similar results can

occur when comparisons are made

across different indicators, geographic

areas, or populations.

Several factors might influence the

choice to measure disparity in terms of

favorable or adverse events. It would

not be appropriate to compare the

relative disparity in one indicator

expressed in terms of favorable events

that occur frequently with the relative

disparity in a second indicator expressed

in terms of adverse events that occur

infrequently. In order to make

comparisons across different indicators,

all of the indicators should be expressed

in either adverse or favorable terms. In

addition, the results of relative

comparisons over time (or across

geographic areas or populations) depend

on whether differences are measured in

terms of favorable or adverse events.

Finally, it would be unusual to measure

the relative disparity for certain types of

health indicators in terms of favorable

events. Death rates are a good example.

The relative difference in survival rates

for some causes of death can become

almost negligible.

Expressing relative disparities in

terms of adverse events would enhance

the consistency and comparability of

relative measures of disparity across

indicators and over time.

Guideline 4

4. When relative measures of disparity

are employed to compare disparities

across different indicators of health,

all indicators should be expressed in

terms of adverse events.

This convention would have no effect

on absolute measures of disparity, and it

is not necessary for purposes of

monitoring changes in relative disparity

over time for a single indicator.

However, confusion concerning the

desired direction of change and the

meaning of changes in relative measures

of disparity over time could be avoided

by consistently expressing indicators in

terms of adverse events, conditions, or

behaviors that are to be reduced or

eliminated. In either case, it should be

clear whether the indicator is being

expressed in terms of favorable or

adverse events, and the reference point

should be clearly identified (guideline

1). Guideline 4 does not apply to health

indicators that are expressed in terms of

means (such as mean blood pressure) or

other quantitative measures (such as life

expectancy) that cannot be expressed in

adverse terms.

Measuring disparity in

pair-wise or in summary

fashion

When there are more than two

groups in a domain, one of the first

decisions to be made is whether the

focus of attention is on individual

groups or on the domain to which these

groups belong. Ideally, a domain

consists of a set of mutually exclusive

and exhaustive population groups that

are based on one or more characteristics

of persons in a population, such as

gender, race and ethnicity, urbanization

level, education, or income. Focusing on

the individual groups implies comparing

one group with another or comparing
Series 2, No. 141 [ Page 7

each component group with a single

reference point, measuring disparity for

each group in the domain. Focusing on

the domain implies quantifying the

degree of disparity across all groups

composing the domain.

Why focus on the domain in addition

to the individual groups?

Most policy and programmatic

applications of disparity measurement

will likely involve measuring disparity

for individual groups. Yet, there are

instances where focusing on disparity

within an entire domain may be not

only relevant but also more appropriate

than focusing on disparities measured

for each component group.

For example, some domains consist

of groups that are somewhat arbitrarily

defined and therefore not inherently

meaningful. Examples include domains

where the component categories are

ordered and reflect some amount of the

underlying dimension being measured,

such as education or income. The

category ‘‘persons with family incomes

between 200 and 300 percent of the

poverty threshold’’ may not be

inherently interesting as a group but

only as they relate to those with less or

more income. That is to say, in the

absence of a policy-related rationale,

few would object to changing this group

to ‘‘persons with incomes between 200

and 400 percent of poverty’’ if this

definition constituted a more statistically

reliable group and the other income

groups changed concomitantly.

It may also be desirable to focus on

disparity within the domain, in addition

to group-specific disparity, for domains

where the groups are inherently

meaningful but the defining aspect of

the domain is also meaningful in a

broader sense. This would characterize

most domains with unordered categories,

such as race and ethnicity. It would also

characterize some forms of ordered

domains, such as urbanization status,

where it could be argued that groups

such as ‘‘rural,’’ ‘‘suburban,’’ and

‘‘central city’’ are inherently meaningful.

Although we might well want to know

the amount of a health disparity of a

specific group, such as Asians and

Pacific Islanders or persons residing in

rural areas, we might also want to know

the extent of disparities within the

domains of ‘‘race’’ or ‘‘urbanization

level.’’

Drawing conclusions about the

amount of disparity within a domain by

examining the disparity for each group

can be difficult, especially if the domain

consists of several groups and the goal

is to make comparisons across health

indicators, across populations, or over

time. In order to measure disparity for a

domain, information on disparities for

the component groups needs to be

combined.

Measures that summarize disparity

for a domain

Measures that summarize disparity

for a domain reflect adding together the

disparities measured for the component

groups. Therefore, summary measures

for unordered groups are generally

analogous to the pair-wise measures

discussed in the preceding sections of

this report; all the issues discussed in

relation to pair-wise measures are

equally relevant to summary measures.

One critical distinction between

summary and pair-wise measures of

disparity is that the signs attached to

differences of each group from the

reference point are ignored when

constructing summary measures, either

by taking the absolute value or squaring

the differences.

In general, summary measures of

disparity for unordered groups are

similar in concept to traditional

measures of variability used in statistics,

such as the mean deviation and the

variance. If the arithmetic mean is used

as the reference point, and the absolute

group differences from the mean are

added together and divided by the

number of groups, the result is the mean

deviation. If the differences are squared

before adding them together and

dividing by the number of groups, the

result is the variance; taking the square

root of the variance yields the standard

deviation.

Other, nontraditional, measures of

disparity can be created by using the

same procedures but altering the

reference point. A mean deviation or

standard deviation can be computed

using differences from the best rate, the

rate for the largest group, the total

population rate, or from a predefined

target. In each procedure an absolute or

squared difference or deviation is

computed for each component group in

the domain; only the reference point

from which the deviation is computed is

changed.

Each procedure produces a

summary measure that expresses

disparity in absolute terms, retaining the

original units of measurement. Each

absolute summary measure can be

converted into a relative measure by

dividing by the reference point. When,

for example, the standard deviation is

divided by the arithmetic mean, the

result is the coefficient of variation, a

commonly used measure of relative

variation.

A summary measure of disparity

can be based on absolute or squared

deviations. Squared deviations give

greater weight to extreme values, and

extreme values may be related to sample

size as well as reflecting true disparity.

On the other hand, squared deviations

are easier to handle statistically than are

absolute values. An advantage of using

the standard deviation and the

coefficient of variation as the measures

of absolute and relative disparity is that

standard errors for these measures can

be obtained from standard statistical

software.

It is important to bear in mind that

all summarization involves a loss of

information. So, when summary

measures of disparity are used, the

implications of the choices made with

respect to how to measure disparity will

be less transparent to the audience than

with pair-wise measures.

As an example, figure 2 shows the

percentage of mothers not receiving

prenatal care in the first trimester of

pregnancy by race and Hispanic origin

in Mississippi and Maine for the years

1997–99. The range in the percentages

not receiving first trimester care across

race and Hispanic origin groups is

nearly identical in the two States. But,

in Maine the values for the three groups

between the extreme values are more

similar than in Mississippi.

Table E shows the mean absolute

deviation of the group rates of no first

trimester prenatal care computed from

different reference points for Maine and
Page 8 [ Series 2, No. 141

Figure 2. Percentages of mothers with no prenatal care in the first trimester by race and Hispanic origin: Maine and Mississippi, 1997–99

Mississippi. Using absolute deviations

from the group with the best rate

(which, in this case, is also the largest

group—non-Hispanic white women),

Mississippi has greater disparity (10.8)

than Maine (8.0). This is also true when

the mean absolute deviation is computed

from the mean of the group rates,

although the difference between the two

States is not as large (5.3 versus 4.2).

But using the percentage of all live

births in the State with no first trimester

care (the total rate) as the reference

point, Maine is shown to have greater

racial and ethnic disparity than

Mississippi (7.7 versus 5.7). Converting

the absolute measure to a relative

measure by dividing by the reference

point magnifies the differences between

these alternative measures of disparity.

Using the best group value as the

reference point, relative disparity in

Mississippi is 26 percentage points

higher than in Maine; using the value

for the total population as the reference

point, relative disparity in Maine is

40 percentage points higher than in

Mississippi; and using the mean as the

reference point indicates nearly equal

levels of disparity for the two States.

Why do the results for the summary

disparity measures vary so greatly

depending on the choice of reference

point? Ninety-five percent of all live

births in Maine are born to nonHispanic white women, so Maine’s total

rate is only slightly higher than the

non-Hispanic white rate, even though

lack of prenatal care is lowest for

non-Hispanic white births. In

Mississippi 53 percent of live births

were to non-Hispanic white women, and

43 percent were to non-Hispanic black

women; thus, the total rate in

Mississippi was 19.3 compared with

11.0 in Maine. As a result, using the

total rate as the reference point

produces, on average, larger group

differences for Maine than for

Mississippi. For Maine, the summary

disparity measure based on deviations

from the best rate (that of non-Hispanic

whites) is very similar to the summary

measure based on deviations from the

Table E. Mean deviations from alternative reference points in the percentage of mothers without prenatal care during the first trimester

by race and Hispanic origin: Maine and Mississippi, 1997–99

Best rate Mean rate Total rate

Alternative values Maine Mississippi Maine Mississippi Maine Mississippi

Reference point .............. 10.5 10.6 18.5 21.4 11.0 19.3

Mean deviations

Absolute ................. 8.0 10.8 4.2 5.3 7.7 5.7

Relative.................. 76% 102% 23% 25% 70% 30%

SOURCE: National Vital Statistics System.
Series 2, No. 141 [ Page 9

total rate because non-Hispanic whites

constitute such a large proportion of the

total. But for Mississippi, the best rate

and the total rate are quite different.

Guidelines 5, 6, and 7

5. Pair-wise comparisons are called for

when the objective is to measure

disparity for each group in a domain.

6. Summary measures can be used to

quantify the degree of disparity

across all groups composing a

domain.

7. Conclusions based on summary

measures always should be

interpreted in conjunction with the

group-specific rates on which they

are based.

Choosing whether to weight

component groups when

calculating summary measures

of disparity

The comparison between Maine and

Mississippi highlights another issue to

consider when deciding how to

summarize disparity across a domain:

deciding whether to weight the group

values by the proportion of the

population they represent. Conceptually,

not weighting the group-specific values

maintains a perspective that focuses on

the individual groups. That is,

unweighted values imply that what is

important is the group itself, regardless

of its share of the population.

Weighting, on the other hand, offers a

population-based perspective on

disparity across a domain. Weighting

implies that the way the domain is

constituted within the overall population

is important. This approach is similar to

looking at absolute measures of

disparity, in that, weighted measures

provide more information about the

impact or consequences of disparity for

the population as a whole.

The implications of these two

approaches can be examined using the

example of no first trimester prenatal

care in Maine and Mississippi (table F).

The first thing to note is that weighting

by the proportion of live births

occurring in each race and Hispanic

origin group eliminates any distinction

between the mean and the total value

for all live births because the weighted

mean equals the total rate. Using either

the best group value or the total rate as

the reference point, the weighted mean

deviations show that racial and ethnic

disparity in prenatal care is greater in

Mississippi than in Maine. The greater

disparity in Mississippi reflects the fact

that non-Hispanic whites, with just over

50 percent of live births, have the lowest

rate of late or no prenatal care, and

non-Hispanic blacks, with just over

40 percent of live births, have the

highest rate. Thus, both extremes of the

distribution represent large shares of the

population of live births. This stands in

stark contrast to Maine, where only

5 percent of all live births occur to

groups other than non-Hispanic whites.

The decision of whether to weight

the component groups when

summarizing disparity across a domain

should take into consideration the reason

for computing the summary measure of

disparity as well as conceptual

considerations. It could be reasoned that,

conceptually, examining disparity among

unweighted racial and ethnic groups is

fairer and, therefore, more appropriate.

That is, it shouldn’t matter that the

group with the highest rate of

inadequate prenatal care in Maine

(American Indian or Alaska Native)

represents less than 1 percent of all live

births. A weighted summary measure

will indicate relatively little racial and

ethnic disparity in prenatal care in

Maine and will therefore obscure the

existence of the very high rate of

inadequate prenatal care among

American Indians, unless this rate is

otherwise highlighted. On the other

hand, it could be reasoned that,

compared with Maine, Mississippi has a

much harder task in attempting to

eliminate racial and ethnic disparity in

prenatal care, and summary measures

designed to influence broad policy

should reflect this burden aspect of

disparity.

The implications of using either

unweighted or weighted group values

when calculating a summary measure of

disparity need to be carefully

considered. Not only does this decision

need to be evaluated with respect to the

purpose and application of the summary

measures, but the implications with

respect to other types of decisions (such

as the choice of a reference point)

should be considered. For example,

calculating a mean deviation from the

total population value produced

summary measures that showed Maine

as having greater racial and ethnic

disparity in prenatal care than

Mississippi, despite there being less

variation in the unweighted group rates

in Maine. Thus, combining unweighted

deviations from a weighted mean may

be as likely to create confusion as to

provide interpretable measures of

disparity.

Guidelines 8 and 9

8. The choice of whether to weight the

component groups when

summarizing disparity across a

Table F. Weighted mean deviations from alternative reference points in the percentage of mothers without prenatal care during the first

trimester by race and Hispanic origin: Maine and Mississippi, 1997–99

Best rate Mean or total rate

Alternative values

Reference point ..............

Weighted mean deviations:

Absolute .................

Relative..................

Maine

10.5

0.5

5%

Mississippi

10.6

8.4

80%

Maine

11.0

0.9

9%

Mississippi

19.3

9.0

47%

SOURCE: National Vital Statistics System.
Page 10 [ Series 2, No. 141

domain should take into

consideration the reason for

computing the summary measures.

In addition, implications with respect

to other types of decisions, such as

the choice of a reference point, need

to be considered.

9. The size of the groups and the

number of persons affected in each

group should be taken into account

when assessing the impact of

disparities.

Creating summary measures of

disparity for domains with

ordered categories

Deciding how to create a summary

measure of disparity becomes even more

complicated when the domain consists

of groups that represent ordered

categories of the characteristic

determining the domain, such as level of

income or level of education. With

domains consisting of ordered groups,

the first decision to be made is whether

to consider the order inherent in the

domain.

Table G shows two hypothetical

populations divided into four income

groups. In population 1, the percentage

in fair or poor health declines steadily

with increasing income. Population 2

has the same set of group values for fair

or poor health, but the values are

ordered differently across the groups so

that the decline in fair or poor health is

no longer monotonic with increasing

income. The question to consider is

whether income-related disparity in this

health indicator should be considered

the same for both populations. Would

we want to indicate that income-related

disparity in health is identical if these

populations represented geographic areas

(such as States) or population subgroups

(such as non-Hispanic whites and

Hispanics) or if they represented the

same population at two different points

in time? If the types of summary

measures discussed in the previous

section are applied to these data, these

two populations would appear to have

the same amount of income-related

disparity in fair or poor health. The

major argument for taking the inherent

order of the groups into account when

measuring disparity for ordered domains

(especially domains reflecting

socioeconomic status) is that interest

generally lies in how health varies with

the amount of the characteristic defining

the domain, not with the groups

themselves.

Similarly, it can be argued that

weighting groups by population size is

more appropriate for domains with

ordered groups, especially those

reflecting socioeconomic status, than for

other types of domains. As mentioned

above, income and education groups are

perhaps more appropriately thought of

as categories reflecting the amount of

income or education that persons have.

Thus, the groups within these domains

differ by the amount of the defining

characteristic, and categories can be

formed by cutting the distribution at any

number of points. Weighting the

categories by their population size helps

compensate for the somewhat arbitrary

nature of category formation for these

variables. Another argument for

weighting summary measures of

disparity for socioeconomic domains is

that they differ from most other domains

when viewed from a policy perspective.

Unlike other domains where health

disparity is a concern (such as sex and

race and ethnicity) the distribution of

the population across socioeconomic

categories can be influenced by policy.

And, although changing the underlying

distributions of income and education

Table G. Percentages of two hypothetical populations in fair or poor health by income

level

Near Middle High

Population Poor poor income income

1 ....................... 30 20 15 5

2 ....................... 30 20 5 15

may not be the intention or focus of

public health policy, it may well be

important to know how changing

socioeconomic distributions influence

health disparities. For example, from a

policy perspective, it could be important

to know if education-related disparity in

obesity declines over 10 years as a

result of a greater percentage of

individuals achieving higher levels of

education, even though the obesity rates

within education-level remain the same.

Over the last two decades, a

considerable amount of work has been

done to develop and apply summary

measures of socioeconomic disparity in

population health that address the

unique aspects of these domains. One

approach has been to use regressionbased measures to summarize disparity

(5,12–14). Conceptually, this approach

can be viewed as a logical extension of

the usual form of graphical presentation

of health indicators by categories of

education or income.

Regression-based measures retain

the inherent order of the categories (like

the usual graphical presentation), but

they incorporate the population weights

of the categories. The size of each

category is taken into account by

placing the groups on an axis that

reflects the cumulative proportion of the

population represented by the ordered

groups. As shown in figure 3, income

levels are ordered from lowest to

highest level of income, and the width

of each bar reflects the proportion of the

total population having that level of

income. The value of the health

indicator—in this case the percentage in

fair or poor health—for each income

category is plotted at the midpoint of

the relevant bar.

An absolute summary index of

disparity is formed using regression to

fit a straight line to these percentages

(figure 3). The slope of this line,

referred to as the Slope Index of

Inequality (SII), can be interpreted as

the average change in the percentage in

fair or poor health over the entire

population ordered by level of income

(15,16). Thus, for the hypothetical

population 1, the SII of –22 (table H)

NOTE: Income levels are defined as a percentage of the poverty threshold. Poor is income less than 100 percent of the poverty indicates that the percentage with fair or threshold. Near poor is 100 to less than 200 percent of the poverty threshold. Middle income is between 200 and less than 400 poor health declines by an average of

percent of the poverty threshold. High income is 400 percent or more of the poverty threshold.
22 percentage points over the population

ranked from lowest to highest income.

With the socioeconomic groups ordered

from lowest to highest, the sign of the

slope will be negative when the health

indicator declines with increasing

education or income, positive when it

increases as the value of the

socioeconomic variable increases, and

will go to 0 when there is no consistent

relationship with the socioeconomic

variable.

Because the x-axis is the cumulative

proportion of the population, and

therefore goes from 0 to 1, the entire

population is the unit over which the

slope changes. This means that the slope

is the difference between the value of X

at 1 (the theoretical highest income

individual) and the value of X at 0 (the

theoretical lowest income individual).

Viewed in this manner, the SII is similar

to the most common way of looking at

disparity, that is, calculating the excess

adverse health in the lowest ranked

group compared with the highest ranked

group. The advantage of the SII as a

summary measure is that it incorporates

the health values for all groups and the

proportion of the population they reflect.

A relative version of the slope

index, referred to as the Relative Index

of Inequality (RII), can be formed in

one of two ways, denoted as RII(mean)

and RII(ratio). The slope index can be

divided by the mean of the weighted

group values, which is equivalent to

dividing by the value of the health

indicator for the total population. Thus,

the RII(mean) formed by dividing the

slope index by the mean is a ratio of the

absolute measure of disparity (the SII)

to the population value of the health

indicator. For population 1, the

RII(mean) of –1.54 (table H) means that

the SII is just over one and one-half

times the percentage in fair or poor

health for the population as a whole

(14.5 percent). This method of forming

the relative index is analogous to the

relative versions of summary measures

for unordered groups, discussed

previously.

A relative measure of disparity can

also be formed by dividing the value of

Y at the intercept (X = 0) by the value of

Y at X = 1. This form of the relative

index, the RII(ratio), has intuitive appeal

for audiences familiar with health

research literature that extensively

employs rate ratios and odds ratios

when comparing groups. It also forms

an intuitive relative complement to the

absolute measure of disparity because

the slope itself (the SII) is the difference

Figure 3. Percentages of hypothetical population in fair or poor health by income level

Table H. Percentages in fair or poor health by income level and regression-based summary indices of disparity for three hypothetical

populations

Income level

Population 1 Population 2 Population 3

Percent in

fair or

poor health

Proportion

of

population

Percent in

fair or

poor health

Proportion

of

population

Percent in

fair or

poor health

Proportion

of

population

Poor1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 0.05 30 0.05 30 0.2

Near poor2 . . . . . . . . . . . . . . . . . . . . . . . . 20 0.15 20 0.15 20 0.2

Middle income3. . . . . . . . . . . . . . . . . . . . . . 15 0.60 5 0.60 15 0.4

High income4 . . . . . . . . . . . . . . . . . . . . . . . 5 0.20 15 0.20 5 0.2

Regression-based summary index of disparity

SII5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . –22 –10 –29

RII6

(mean) . . . . . . . . . . . . . . . . . . . . . . . . –1.54 –0.94 –1.70

RII6

(ratio) . . . . . . . . . . . . . . . . . . . . . . . . . 7.7 2.8 12.5

1

Poor is income less than 100 percent of the poverty threshold.

2

Near poor is 100 to less than 200 percent of the poverty threshold.

3

Middle income is between 200 and less than 400 percent of the poverty threshold.

4

High income is 400 percent or more of the poverty threshold.

5

SII is Slope Index of Inequality.

6

RII is Relative Index of Inequality.

Series 2, No. 141 [ Page 11
between the predicted value of Y at

X = 1 and the predicted value of Y at

X = 0 but avoids the negative sign

associated with the difference. The

RII(ratio) for population 1 (see table H)

indicates that the regression-predicted

percentage in fair or poor health at the

lowest point on the income distribution

(27.3) is 7.7 times the predicted value at

the highest point (3.3). It should be

recognized, however, that the RII(ratio)

will tend to amplify differences in

disparity between populations compared

with the RII(mean).

Because regression analysis can

take so many forms, there have been

other adaptations of the original

formulation (the use of logistic (17,18)

and Poisson regression models (19), for

example) that researchers deemed more

appropriate to their particular analyses

and data. But the underlying conceptual

model remains the same over all these

various formulations. For the

hypothetical examples discussed here,

the SII and RII are calculated by fitting

a linear regression line to the

category-specific values by means of

weighted least-squares, with the weights

being the proportion of the population in

each category.

The implications of using summary

measures of disparity that retain the

inherent order of the categories are

demonstrated by comparing the SIIs and

RIIs for population 1 with those for

population 2 (table H). This comparison

demonstrates what happens in the case

of the hypothetical reversal of rates in

the two highest income categories. If the

percentage in fair or poor health is

greater among persons in the highest

income category than among persons

with middle incomes (as in population

2), the slope decreases, both absolutely

and relatively, indicating a reduction in

income-related disparity.

Table H also shows the effect of

changing the income distribution on

these regression-based indices of

disparity. Comparing population 3 with

population 1 shows that an increase in

the proportion of the population that is

poor or near poor (with a proportionate

reduction in the proportion of the

population in the middle income range)

raises the SII and RII, even if the

income category-specific rates remain

the same. The increase in these disparity

measures reflects the greater proportion

of the population experiencing higher

rates of fair or poor health compared

with population 1.

An alternative approach to

summarizing socioeconomic disparities

in health is based on adapting the

Lorenz curve approach to measuring

income inequality for individuals to the

measurement of health disparities across

ordered socioeconomic groups.

The Lorenz curve plots the

cumulative proportion of income

received by individuals in a population

proceeding from the lowest income

individual to the individual with the

highest income (see figure 4). By

looking at the curve, you can tell what

proportion of income is received by

each cumulative percentile of the

income distribution. Complete income

equality would be described by a

diagonal line, indicating, for example,

that the bottom 20 percent of the

population received 20 percent of total

income, and the bottom half received

50 percent of total income. The Gini

coefficient, the most common summary

measure of income inequality, is the

area between the Lorenz curve and the

diagonal expressed as a proportion of

the total area under the diagonal. Values

closer to 0 indicate less income

inequality, and values closer to 1

indicate high levels of inequality.

Adapting income inequality

measures to apply to socioeconomic

health disparities implies using the

socioeconomic groups—rather than

individuals—and plotting the cumulative

proportion of the population obtained

when the groups are ordered by

socioeconomic level along the X axis.

For example, figure 5 shows the income

groups for our hypothetical population 1

ordered along the X axis. The Y axis

represents the cumulative proportion of

the population reflecting the health

indicator—in our example, the

cumulative proportion of the population

in fair or poor health.

The curve that is generated by this

plot is referred to as the concentration

curve (rather than a Lorenz curve), and

the summary index of disparity derived

from this curve is known as the

concentration index (C). The

concentration index is 2 times the net

area between the curve and the diagonal

(13). The concentration index is a

measure of relative disparity, but an

absolute version can be calculated by

using the actual cumulative number of

health events rather than their

cumulative proportion (13).

If the values of the health indicator

decline uniformly with increasing

Figure 4. Lorenz curve for a hypothetical population

Page 12 [ Series 2, No. 141
Figure 5. Concentration curve for hypothetical population 1

socioeconomic level, all points defining

the concentration curve will lie above

the diagonal, and C will carry a negative

sign. If the values of the health indicator

increase uniformly with increasing

socioeconomic level, all points defining

the concentration curve will lie below

the diagonal, and C will have a positive

sign. If the health indicator does not

change monotonically with increasing

socioeconomic level, the curve can cross

the diagonal. When this happens, C will

move closer to 0 because that portion of

the area on the opposite side of the

diagonal will be subtracted. Thus, C

reflects the net area with a given sign.

For example, figure 6 shows the

concentration curve generated for the

hypothetical population 2 and

demonstrates what happens in the case

of a reversal of rates in the two highest

income categories (compared with

population 1).

Because the percentage in fair or

poor health is now greater among

persons in the highest income category

than among persons with middle

incomes, the concentration curve crosses

the diagonal and the net area with the

negative sign decreases compared with

population 1. The value of C is now

disparity in fair or poor health across

income groups.

Table J shows C and the RII

(formed by dividing the SII by the

mean) for all three hypothetical

populations described previously. Both

measures indicate that relative income

disparity in fair or poor health is least

for population 2 and greatest for

Series 2, No. 141 [ Page 13

population 3, differing from population

1 by similar relative amounts.

The similarity between the results

obtained from the two measures is not

merely fortuitous. Wagstaff and

colleagues identified the straightforward

mathematical relationship between C

and the RII(mean) (13). Both the slope

of the regression line and the

concentration index are based on the

weighted covariance of X and Y, where

X is the ranked cumulative population

and Y is the health indicator.

Multiplying the RII by twice the

weighted variance of X produces the

concentration index.

Therefore, the choice between the

regression-based and the concentration

curve-based approaches to summarizing

socioeconomic disparity in health

depends primarily on practical

considerations rather than on conceptual

differences. In some instances, the

visual comparison of disparity between

two or more populations or two or more

points in time can be simpler and more

intuitive with graphs of concentration

curves than with graphs of regression

slopes, especially if the actual values of

the health indicator are included on the

figure as the data points through which

the regression line is fitted. On the other

hand, regression-based measures are

likely to be more intuitively meaningful

closer to 0, indicating a reduction in the Figure 6. Concentration curve for hypothetical population 2
Page 14 [ Series 2, No. 141

Table J. Summary indices of disparity for three hypothetical populations

Summary index of disparity Population 1 Population 2

Concentration index ( C ) ........ –0.20 –0.12

RII1 (mean) ................. –1.54 –0.94

Population 3

–0.26

–1.70

+

to understand changes over time

more completely.

Disparities are measured in terms of

adverse events in order to facilitate

comparisons across indicators.

1

RII is Relative Index of Inequality.

to persons concerned with public health.

This, combined with inclusion of

regression procedures in software

commonly used by health researchers,

probably accounts for the larger number

of studies that have used the SII or RII.

Guideline 10

10. When the primary interest is in

how health varies with the amount

of the characteristic defining the

domain rather than with the groups

themselves, summary measures of

disparity that take into account the

order of groups should be

considered.

Precision of disparity measures

The precision of the statistics used

to measure disparity should also be

considered when these statistics are

interpreted. The precision of a measure

of disparity depends on the precision of

the estimated rates used to compute the

statistic. The precision of the rates

depends on sampling error or other

sources of random variation in the data

used to compute the rates.

Precision is usually expressed in

terms of the standard error of a statistic

or the width of a confidence interval

based on the statistic. The narrower the

confidence interval, the more precise the

estimate for a given level of confidence

will be. A 95-percent confidence interval

is frequently employed. The upper and

lower limits of a confidence interval can

be produced for the statistics used to

measure disparity whenever quantitative

estimates of variability (standard errors)

are available for the rates, percentages,

etc. on which these measures of

disparity are based.

Guideline 11

11. Whenever possible, a confidence

interval should accompany each

measure of disparity.

In general, the upper and lower limits of

a 95-percent confidence interval for a

statistic are calculated as:

Lower limit = S – (1.96 c SEs)

Upper limit = S + (1.96 c SEs)

where S is the point estimate for a

statistic, and SES is the standard error

for the estimate of S. Estimates of

precision for summary measures can be

produced using a re-sampling or

bootstrap procedure whenever standard

errors are available for the underlying

rates (20). This procedure uses the rate

and standard error for each group to

re-estimate each group rate many times

assuming a random normal distribution.

Based on these group rates, the same

number of summary measure estimates

is generated, and the distribution of

these estimates is used to compute a

standard error for the summary measure.

Confidence limits for the summary

measure are then computed as shown

above.

Techniques for testing the statistical

significance of differences between rates

and differences in measures of disparity

are described elsewhere (7,8,21,22).

Discussion

The definition of disparity in terms

of differences in group rates is

consistent with the second goal of

Healthy People 2010, ‘‘to eliminate

health disparities among segments of the

population, . . .’’(1). In Healthy People

2010 the following choices have been

made concerning the measurement of

disparities (7):

+ Disparities are measured from the

best group rate in each domain to

emphasize the potential for

improvement.

+ Disparities are measured in both

absolute and relative terms to

emphasize the difference between

absolute and relative differences and

+ Pair-wise measures are used to

monitor progress toward the

elimination of disparity for

individual groups, and summary

measures are used to monitor

progress toward the elimination of

disparity for each domain of three or

more groups (race and ethnicity,

education, and income).

+ Component groups are not weighted

when summarizing disparity across a

domain. However, the size of the

groups is considered when assessing

the impact of disparities.

+ In the interest of simplicity and

consistency, summary measures are

estimated the same way for domains

with ordered and unordered groups.

The choices that are appropriate for

monitoring progress toward the

elimination of disparity in Healthy

People 2010 may not be appropriate in

other situations. The best group rate

cannot be used as a reference point

when it is not reliable because of small

numbers. Absolute differences in rates

cannot be compared across indicators

based on different units of measurement.

Indicators such as mean blood pressure

or life expectancy cannot be expressed

in terms of adverse events. And

comparison of summary measures of

disparity across indicators depends on

comparability in the number of groups

and in the assignment of persons to

groups.

In this report, the words ‘‘disparity’’

and ‘‘difference’’ are used

interchangeably. In common usage,

however, disparity frequently connotes a

negative judgment or inequity. Indeed,

judgments are needed to identify

disparities that require public health

action. The absolute size of a disparity

is not a sufficient basis for taking

action. The absolute difference between

1 and 4 deaths per 100,000 may not

have the same meaning as the difference

between 401 and 404 deaths per

100,000. The relative size of a disparity

is also not sufficient. A relative

difference of 10 percent in the
Series 2, No. 141 [ Page 15

percentage of women who did not have

a mammogram may not have the same

meaning as a 10 percent difference in

infant mortality rates. Nor is the

statistical significance of a disparity

sufficient. In sample surveys, for

example, drawing a larger sample or

combining years of data can change a

nonsignificant difference into a

significant difference. A deliberative

process involving a review of what is

known about the determinants of the

observed disparity is needed to identify

disparities that are inequitable (23,24).

Conclusions

In this report disparity is defined as

the difference between a group and a

reference point—expressed in terms of a

rate, percent, proportion, or some other

quantifiable measure. The effects of

different choices on measures of

disparity were examined. Based on this

discussion, 11 guidelines concerning the

measurement of disparity are proposed.

These guidelines do not prescribe a

single way to measure disparity, they are

not applicable in all situations, and they

are not applicable to all of the ways that

differences in indicators of health are

measured. Nevertheless, these guidelines

are intended to bring greater consistency

to the examination of disparities as a

function of differences between groups

in quantifiable indicators of health.

Guidelines for Measuring

Disparities in Terms of

Differences Between One

or More Group Rates and

a Reference Point

1. When disparities are measured, the

reference point should be explicitly

identified and the rationale for

choosing a particular reference

point should be provided.

2. If comparisons are made between

two groups, the more favorable

group rate should be used as the

reference point. (This would be the

lowest rate assuming that rates are

expressed in terms of adverse

events—see guideline 4 below.)

3. Disparities should be measured in

both absolute and relative terms in

order to understand their

magnitude.

4. When relative measures of disparity

are employed to compare

disparities across different

indicators of health, all indicators

should be expressed in terms of

adverse events.

5. Pair-wise comparisons are called

for when the objective is to

describe disparities between one or

more individual groups and a

specific reference point.

6. Summary measures can be used

when disparities are measured for a

domain of several groups and

comparisons are to be made over

time or across indicators,

geographic areas, or populations.

7. Conclusions based on summary

measures always should be

interpreted in conjunction with the

group-specific rates on which they

are based.

8. The choice of whether to weight

the component groups when

summarizing disparity across a

domain should take into

consideration the purpose and

application of the summary

measures. In addition, implications

with respect to other types of

decisions, such as the choice of a

reference point, need to be

considered.

9. The size of the groups and the

number of persons affected in each

group should be taken into account

when assessing the impact of

disparities.

10. When the primary interest is in

how health varies with the amount

of the characteristic defining the

domain, rather than with the groups

themselves, summary measures of

disparity that take into account the

order of groups should be

considered.

11. Whenever possible, a confidence

interval should accompany each

measure of disparity.

References

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hhsplan/

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Vital and Health Statistics

series descriptions

SERIES 1. Programs and Collection Procedures—These reports

describe the data collection programs of the National Center

for Health Statistics. They include descriptions of the methods

used to collect and process the data, definitions, and other

material necessary for understanding the data.

SERIES 2. Data Evaluation and Methods Research—These reports

are studies of new statistical methods and include analytical

techniques, objective evaluations of reliability of collected

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also include experimental tests of new survey methods and

comparisons of U.S. methodology with those of other

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the expository types of reports in the other series.

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registration laws and revised birth and death certificates.

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vital and health statistics with those of other countries or

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care utilization. They are based on data collected in a

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SERIES 11. Data From the National Health Examination Survey, the

National Health and Nutrition Examination Surveys, and

the Hispanic Health and Nutrition Examination Survey—

Data from direct examination, testing, and measurement on

representative samples of the civilian noninstitutionalized

population provide the basis for (1) medically defined total

prevalence of specific diseases or conditions in the United

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(2) analyses of trends and relationships among various

measurements and between survey periods.

SERIES 12. Data From the Institutionalized Population Surveys—

Discontinued in 1975. Reports from these surveys are

included in Series 13.

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reports contain statistics on health resources and the public’s

use of health care resources including ambulatory, hospital,

and long-term care services based on data collected directly

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Discontinued in 1990. Reports on the numbers, geographic

distribution, and characteristics of health resources are now

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systems of the National Center for Health Statistics.

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