Methods for Measuring Cancer Disparities:

Using Data Relevant to Healthy People 2010

Cancer-Related Objectives

Sam Harper

John Lynch

Center for Social Epidemiology and Population Health

University of Michigan

Current contact information:

Department of Epidemiology, Biostatistics and Occupational Health

McGill University, Purvis Hall

Montreal QC H3A 1A2

Email: sam.harper@mcgill.ca / john.lynch@mcgill.ca

Phone: (514) 398–6261

Fax: (514) 398–4266

This report was written under contract from the Surveillance Research Program (SRP) and the Applied

Research Program (ARP) of the Division of Cancer Control and Population Sciences of the National

Cancer Institute, NIH. Additional support was provided by the Office of Disease Prevention in the Office

of the Director at the National Institutes of Health. It represents the interests of these organizations in

health disparities related to cancer, quantitative assessment and monitoring of these disparities, and

interventions to remove them. NCI Project Officers for this contract are Marsha E. Reichman, Ph.D. (SRP),

Bryce Reeve, Ph.D. (ARP), and Nancy Breen, Ph.D. (ARP).
Table of Contents

iii

Executive Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Initiatives to Eliminate Health Disparities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Brief History of Measuring Disparities in the United States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Health Inequality and Health Inequity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Defining Health Disparities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Issues in Evaluating Measures of Health Disparity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Total Disparity vs. Social-Group Disparity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Relative and Absolute Disparities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Reference Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Social Groups and “Natural” Ordering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

The Number of Social Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Population Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Socioeconomic Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Monitoring Over Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Transfers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Subgroup Consistency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Decomposability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Scale Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Transparency/Interpretability for Policy Makers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
iv

Measures of Health Disparity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Measures of Total Disparity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Measures of Social-Group Disparity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Measures of Average Disproportionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Choosing a Suite of Health Disparity Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Summary Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Appendix: Example Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Figures

Figure S1. Absolute and Relative Gender Disparity in Stomach Cancer Mortality, 1930–2000 . . . . . . . . . . 1

Figure S2. Proportion of Women Age 40 and Over Who Did Not Receive a Mammogram in the

Past 2 Years by Level of Educational Achievement, 1990–2002, Trends in Absolute and

Relative Disparity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Figure 1. Lung Cancer Mortality, Females, U.S., 1995–1999 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Figure 2. Lung Cancer Incidence by Gender and Race/Ethnicity, 1992–1999 . . . . . . . . . . . . . . . . . . . . . . . . 8

Figure 3. Mean and 10th–90th Percentiles of Body Mass Index by Education, NHIS, 1997 . . . . . . . . . . . . 20

Figure 4. Hypothetical Distributions of Life Expectancy in Two Populations . . . . . . . . . . . . . . . . . . . . . . . 21

Figure 5. Absolute and Relative Gender Disparity in Stomach Cancer Mortality, 1930–2000 . . . . . . . . . . 22

Figure 6. Relative Risk (RR) of Incident Cervical Cancer Among Hispanics According to Varying

Reference Groups, 1996–2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Figure 7. Age-Adjusted Incidence of Kidney/Renal Pelvis Cancer and Myeloma by Race and Ethnicity,

1996–2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Figure 8. Proportion of Men Reporting Recent Use of Screening Fecal Occult Blood Tests (FOBT),

by Race and Ethnicity, 1987–1998 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Figure 9. Percent Change in Population Size by Race and Hispanic Origin, 1980–2000 . . . . . . . . . . . . . . 28

Figure 10. Absolute and Relative Black-White Disparities in Prostate and Stomach Cancer Incidence,

1992–1999 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Figure 11. Example of a Simple Regression-Based Disparity Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Figure 12. Income-Based Slope Index of Inequality for Current Smoking, NHIS, 2002 . . . . . . . . . . . . . . . 40

Figure 13. Example of the Population-Attributable Risk Percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Figure 14. Disparity in Mammography Screening Among Racial/Ethnic Groups, NHIS, 2000 . . . . . . . . . 45

Figure 15. Age-Adjusted Lung Cancer Mortality by U.S. Census Division, 1968–1998 . . . . . . . . . . . . . . . . 46

Figure 16. Example of the “Disproportionality” of Deaths and Population, by Gender and Education,

2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Figure 17. Representation of the Gini Coefficient of Disparity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Figure 18. Representation of the Health Concentration Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Figure 19. Relative Concentration Curves for Educational Disparity in Obesity in New York State,

BRFSS, 1990 and 2002 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Figure 20. Absolute Concentration Curves for Educational Disparity in Obesity in New York State,

BRFSS, 1990 and 2002 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Figure A1. Proportion of Women Age 40 and Over Who Did Not Receive a Mammogram in the

Past 2 Years by Educational Attainment, 1990–2002 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Figure A2. Trends in Education-Related Disparity and Prevalence for the Proportion of Women

Age 40 and Over Who Did Not Receive a Mammogram in the Past 2 Years, 1990–2002 . . . . . . . . . . . . . . 69

Figure A3. Trends in Mortality from Colorectal Cancer by Race, Ages 45–64, 1990–2001 . . . . . . . . . . . . . 71

Figure A4. Racial Disparity Trends in Working-Age (45–64) Mortality from Colorectal Cancer

by Race, 1990–2001 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Tables

Table 1. Incidence of Esophageal Cancer, Ages 25–64 by Race, 12 SEER Registries, 1992–2000 . . . . . . . . . 44

Table 2. Commonly Used Disproportionality Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Table 3. Educational Disparity in Lung Cancer Mortality, 1999 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Table 4. Example of Extended Relative and Absolute Concentration Index Applied to the Change

in Educational Disparity in Current Smoking, Michigan, 1990 and 2002 . . . . . . . . . . . . . . . . . . . . . . . . . 56

Table 5. Summary Table of Advantages and Disadvantages of Potential Health Disparity Measures . . . . . 64

Table A1. Example of Relative and Absolute Concentration Index Applied to the Change in

Educational Disparity in Mammography, 1990 and 2002 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

Table A2. Example of Theil Index and the Between-Group Variance Applied to the Change in Racial

Disparity in Colorectal Cancer Mortality, 1990 and 2001 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

v

Executive Summary

1

Healthy People 2010 has two overarching goals: to

increase the span of healthy life and to eliminate

health disparities across the categories of gender,

race or ethnicity, education or income, disability,

geographic location, and sexual orientation (1).

This report raises some conceptual issues and

reviews different methodological approaches

germane to measuring progress toward the goal of

eliminating cancer-related health disparities (2).

Despite the increased attention to social

disparities in health, no clear framework exists to

define and measure health disparities. This may

create confusion in communicating the extent of

cancer-related health disparities and hinder the

ability of public health organizations to monitor

progress toward the Healthy People 2010 cancer

objectives. The recommendations in this report

are based on the following considerations: 

• Choosing a particular measure of health

disparity reflects, implicitly or explicitly, different

perspectives about what quantities or

characteristics of health disparity are thought to

be important to capture. For instance, most

research in health disparities is based on relative

comparisons (e.g., a ratio of rates), but it is equally

appropriate to make absolute comparisons (e.g.,

the arithmetic difference between rates). Figure S1

shows male/female disparities in stomach cancer

mortality during the 20th century. If we use an

absolute comparison (arithmetic difference in

rates), disparities have declined since about 1950;

if we use a relative comparison (ratio of rates),

they have increased almost continuously. This is

an example of how the same underlying data

potentially could generate two divergent

interpretations of trends in cancer-related health

Figure S1. Absolute and Relative Gender Disparity in Stomach Cancer Mortality, 1930–2000 

50

40

30

20

10

2.5

2.0

1.5

1.0

0.5

0.0

19301940195019601970198019902000

R t p 100 000 P p l ti

R l ti Di p ity

Females

Males

Relative Disparity

50

40

30

20

10

16

12

19301940195019601970198019902000

R t p 100 000 P p l ti

Ab l t Di p ity

Females

Males

Absolute Disparity

Figure S1. Absolute and Relative Gender Disparity in Stomach Cancer Mortality, 1930-2000
outcomes—dependent on which measure of

disparity is used.

• In this report, we adopt a “population health”

perspective on health disparities. A population

health perspective reflects a primary concern for

the total population health burden of disparities

by considering the number of cases of the cancerrelated health outcome (e.g., mortality, incidence,

screening, etc.) that would be reduced or

eliminated by an intervention. This perspective

emphasizes absolute differences between groups

and the size of the population subgroups

involved. We believe that such an approach offers

a justifiable basis on which to assess the total

population burden of disparity and thus provides

useful epidemiological input into decision making

about policy to reduce cancer-related health

disparities. This in no way precludes that there

may be other valid inputs into the policy-making

process that are based on different perspectives,

such as a purely relative assessment of cancerrelated health disparities. 

• To better monitor the population health

burden of disparities over time, disparity

indicators should be sensitive to two sources of

change: change in the size of the population

subgroups involved and change in the level of

health within each subgroup. For instance, social

policy can change both the number of people

who are poor and the behavior and health status

of the poor. 

Recommendations

We recommend using a sequence of steps,

described below, to assess health disparity. The

first step is to inform any assessment of health

disparity with a simple tabular and graphical

examination of the underlying “raw” data (rate,

proportion, etc., and subgroup population size).

This may provide valuable insights into the basic

question of whether the particular disparity has

increased or decreased over time. The graphical

presentation of the underlying data is depicted in

Figure S2 (page 3), which shows educational

disparity trends in the proportion of women not

having had a mammogram for the past 2 years.

If, as for Healthy People 2010, the goal is to

quantitatively monitor progress toward the

elimination of health disparities across all social

groups, then summary measures of health

disparity are warranted. Figure S2 also contains

two summary measures of health disparity—an

absolute measure, the Absolute Concentration

Index (ACI), and a relative measure, the Relative

Concentration Index (RCI). The choice of specific

summary measures also will be guided by whether

the groups have an inherent ranking (such as

education) or are unordered (such as gender). 

Choosing measures of health disparity

involves consideration of conceptual, ethical, and

methodological issues. This report discusses some

of these issues and provides recommendations for

a suite of measures that can be used to monitor

health disparities in cancer-related health

outcomes.

Our recommendations for measuring

disparity are:

1. To visually inspect tables and graphs of the

underlying “raw” data.

2
2. When the question involves only comparisons

of specific groups, then pairwise absolute and

relative comparisons may be sufficient. When the

objective is to provide a summary across all

groups, then the use of summary measures of

health disparity is warranted.

3. If the social group has a natural ordering, as

with education and income, then we recommend

using either the Slope Index of Inequality (SII) or

the Absolute Concentration Index (ACI) as a

measure of absolute health disparity, and either

the Relative Index of Inequality (RII) or the

Relative Concentration Index (RCI) as a measure

of relative disparity.

4. When comparisons across multiple groups that

have no natural ordering (e.g., race/ethnicity) are

needed, we recommend the Between-Group

Variance (BGV) as a summary of absolute

disparity, and the general entropy class of

measures, more specifically the Theil index and

the Mean Log Deviation, as measures of relative

disparity.

3

Figure S2. Proportion of Women Age 40 and Over Who Did Not Receive a Mammogram in the Past

2 Years by Level of Educational Achievement, 1990–2002, Trends in Absolute and Relative Disparity

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001* 2002

60

50

40

30

20

10

Pre alence Rate

–2

–4

–6

–8

–10

–12

–14

Concentration Inde

<8y 9–12y 12y 13–15y 16+y RCIx100 ACI

Relative Disparity [RCIx100]

Absolute Disparity [ACI]

igure S2. Proportion of Women Age 40 and Over Who Did Not Receive a Mammogram in the

 Past 2 Years by Level of Educational Achievement, 1990-2002, Trends in Relative Disparity

Source: CDC, Behavioral Risk Factor Surveillance Surveys 1990–2002. 

*Note: Question not asked in 2001.

Source: CDC, Behavioral Risk Factor Surveillance Surveys 1990–2002.

*Note: Question not asked in 2001.
5

Introduction

The goals of this report are to:

1. Highlight major issues that may affect the

choice of disparity measure.

2. Systematically review measures of health

disparity.

3. Provide a basis for selecting a “suite of

indicators” to measure disparities in screening,

risk factors, and other cancer-related health

objectives.

Initiatives to Eliminate Health

Disparities

In 1979, U.S. Surgeon General Julius B. Richmond

first conceptualized the idea for national public

health goals (3) and established specific public

health objectives for reducing mortality and

chronic illness in five age groups, which later were

to be implemented in 15 strategic areas during the

1980s (4). Building on this foundation, Healthy

People 2000 subsequently replaced the age-specific

goals of 1990 with three overarching goals for the

year 2000: increase the span of healthy life,

reduce health disparities, and provide access to

preventive health services (5). The explicit focus

on reducing health disparities in Healthy People

2000 represented an important step toward

establishing health disparities as a part of routine

public health surveillance. Establishing different

health targets for different social groups, however,

could be construed as implying that a group’s

health potential was somehow constrained by its

social-group membership, a factor over which

group members may have little or no control. For

example, the year 2000 target rate (per 100,000)

for cancer mortality was 130 for the total

population, but it was 175 for blacks. 

The implication of setting different targets

for different social groups was not lost on public

health policy makers or politicians. In a 1998

radio address that celebrated Black History

Month, President Clinton put forth a somewhat

more radical national public health goal: “By the

year 2010, we must eliminate racial and ethnic

disparities in infant mortality, diabetes, cancer

screening and management, heart disease, AIDS,

and immunization.” Racial and ethnic disparities

in these and other areas are extensive and well

documented, and given the context of their

origins in the United States, there is ample reason

to focus attention on their elimination. Similar

health disparities, however, are evident not just

between racial/ethnic groups but also between

other social and demographic groups, a fact that

now is reflected in the goals of Healthy People

2010 that specify eliminating health disparities by

gender, income and education, disability,

geographic location, and sexual orientation in

addition to race and ethnicity (1). Similar health

disparity targets also have been adopted by a

number of state and local health agencies (see

6,7,8). The Healthy People 2010 policy goals thus
represent an important shift toward “elimination,” and not just “reduction,” of existing health

disparities. 

The goal of eliminating health disparities also

implies that a systematic scientific framework

exists to measure health disparities and to

monitor them over time across multiple social

groups and measures of health status. We argue

that no such clear-cut consensus framework

currently exists in the United States, within either

the research or the policy communities as to how

health disparity should be measured. An

important first step toward the elimination of

health disparities is to carefully consider the

conceptualization of health disparity to better

understand what we mean by the term “health

disparity,” how we operationalize the concept of

“eliminating health disparity,” and how then to

apply appropriate health disparity monitoring

strategies.

Cancer-Related Goals of Healthy People 2010

The specific issues that motivate this project are

related to the Healthy People 2010 framework for

cancer-related goals, of which the overarching

goal is to “reduce the number of new cancer

cases as well as the illness, disability, and death

caused by cancer” (9, page 3-3). The objectives

for specific cancers are to reduce the rates of

melanoma, lung, breast, cervical, colorectal,

oropharyngeal, and prostate cancers, and, in

keeping with the goals of Healthy People 2010,

disparities in the above cancers and their major

risk factors also should be eliminated. Thus, this

report focuses on social-group and geographical

disparity in cancer-related outcomes such as risk

behaviors, screening, incidence, survival, and

mortality.

Figure 1 (page 7) is typical of the sort of

cancer-related data that motivate this project.

These data show socioeconomic and racial/ethnic

disparities in lung cancer mortality among U.S.

females for 1995–1999. Although these data help

to characterize disparity, they do not explicitly

quantify the extent or variability in disparity.

Several questions may be asked about this data.

For instance, is the socioeconomic disparity in

lung cancer mortality larger among Asian/Pacific

Islanders or blacks? Or is the racial/ethnic

disparity between non-Hispanic whites and blacks

larger than the socioeconomic differences within

each group? Additionally, variation exists in the

direction of the socioeconomic disparity in

different racial/ethnic groups. Among Hispanics,

the age-adjusted death rate increases as area

poverty decreases; among American Indian/Alaska

Natives, however, rates increase as area poverty

increases. Casual visual inspection of such graphs

reveals that there are differences between and

among groups. The challenge is whether we can

move beyond the simple recognition of such

differences (disparities) toward a strategy to

quantify their magnitude in a scientifically

reliable and transparent way that can be

understood by all stakeholders. This will be even

more important when monitoring changes in

disparity over time.

Figure 2 (page 8) shows the annual rate of

lung cancer incidence by race and gender for the

period 1992–1999. How should we summarize the

disparity in trends in lung cancer incidence? We

might focus on comparing pairs of rates over

6
7

Figure 1. Lung Cancer Mortality, Females, U.S., 1995–1999

A g A l Ag Adj t d D th R t p 100 000 P p l ti 40

30

20

10

American Indian/

Alaska Native

Asian/Pacific

Islander

on-Hispanic lack Hispanic

White

All Races

43.9

42.7

45.3

0.9 41.3

39.8 0.5

41.7

37.5

29.7

25.6

22.5

20.9

19.3

15.4

2.0

3.3

15.5

ercent of County Population Below Poverty Level in 1990

<10% 10% to 19.9% 20% or higher

Figure 1. Lung Cancer Mortality, Females, U.S., 1995-1999

Source: Gopal Singh et al. Area Socioeconomic Variations in U.S. Cancer Incidence, Mortality, Stage, Treatment, and Survival, 1975–1999, 200

Source: Gopal Singh et al. Area Socioeconomic Variations in U.S. Cancer Incidence, Mortality, Stage, Treatment, and Survival, 1975–1999, 2003.

time—e.g., the gap between white and

Asian/Pacific Islander females or between black

males and black females. As the number of groups

and years of data increase, however, there are

diminishing returns to such a strategy because of

the large number of possible pairwise comparisons

and the inherent difficulty in summarizing them.

For example, from Figure 2 in 1992, one could

calculate the following incidence ratios: black to

white males, 1.55; Asian/Pacific Islander to

American Indian/Alaska Native males, 2.11; black

to white females, 1.03; and Asian/Pacific Islander

to American Indian/Alaska Native females, 1.71.

The same comparisons in 1999 provide respective

ratios of 1.48, 2.29, 1.12, and 3.33. What can we

conclude about the racial disparity in lung cancer

incidence, given that incidence ratios are

decreasing for some comparisons (e.g., black vs.

white males) but increasing for others (e.g.,

Asian/Pacific Islander to American Indian/Alaska

Native males)? There is no clear way to summarize

the changes in these relative pairwise

comparisons. Therefore, in addition to seeing how

a particular social group’s cancer-related health

outcomes change with respect to another group,

we also may be interested in whether we are

making progress toward eliminating disparities

across all racial/ethnic or socioeconomic groups,
which is consistent with the overarching goals of

Healthy People 2010. That is, we may want to

know whether the disparity in lung cancer

incidence across all racial groups is decreasing.

How should we answer that question when there

are a multitude of pairwise and time-related

comparisons that can be made? Pairwise

comparisons have been the mainstay of

epidemiological effect measures and clearly are

central to disparity measurement, but there also is

a place for summary measures of overall disparity.

Brief History of Measuring Disparities

in the United States

Measuring Disparities in Public Health

This section briefly reviews selected historical

studies of social-group disparities in health

outcomes. Generally, the strong reliance in the

past on pairwise relative and, less frequently,

absolute disparity, and the difficulties such a 

8

Figure 2. Lung Cancer Incidence by Gender and Race/Ethnicity, 1992–1999

1992 1993 1994 1995 1996 1997 1998 1999

160

140

120

100

80

60

40

20

Rate per 100 000

Year of Diagnosis

Black Male

White Male

API* Male

Black Female

White Female

API* Female

AI/AN** Male

AI/AN** Female

Figure 2. Lung Cancer Incidence by Gender and Race/Ethnicity, 1992-1999

* API = Asian/Pacific Islander

** AI/AN = American Indian/Alaska Native

Source: Surveillance, Epidemiology, and End Results (SEER) Program SEER*Stat Database: 11

Registries, National Cancer Institute, DCCPS, Surveillance Research Program, Cancer Statistics Branch.

*API = Asian/Pacific Islander

**AI/AN = American Indian/Alaska Native

Source: Surveillance, Epidemiology, and End Results (SEER) Program (www.seer.cancer.gov) SEER*Stat Database: Incidence—Seer 11 Regs

Public-Use, Nov. 2001 Sub for Expanded Races (1992–1999), National Cancer Institute, DCCPS, Surveillance Research Program, Cancer

Statistics Branch. 
strategy may raise for a broader, more populationfocused understanding of health disparities and

their assessment over time, are emphasized. The

task of measuring disparity in public health

outcomes usually has been taken on by

epidemiologists, who tend to rely on relative risk

measures to characterize effect estimates (10). It is

interesting that few references can be found to

measuring health disparity per se in standard

epidemiological texts. In some ways this is not

surprising, but it helps to explain why standard

epidemiologic metrics, such as relative and

absolute risk differences, have been the general

method of choice applied to measuring health

disparity. A brief guide to health disparity

measurement can be found in a recent textbook

on epidemiologic methods in health policy (11),

but this topic is not addressed in more recent

foundational texts in either general epidemiology

(12,13) or social epidemiology (14). This is not to

suggest that more traditional epidemiologic

measures are not applicable to the measurement

and monitoring of health disparities, but that,

before choosing the methods to best capture

social concerns over the extent of health disparity

and before attempting to devise policies to

reduce/eliminate such disparities, one should be

aware that such measures have certain limitations.

These issues will be discussed in more detail later

in this monograph.

Trends in Social Group Health Disparities

Are health disparities increasing in the United

States? Despite consistent interest in social-group

disparities in public health, limited data provide

information on both social-group characteristics

and health at the national and local levels

(15–17). This in turn has resulted in a relatively

small number of studies of health disparity trends

for the United States as a whole. The landmark

study in the social epidemiology of mortality by

Kitagawa and Hauser (18), which involved a

special matching of 1960 death-certificate records

to the 1960 U.S. decennial census, serves as the

benchmark against which most socioeconomic

disparity trends are referenced. In that study,

Kitagawa and Hauser measured disparity in terms

of the standardized mortality ratio (SMR). The SMR

is calculated as the ratio of the number of

observed deaths to the number expected based on

the mortality rates of the United States as a whole.

If, for example, there is no educational disparity

among white males ages 25–64, then the number

of observed deaths in each educational group

should equal the number expected based on the

mortality rate for all white males ages 25–64,

corresponding to an SMR of 1.0. Kitagawa and

Hauser found, however, that the SMR for white

males ages 25–64 with less than 5 years of

education was 1.15 (i.e., 15% more deaths were

observed than were expected) and was 0.70

among those with a college degree (i.e., 30% fewer

deaths were observed than were expected).

Generally, Kitagawa and Hauser found that higher

socioeconomic position—whether measured by

income or education—was associated with lower

mortality and that mortality was higher among

nonwhite and nonmarried individuals.

Interestingly, they also reported that education

and income had independent effects—income

disparities existed within education groups and

educational disparities existed within income

groups. It is important to note that, in terms of

measuring disparity, this important study relied

on pairwise comparisons of specific groups to the

population average and did not use any summary

measure of disparity.

9
Health Disparities According to Income

Pappas and colleagues (19) used the National

Mortality Followback Survey (NMFS) from 1986 to

evaluate trends in education and income

disparities since Kitagawa and Hauser’s 1960

study. To use the information from all

socioeconomic groups, Pappas and colleagues

created a summary disparity measure. Similarly to

Kitagawa and Hauser, they calculated an SMR for

each socioeconomic group within gender and

racial categories based on the sex-race-specific

mortality rates for the entire United States. They

then took the absolute value of the difference

between each socioeconomic subgroup’s (e.g.,

those with <12 years of education) SMR and 1.0

and weighted it by the respective proportion of

the population in that socioeconomic subgroup.

Their index was the sum of these weighted

absolute differences across all subgroups; thus, a

value of 0.5 would be interpreted as the weighted

average deviation of the socioeconomic groups’

SMRs from 1.0. Pappas and colleagues found that

mortality disparities had increased since 1960 for

both whites and blacks, with steeper increases for

income as compared with education as the

measure of socioeconomic position. Thus, because

the sum of population-weighted SMR differences

for income increased more than for education,

they concluded that income-related disparities

increased more than educational disparities. Note

that because each group’s SMR was weighted by its

population share, an increase in disparity when

using this index could be observed even in the

absence of changes in subgroup-specific mortality

rates if the subgroups with the largest SMR

differentials increased their share of the

population. 

Duleep (20) used data linking the 1973

Current Population Survey (CPS) to Social Security

longitudinal mortality data up to 1978 and also

measured disparity by SMRs. Unlike Kitagawa and

Hauser, however, she used her entire CPS

sample—rather than the total U.S. population—to

generate the expected number of deaths in each

income group. She also concluded that

socioeconomic disparities had not narrowed

because the ratio of observed-to-expected deaths

for most but not all income groups was further

from 1.0 in 1973–1978 than it was in 1960. For

example, the SMR for individuals earning $10,000

or more (the richest group) decreased from 0.84 in

1960 to 0.71 in 1973–1978. Schalick and

colleagues (21), using the 1967 and 1986 NMFS,

investigated disparity trends in mortality by

income with different measures of disparity, the

slope index and relative index of inequality. These

disparity measures are similar to the index used

by Pappas and colleagues (19) in that they weight

each socioeconomic group by its population

share, but the index is not based on SMRs. Rather,

income groups are ordered from lowest to highest,

and a line is fitted to the data using weighted

linear regression. The slope of this line is the

resulting “slope” index and is interpreted as the

absolute difference in mortality across the entire

range of income. Dividing this slope index by the

actual mortality rate in the population gives the

“relative” index and is the percent difference in

mortality across the entire range of income.

Similarly to Pappas and colleagues (19), Schalick

and colleagues found that relative mortality

disparities increased when measured by the

relative index of inequality, particularly for males;

they also found that absolute disparities decreased

during the same period when measured by the

10
slope index of inequality, primarily because the

absolute declines in mortality were greater for the

least well-off groups. 

Finally, using a different measure of disparity,

the Population Attributable Risk percent (PAR%),

Hahn and colleagues reported that the share of

mortality in the United States due to poverty had

increased from 1973 to 1991 (22). The PAR%

essentially is a summary index designed to

estimate the population health impact of

eliminating health-damaging exposures and is a

function of the prevalence of the exposure and its

associated relative risk. In this case the exposure is

poverty, and the interpretation of the index is the

percent by which the population death rate would

decrease if poverty were eliminated. Thus, the

PAR% is a population-focused disparity index in

that it measures the impact on the total

population of eliminating the health disparity

between the poor and the nonpoor. If the poor

represent a small fraction of the population, or if

the health effects of being poor are small, then

the PAR% will show that the elimination of the

exposure—poverty—will have a marginal effect on

population health. Hahn et al. report that, from

1973 to 1991, the PAR% increased from 16.1% to

17.7%, indicating that the population health

benefit of eliminating mortality disparities by

poverty status increased. The increase, however,

was due entirely to an increased PAR% among

men, as the PAR% decreased for both black and

white women. 

Health Disparities According to Education

Feldman and colleagues (23) investigated trends

in educational disparities in mortality among

whites between 1960 and 1971–1984 using the

matched data of Kitagawa and Hauser and the

first National Health and Nutrition Examination

Survey Epidemiologic Followup Study (NHEFS).

They measured disparity using a standard

epidemiological “rate ratio”—the mortality rate in

the least-educated group divided by the mortality

rate in the most-educated group (i.e., a pairwise

comparison of extreme socioeconomic groups).

The researchers concluded that educational

disparities increased, but this effect was primarily

seen among white men. Interestingly, in their

discussion, Feldman and colleagues noted that the

distribution of education changed enormously

over the period of study but concluded that the

magnitude of the increase was “probably not large

enough to have a major impact on trends in

differentials” (23, page 929). The researchers,

however, did not empirically examine this

assumption, which perhaps is why Elo and

Preston revisited this question using the same

data (24) and conducted a similar analysis of

trends in educational disparity in mortality using

multiple measures of disparity (slope index of

inequality, relative index of inequality) that

account specifically for the changing distribution

of education over time. Similar to previous

analyses (19,23), Elo and Preston found that the

educational disparity had increased among white

men. Whereas Feldman and colleagues found no

change or a small disparity increase for white

women, however, Elo and Preston found that

both absolute and relative disparities had

decreased for white women of all ages. These

studies highlight the important issue of whether

measures of health disparity should be sensitive to

changes in the size of the “exposed group”—in

this case, the most disadvantaged in terms of

income or education. The issue of the effect on

health disparities of the movement of individuals

11
into and out of different social groups over time

also is important and has been neglected

somewhat in the United States, despite having

received consistent emphasis in the health

disparities literature (25–27).

The above studies indicate that relative

mortality disparities generally appear to have

increased since 1960, but the extent of disparity

differs with different measures of disparity and

socioeconomic position. Because all of the above

analyses use different data sources and different

measures of health disparity, it is difficult to reach

a firm conclusion as to how much the

socioeconomic disparity in overall mortality has

increased or decreased over time. This perhaps is

not surprising given that, even for simple

disparity measures such as the relative comparison

of the lowest and highest social groups, different

national data sources can provide different

estimates of the size of the same health disparity

(28).

Health Disparities According to Race/Ethnicity

Despite the longstanding interest in health

disparities between racial/ethnic groups in the

United States, surprisingly few studies have

analyzed racial/ethnic disparity trends.

Additionally, the major racial/ethnic focus in the

United States has been on disparities between

blacks and whites (or nonwhites and whites),

which makes understanding trends somewhat less

difficult because the inequality between two

groups may be summarized easily with either a

simple difference or ratio measure. The

continuing increase in U.S. racial/ethnic diversity

and the growing need to compare multiple

racial/ethnic groups and to examine individual

populations that usually are grouped together

(i.e., Chinese with Japanese or Mexican Americans

with Puerto Ricans), however, make the use of

pairwise comparisons for summarizing inequality

trends more difficult to understand and

communicate. The inherent difficulty of talking

about trends in health inequality by reference to

several relative risks is one reason for attempting

to summarize inequality with a single index. One

potential summary measure, the Index of

Disparity (IDisp), was introduced formally by

Pearcy and Keppel (30) and was applied to 17

health status indicators during the period

1990–1998 for five racial/ethnic groups: nonHispanic whites, non-Hispanic blacks, Hispanics,

American Indian/Alaska Natives, and Asian/Pacific

Islanders (31). The IDisp measures variations in

health across dimensions of a social group (e.g.,

race/ethnicity) relative to some reference point—

in this case, the total population rate. Thus, a

decline in the IDisp indicates that the variation in

health across racial/ethnic groups declined relative

to the total population rate. From 1990 to 1998,

the researchers found that the IDisp decreased for

most mortality measures and infant health

outcomes (i.e., racial/ethnic disparity decreased),

but increased for teenage pregnancy, motor

vehicle deaths, suicide, work-related injury deaths,

and tuberculosis case rates. It is important to note

that, unlike some disparity measures mentioned

previously, the IDisp does not weight social groups

by their population share. That is, the IDisp takes a

perspective on disparity that what matters is the

difference in subgroup rates of health, regardless

of the number of individuals that may be affected.

Thus, it is more focused on strict equality of

health status measures, regardless of social-group

size and the extent to which social-group health

differences may impact population health.

12
Socioeconomic Disparity Trends in Cancer

In general, there have been fewer studies of

socioeconomic disparity trends in cancer

incidence and mortality. One of the difficulties in

monitoring disparity trends in cancer with respect

to socioeconomic groups is that the major source

of data on cancer incidence and survival, the

National Cancer Institute’s Surveillance,

Epidemiology, and End Results (SEER) Program,

does not collect socioeconomic data on

individuals (17). A number of studies, such as

those by Singh and colleagues (32) and Krieger

and colleagues (33), however, have used

information on residential location collected on

incident cancer cases to create a measure of

socioeconomic position. This is accomplished by

linking the neighborhood or county in which an

individual cancer case resides to the U.S. census to

get a measure of the socioeconomic status of that

area—for example, the poverty rate. Such “areabased” measures of socioeconomic position

certainly are an improvement over having no

measure at all, but they also require additional

assumptions that may hinder their utility for

monitoring cancer-related disparities. For

example, the use of area-based measures assumes

that the average socioeconomic status of the area

is representative of the status of the individual,

and that, because the census is conducted only

every 10 years, the socioeconomic status of an

area in, say, 1990 is an accurate representation of

the same area for a cancer case diagnosed in 1997.

Using area-based measures of socioeconomic

position (e.g., census tract poverty rates), Singh

reported a reversal in the socioeconomic gradient

among men in overall cancer mortality from 1950

to 1998 (34). Singh used relative pairwise

comparisons of the highest and lowest

socioeconomic groups and showed that, in 1950,

mortality rates were 49% higher in higher

socioeconomic areas; this disparity decreased over

the next 30 years and, by the late 1980s, cancer

mortality rates were 19% higher in lower

socioeconomic areas. Thus, over the past 50 years,

the pattern of higher cancer mortality among

individuals in higher socioeconomic areas

disappeared and was replaced by a pattern of

higher cancer mortality among individuals of

lower socioeconomic position. A similar pattern of

reversing gradients also was evident for lung

cancer and colorectal cancers (35). With regard to

cancer incidence, from 1975 to 1999, the trend in

socioeconomic disparity for all cancers among

both men and women was inconsistent (32) as

measured by the incidence rate among those

living in areas with >20% of the population in

poverty relative to the rate in areas with <10% in

poverty (i.e., relative pairwise comparison of

extreme groups). This likely is due to differing

disparity trends for specific cancer sites.

Compared to the highest socioeconomic group,

cancer mortality rates were higher among the

lowest socioeconomic group for lung and prostate

cancers among males, and the ratio of the lowest

to the highest socioeconomic area widened from

1975 to 1999. Incidence of melanoma was higher

among males in higher socioeconomic areas in

1975, and this relative difference increased by

1999. Colorectal cancer was more frequent among

males in higher socioeconomic areas in 1975; the

relative difference decreased by 1999. Among

females, women in poorer socioeconomic areas

had higher incidences of lung and cervical cancers

in 1975; the disparity in lung cancer incidence

13
remained relatively constant, whereas the

disparity for cervical cancer declined. Women

living in higher socioeconomic areas had a higher

incidence of melanoma, colorectal, and breast

cancers in 1975; by 1999, this disparity narrowed

for colorectal cancer and widened for breast

cancer and melanoma. This analysis highlights

the importance of examining site-specific rather

than overall cancer trends, as the overall cancer

rate is a diverse amalgam of specific types of

cancer that differ in their etiology and, therefore,

their social distribution. 

Few studies have assessed trends in

educational disparities in cancer. Steenland and

colleagues (36) analyzed trends in educational

disparities in cancer mortality using data from the

American Cancer Society’s Cancer Prevention

Study cohorts (CPS-I and CPS-II). They used

ordinary least squares regression to calculate a

regression-based relative effect of education.

Instead of simply comparing the most- and leasteducated groups, this disparity measure uses the

mortality rates for all educational groups and is

interpreted as the increase in cancer mortality for

each 1-year decrease in the number of years of

education. The study found that educational

disparities increased from 1959–1972 to

1982–1996 for lung and colorectal cancers and

decreased for breast cancer. The researchers did

not, however, account for changes in the social

distribution of education during this period and

were forced to conclude that “the educational

categories were not comparable between the two

populations.” (36, page 20). Thus, their

conclusions were less than clear. If the education

categories are not comparable, and this fact is not

accounted for in the disparity measure, then it is

difficult to know how to interpret the reported

disparity trend among these cohorts.

Racial/Ethnic Disparity Trends in Cancer

Although racial/ethnic disparities in cancer have

received significant attention, especially with

regard to treatment (2,37), relatively few studies

have assessed long-term trends in these disparities.

Again, the general lack of detailed historical

racial/ethnic information in cancer-related data

sources often limits analyses of long-term

disparity trends to a pairwise comparison of

whites and blacks or whites and nonwhites.

Within the last decade, focus on and efforts to

promote population health data for major ethnic

groups have increased. Ten-year trends now are

available for some groups. For subgroups within

major racial/ethnic groups, this is complicated

further by the lack of inter-censal estimates of

population size as well as issues of comparability

of reporting for numerator (incidence) and

denominator (population size) data. Other issues

that arise in comparing groups by race/ethnicity

include differences between subpopulations

commonly grouped together, such as differences

in cancer incidence rates between American

Indians and Alaska Natives and between various

American Indian tribes. 

With regard to mortality from all cancers,

whites had higher mortality rates than nonwhites

until the middle of the 20th century, after which

nonwhites have had higher mortality rates. The

gap between whites and nonwhites increased

from the mid-20th century until the early 1990s,

after which it declined (38,39). The primary

reasons for the widening gap between white and

14
nonwhite cancer mortality since mid-century

were relatively larger increases in nonwhite

mortality from lung, prostate, colorectal, breast,

and ovarian cancers (39). 

Still fewer studies have attempted to use any

summary measure of health disparity across

several racial/ethnic groups. Keppel and colleagues

used the Index of Disparity to compare lung and

female breast cancer mortality rates in 1990 and

1998 across five racial/ethnic groups: nonHispanic whites, non-Hispanic blacks, Hispanics,

American Indian/Alaska Natives, and Asian/Pacific

Islanders (31). Racial/ethnic disparity declined for

both cancers—significantly so for lung cancer. 

Health Inequality and Health Inequity

The language of “eliminating health disparities”

seems simple and straightforward—something

that everyone understands in the same way and

can agree on. When we say we want to eliminate

health disparity, do we really mean we want

everyone to have the same level of health? Is the

goal that all individuals/social groups should have

the same health, regardless of how healthy or sick

they might be? Or do we mean that it is

improving the health of the most disadvantaged

individuals/social groups so that they approach

the health of the more advantaged (i.e., priority to

the worst-off/least healthy)? In regard to reducing

income disparities, we are comfortable as a society

in considering the need to reduce the incomes of

the advantaged via taxation in order to increase

the incomes of the impoverished. In other words,

we are willing to engage in policy discussions

focused on income redistribution from the rich to

the poor. It is not clear that this idea applies to

health disparity. That is to say, in public health we

generally are not willing to accept health declines

in a healthier or more socially advantaged group

to foster improved health in those who are less

healthy or socially disadvantaged. Yet, it is

plausible that, for example, the health of the rich

and the poor both improve, but the rich improve

at a better rate, therefore increasing the relative

disparity between the two groups. This situation

highlights the possible tension that may arise in

designing policies to simultaneously achieve the

two overarching goals of Healthy People 2010—

improving average health and eliminating health

disparities. Such questions only scratch the surface

but underscore the potential implications of a

literal interpretation of the language of the

Healthy People 2010 initiative to “eliminate”

health disparities (1).

The health disparity concept involves both

descriptive and normative elements. The task is to

understand what the elements are and to develop

sensible measures of disparity that capture both of

these dimensions (40,41). In the United States the

use of the term “disparity” implies two core

concepts. First, it suggests that there are health

“differences” between individuals or social groups;

second, it suggests that such differences in some

way are unfair and an affront to our moral

concepts about social justice. Thus, the term

“disparity” often mixes ideas of “inequality” and

“inequity.” The term “inequality” literally means

difference—that two quantities are not the same—

but the term “inequity” implies an ethical

judgment about those differences. Inequality is a

measurable, observable quantity that can be

reasonably and unambiguously judged; inequity

relies on a moral, ethical judgment about justice

15
and thus is not unambiguously measurable or

observable. The classification of health differences

as unequal is a relatively easy task compared to

the classification of health differences as

inequitable. Judgements concerning inequity rely

on social, political, and ethical discourse about

what a society believes is unfair (42).

Another crucial dimension to ideas of

inequity and concepts of justice comes from

discussions about disparities in health that are

avoidable and those that are unavoidable (43,44).

Both types contribute to health disparities, but

only potentially avoidable determinants

contribute to inequity (45). Thus, “avoidability”

implies a capacity to intervene (via social policy,

medical care, etc.) with respect to the

determinants of disparity. It often is difficult to

identify the determinants of disparities or to

distinguish between avoidable and unavoidable

determinants. Determinants of disparity may be

unavoidable in the short run and avoidable in the

long run. It is easier to measure disparity between

groups than it is to identify the determinants of

the disparity or to decide which determinants are

avoidable and which are unavoidable. To

eliminate disparities in health between groups,

however, the determinants of disparities in health

must be identified and avoidable determinants

modified. The first task, though, is to arrive at

methods to identify and quantify health

disparities over time as the basis for evaluation

and action.

16
17

Defining Health Disparities

This section introduces concepts of health

disparity and discusses important issues involved

in their measurement. It also highlights the fact

that “disparity” is a fundamentally ambiguous

concept with multiple dimensions that different

measures of disparity emphasize to a greater or

lesser extent. On its face, the concept of a health

disparity seems rather simple. In fact, when one

attempts to formally define what constitutes a

health disparity, difficulties emerge. For example,

consider the following definitions of what

constitutes a health disparity for the purposes of

measurement: 

“Health disparities occur when one group of

people has a higher incidence or mortality

rate than another, or when survival rates are

less for one group than another.”—NCI

Center to Reduce Cancer Health Disparities,

2003 (46) 

“A population is a health disparity population if...there is a significant disparity in the

overall rate of disease incidence, prevalence,

morbidity, mortality, or survival rates in the

population as compared to the health status

of the general population.”—Minority Health

and Health Disparities Research and

Education Act of 2000 (47, page 2498) 

“For all the medical breakthroughs we have

seen in the past century, there remain

significant disparities in the medical

conditions of racial groups in this country....

[W]hat we have done through this initiative

is to make a commitment—really, for the first

time in the history of our government—to

eliminate, not just reduce, some of the health

disparities between majority and minority

populations.”—Dr. David Satcher, Former

U.S. Surgeon General, 1999 (48, page 18–19)

“Health disparities are differences in the

incidence, prevalence, mortality, and burden

of diseases and other adverse health

conditions that exist among specific

population groups in the United States.”

—NIH Strategic Research Plan and Budget to

Reduce and Ultimately Eliminate Health

Disparities, Vol. 1, Fiscal Years 2002–2006

Although these definitions share the same

basic sentiment, there are some potentially

important differences that reflect underlying

assumptions (explicit or implicit) about what

constitutes a health disparity. For instance, under

the first definition above, a disparity is a

difference in health between any two populations,

whereas in the second definition (from the law

that established the NIH initiative), a disparity is a

difference in health between some specific

population and the general population. This

definition also introduces the idea that a disparity

must be “significant” in magnitude. These

differences may seem to be inconsequential

semantics, but for the purposes of monitoring
progress toward eliminating health disparities, the

different definitions imply different metrics for

assessing progress. One could imagine a scenario

in which two minority groups have identical

mortality rates, both of which differ substantially

from that of the general population. A more

extreme (but unlikely) scenario might be a case in

which one minority group’s health is better but

not “significantly” different from that of the

general population, whereas another minority

group’s health is worse but also not “significantly”

different from that of the general population. It is

possible, however, that the difference in health

between the two minority groups is “significant.”

Thus, for the same observed data we might

conclude either that a disparity exists (under the

first definition above) or that a significant

disparity does not exist (under the second

definition above). Also note that the definition

offered by former Surgeon General Satcher states

that disparity exists between the minority and

majority population, which suggests a third

possible reference point—the majority

population—though it is not clear how that

majority is to be defined.

Our purpose is not to focus on semantics but

rather to illustrate the lack of clarity in health

disparity definitions and how this is important in

choosing measures to monitor disparity. It is

unlikely we will agree on a single definition of

disparity. It is more likely that there are several

legitimate, competing perspectives on health

disparity that can be adopted. We want to

emphasize the importance of understanding the

link between ethical perspectives and the choice

of quantitative health disparity measures.

18
19

Issues in Evaluating Measures of Health Disparity

This section discusses several issues—conceptual,

pragmatic, and technical—that potentially are

important in choosing health disparity measures.

Many of these issues receive expanded discussions

in the more technical descriptions of the measures

that follow in later sections. The intention here is

to highlight the set of main issues that might be

considered.

Total Disparity vs. Social-Group

Disparity 

There is an important conceptual issue regarding

the specific quantity to be determined when

evaluating health disparities. The fundamental

distinction to be made is between measuring total

disparity, or total variation, and measuring

disparities between social groups. The former

involves evaluating the univariate distribution of

health among all individuals in a population,

without regard to their group membership; the

latter involves assessing health differences

between individuals from certain a priori chosen

social groups. The World Health Organization

(WHO) initiative to measure health inequality, led

by Chris Murray and colleagues, has advocated

strongly for an approach to the measurement of

health disparity as total health disparity among

individuals that is blind to social groups (49,50).

Initially, this seems at odds with our notions of

why we are evaluating disparity in the first place

(51). That is, the initiative to eliminate health

disparities arose within the United States because

of the persistent presence of social-group health

disparities, not out of concern for a widening

overall distribution of health. Yet, a deeper

understanding of the overall task of determining

variation in population health requires that we

appreciate the concept of total health disparity. It

is likely that the between-group disparity we seek

to measure in regard to initiatives such as those in

the United States may be relatively small

compared to the total disparity that exists

between individuals in a population.

Figure 3 (page 20) shows the average body

mass index (BMI) for five education groups in the

1997 National Health Interview Survey (NHIS). It

is clear that there is a gradient of decreasing BMI

with increasing education when comparing

average BMI among education groups. The plots

of the 10th through the 90th percentiles of BMI,

however, show that there is much greater

variation in BMI within education groups than

between education groups. Thus, basing the

measure of health disparity on between-group

average differences may not capture much of the

total health variation among individuals. This is

not a problematic statement itself but should be

understood—and is why indicators of total health

inequality can be informative. Thus, based on the

group averages and a desire to reduce obesity in

the population, focusing a health intervention on

the “high-risk” social group (those with less than

an 8th-grade education) will in practice target only

a limited proportion of those at high risk, because
high-risk individuals exist in every education

group. 

Measures of total health disparity may mask

substantial social-group disparities, however.

Figure 4 (page 21), adapted from Asada and

Hedemann (52), shows the population

distributions of life expectancy in two

hypothetical societies, A and B. Both populations

have the same average life expectancy, but Society

A has a much narrower overall distribution of life

expectancy; were we to use a measure of total

disparity, we would judge Society A to have the

smaller disparity. Within Society A, however, there

is a substantial gap in life expectancy between

social groups 1 and 2, whereas in Society B,

groups 1 and 2 have nearly identical life

expectancy distributions. If we use a measure of

social-group disparity, we likely would judge

Society A as having the greater disparity because

the distribution of life expectancy between the

groups is unequal. The point of this example is to

show that measures of total disparity and

measures of group disparity may or may not lead

to similar judgments about the extent of disparity

in two populations or at two time periods. Thus

far, the evidence seems to indicate that total

disparity and social-group disparity measure

different aspects of population health. Two crossnational studies found little correspondence

between measures of total disparity and measures

of socioeconomic disparity for either child (53) or

adult (54) mortality. That is, countries with the

largest amount of overall mortality variation did

20

Figure 3. Mean and 10th–90th Percentiles of Body Mass Index by Education, NHIS, 1997

<8th

40

35

30

25

20

15

Body Mass Index (BMI)

Some HS HS/GED Some College College+

Mean BMI

10th–90th percentile of BMI

Figure 3. Mean and 10th-90th Percentiles of Body Mass Index by Education, NHIS, 1997
not necessarily have larger socioeconomic

mortality variation, and countries with the largest

socioeconomic mortality disparities did not have

the largest overall mortality disparities.

Relative and Absolute Disparities

The most frequent method of communicating

information about social disparities in public

health and epidemiology is in relative terms—

through measures of association such as the

relative risk. In epidemiology, relative risks are the

most common measures of “effect size,” partly

because they have advantageous properties not

shared by absolute risk differences (12,55).

Relative and absolute health differences between

social groups are the primary language of health

disparities, but they provide fundamentally

different types of information. Figure 5 (page 22)

demonstrates this essential point by showing

trends in absolute and relative disparity between

males and females in stomach cancer mortality

over the past 70 years. Clearly, there was

enormous progress in reducing stomach cancer

mortality rates among both males and females

during the 20th century. As the rates for both

groups declined, however, the ratio of male-tofemale mortality (i.e., the relative disparity)

21

Figure 4. Hypothetical Distributions of Life Expectancy in Two Populations

Distribution of

Life Expectancy

Percent of Population

Distribution of

Life Expectancy

Society A Society B

Group 1

Group 2

Group 1

Group 2

Figure 4. Hypothetical Distributions of Life Expectancy in Two Populations

Average Life Expectancy: Society A = Society B

Total Disparity in Life Expectancy: Society A < Society B

Group Disparity in Life Expectancy: Society A > Society B
steadily increased. If the difference between male

and female mortality (i.e., the absolute disparity)

is used as the measure of disparity, however, we

observe a different trend. The male-female gap

increased from 1930 to about 1950, as female

rates declined faster than male rates, and has

declined steadily since 1950. Thus, Figure 5

illustrates the possibility that one might arrive at

opposite conclusions about what happened to this

health disparity, depending on which measure

was chosen—the absolute or relative disparity. The

reason is that the relative disparity cannot reflect

changes in absolute rates—the disparity is relative

to the rate in the comparison group.

Reference Groups

The language of disparity—defined literally as

“difference”—implies a comparison group. A

major question in choosing disparity measures is

the choice of comparison group. As noted above,

the different definitions of disparity imply

different comparison groups, and thus the answer

one would get about the extent and patterning of

disparity may differ according to which groups are

compared. Figure 6 (page 23) shows the situation

for cervical cancer mortality rates among several

racial/ethnic groups. Hispanic women clearly have

the highest incidence of cervical cancer, but how

22

Figure 5. Absolute and Relative Gender Disparity in Stomach Cancer Mortality, 1930–2000

1930 1940 1950 1960 1970 1980 1990 2000

50

45

40

35

30

25

20

15

10

Rate per 100 000 Population

2.5

1.5

0.5

Relative Disparity

Male/Female Ratio

Relative Disparity

(Male ÷ Female)

Absolute Disparity

(Male – Female)

Males

Figure 5. Absolute and Relative Gender Disparity in Stomach Cancer Mortality, 1930-2000

Source: Wingo et al. Cancer 2003;97(11 Suppl):3133–275, and SEER Cancer Statistics Review, 1975–2000.

Females

Source: Wingo et al. Cancer 2003;97(11 Suppl):3133–275, and SEER Cancer Statistics Review, 1975–2000.
large is the disparity in cervical cancer incidence?

The answer depends on the choice of the

reference group. If the Hispanic disparity is

measured relative to the general population (i.e.,

the total rate), then the relative disparity is 1.75.

If, however, we follow Dr. Satcher’s recommendation (48) and focus on the disparity from

the majority population—non-Hispanic whites—

the relative disparity is 2.21. Or, if the “best-off”

group—American Indian/Alaska Natives—is

chosen as the reference group, we obtain a relative

disparity of 2.43. 

Average Population Member

One logical reference group might be the

population average, where the disparity measure

reflects the gap between the health of different

social groups and the mean health of the entire

population. The population average is appealing

intuitively as a reference point and, as noted

above, often is also used explicitly in defining

what constitutes a health disparity.

23

Figure 6. Relative Risk (RR) of Incident Cervical Cancer Among Hispanics According to Varying Reference

Groups, 1996–2000

Total

20

18

16

14

12

10

8

6

4

2

0

Rate per 100 000

Non-Hispanic

White

Black Hispanic AI/AN* API**

12.4

7.6

9.6

16.8

6.9

10.2

Figure 6. Relative Risk (RR) of Incident Cervical Cancer Among Hispanics 

According to Varying Reference Groups, 1996-2000

* AI/AN = American Indian/Alaska Native

** API = Asian/Pacific Islander

Source: SEER Cancer Statistics Review, 1975-2000

RRHispanic vs. Total

RRHispanic vs. NH White

RRHispanic vs. Am Ind/AN

= 1.75

= 2.21

= 2.43

*AI/AN = American Indian/Alaska Native

**API = Asian/Pacific Islander

Source: SEER Cancer Statistics Review, 1975–2000. 
Best-Off Group/Person/Rate

This perspective suggests that one might measure

disparity as a difference between each social group

compared to the healthiest group (or even the

healthiest person). This is similar to Sen’s concept

of shortfalls (56), in which it is assumed implicitly

that every social group in the society has the

potential to achieve the health of the best-off

group. It should be noted, however, that the bestoff social group may be relatively small in size,

which may lead to substantial variation and

instability and could make assessing trends in

disparities more difficult.

All Those Better Off

It also is possible to measure disparities by

comparison to all those individuals or groups that

are better off than a particular group or person.

This may seem similar to the “best-off group”

reference point, but it differs in a subtle way that

may best be illustrated with an example using

actual cancer data. Figure 7 (page 25) shows

cancer incidence from 1996–2000 by race and

ethnicity for two different cancers, kidney/renal

pelvis and myeloma. In both cases, there is a

substantial difference between the group with the

highest incidence rate, blacks, and the group with

the lowest or “best” rate, Asian/Pacific Islanders.

When we look at the incidence rates of other

groups, however, we see two different situations.

In the case of kidney cancer, Hispanics and whites

have rates more similar to blacks, whereas, in the

case of myeloma, they have rates more similar to

Asian/Pacific Islanders. Relative to all those better

off than blacks, most people might judge the

disparity to be worse in the case of myeloma

compared to kidney cancer; yet, if measured

relative to the “best-off” group perspective, we

would be unable to capture this nuance.

Fixed/Target Rate

The prior three reference groups are inherently

relative as they change over time, which may

make assessments of trends in disparities

inconclusive if using pairwise comparisons. One

advantage of a fixed or target rate is that the

reference level does not change over time unless a

new target is adopted. 

Social Groups and “Natural”

Ordering

The Healthy People 2010 initiative mandates

eliminating health disparities within a number of

different types of social groupings: gender, income

and education, disability, geographic location,

sexual orientation, and race and ethnicity. Such

groupings were chosen because they represent

important normative dimensions of U.S. society,

and it has been shown repeatedly that health

differences exist between these social groups. The

above groups, however, also differ in ways that

may have implications for monitoring health

disparities. The social groups that measure

dimensions of socioeconomic position—education

and income—have an inherent ordering regardless

of the health status of their members. Individuals

with less than a high-school education

unambiguously have less formal education than

do individuals with a college degree. The same

cannot be said for the other groups targeted by

the Healthy People 2010 initiative. There simply is

24
no inherent way to rank individuals by their race,

ethnicity, disability status, or sexual orientation.

Certain measures of disparity cannot be used to

measure or monitor disparities between groups

that have no implicit ranking. For example, the

slope index of inequality and the concentration

and achievement indices cannot be used except in

the case of education and income, because there

is no inherent way to rank some social groups

such as racial/ethnic groups or genders (except by

their health level). In the Healthy People 2010

parlance, groups with a “natural” ordering include

education and income but do not include gender,

race/ethnicity, sexual orientation, disability status,

and geography.

The Number of Social Groups

Should the measure of disparity include

information from all social groups (i.e., the entire

population), or is it sufficient to reflect only the

experiences of the best- and worst-off (extreme)

groups? Many empirical studies of health

disparities measure disparity by comparing the

extreme groups (e.g., the lowest income group

compared with the highest income group). This,

however, ignores the health status of other groups

and additionally may only reflect the disparity

between two very small population groups. For

example, in 2000 there was a three-fold relative

difference in death rates from melanoma of the

25

Figure 7. Age-Adjusted Incidence of Kidney/Renal Pelvis Cancer and Myeloma by Race and Ethnicity,

1996–2000

Kidney and Renal Pelvis

20

15

10

5

0

Incidence Rate per 100 000

Myeloma

All Races Black Hispanic White Asian/Pacific Islander

Figure 7. Age-Adjusted Incidence of Kidney/Renal Pelvis Cancer and Myeloma 

by Race and Ethnicity, 1996-2000

Source: SEER Cancer Statistics Review, 1975–2000.

Source: SEER Cancer Statistics Review, 1975–2000. 
skin across U.S. states. The states with the lowest

(North Dakota, 1.3 per 100,000) and the highest

(Wyoming, 3.7 per 100,000) rates, however,

collectively accounted for only 0.4% of the U.S.

population in that year. Eliminating this disparity

would have little impact on reducing the

population burden of melanoma mortality

because only a fraction of melanoma cases reside

in these two states. Additionally, although there

are good reasons for focusing attention on specific

comparisons, such as the disparity between blacks

and whites in the receipt of treatment for cancers

of similar stage (57), such pairwise comparisons

do not quantify the disparity across all

racial/ethnic groups, which is precisely the goal of

initiatives to eliminate health disparities by the

year 2010. For example, the gap between white

and black men in the recent use of fecal occult

blood test (FOBT) screening for colorectal cancer

narrowed between 1987 and 1998 (58); however,

this pairwise comparison conceals the fact that

the gap between Hispanics and whites and

between Hispanics and blacks increased (see

Figure 8). Despite the utility of measuring

disparities between two groups, pairwise

comparisons may conceal important

heterogeneity and thus provide a limited view in

monitoring progress toward eliminating health

disparities across the entire range of social groups.

26

Figure 8. Proportion of Men Reporting Use of Screening Fecal Occult Blood Tests (FOBT), by Race and

Ethnicity, 1987–1998

1987

40

30

20

10

0

Percent Reporting Screening

1998

White Black Hispanic

1992

19.5

11.5

6.8

25.0

19.3

10.2

29.9

24.3

15.9

Figure 8. Proportion of Men Reporting Use of Screening Fecal Occult Blood Tests 

 (FOBT), by Race and Ethnicity, 1987-1998

Source: Breen et al. J Natl Cancer Inst 2001;93:1704–13.

Source: Breen et al. J Natl Cancer Inst 2001;93:1704–13. 
Population Size

Should the disparity measure incorporate the size

of the groups being compared? If we use a

pairwise comparison of extreme groups, would it

matter that one or both of those groups comprises

a very small proportion of the population? For

example, Pearcy and Keppel’s Index of Disparity

(30) gives equal weight to each group, even

though the groups may represent different

proportions of the population. This has important

implications for monitoring disparities and is

another case in which a statistical choice reflects

an ethical choice. That is, the decision of whether

or not to weight social groups by their population

size also is a decision regarding how much weight

to give individuals within each social group. For

example, if we measure the disparity in prostate

cancer mortality among U.S. states in 2000

without weighting states by their population size,

California and Wyoming receive equal weight

despite the fact that California has nearly 70

times as many males as Wyoming. Thus, in an

unweighted analysis of U.S. states, individual

males in California receive approximately 1/70th

the weight of males in Wyoming. 

Another important issue in using unweighted

measures of health disparity is their inability to

incorporate the demographic changes that

inevitably occur over time. For example, Figure 9

(page 28) shows the percentage increase in

population subgroups between the 1980 and 2000

Census (59). These demographic shifts can have

enormous impact on the population’s health and

should be factored into the assessment of health

disparity. In their analysis of the effects of

education on all-cause and cause-specific

mortality in the American Cancer Society’s Cancer

Prevention Study cohorts (CPS-I and CPS-II),

Steenland and colleagues (who used ordinary least

squares regression) noted that changes in the

distribution of education made it difficult to

compare the extent of disparity between the two

populations studied (36). The proportion of the

population with less than a high-school education

was 20% in CPS-I and 6% in CPS-II, while those

with a college degree were 16% and 30% of the

population in the two respective cohorts. In

epidemiological language, the proportion of the

population “exposed” changed dramatically with

large population shifts out of the most

disadvantaged groups. For a measure of health

disparity to allow for an unambiguous

comparison across time, it should be sensitive to

changes in the distribution of social groups over

time. This sensitivity to changes in the proportion

of people exposed to disadvantageous social

positions especially is important when

considering the so-called “upstream”

determinants of health disparities. It is

commonplace in health disparity research to

discuss how distal social policy affects health and

health disparity. The policies and programs that

define the nature of stratification in a society

create educational opportunity, allocate income,

and affect the types of jobs that are available.

When these “upstream” social policy factors affect

the nature of social stratification by reducing the

number of minimally educated individuals, for

instance, thus reducing the number of individuals

exposed to that form of social disadvantage, then

measures of health disparity should account for

that change. The same situation exists when the

proportion of a particular population subgroup

changes over time, as in the case of the migration

of Hispanics and Asian/Pacific Islanders as shown

in Figure 9.

27
Socioeconomic Dimension

Another potential criterion for a measure of

health disparity, first articulated by Wagstaff and

colleagues (60), is whether the measure is able to

capture health gradients associated with

socioeconomic position. By health gradients, we

mean a situation where a measure of health status

either increases or decreases with increasing

socioeconomic position. A good example is the

increasing rate of cancer incidence among

individuals living in U.S. counties with

successively higher poverty rates (32). That is, is

the measure sensitive to the direction of the

association between social group and health? For

instance, if at one time health status increases

with social-group ordering and at another time

health decreases with the same social-group

ordering, the disparity measure will reflect this

change if it is sensitive to the direction of the

gradient. Of necessity, this criterion is applicable

only for measuring inequality between social

groups that have an inherent ranking. The lack of

inherent ordering among racial/ethnic groups, for

example, means that the “socioeconomic

dimension” criterion cannot be applied to

disparity measures used to monitor racial/ethnic

health disparities. 

Figure 9. Percent Change in Population Size by Race and Hispanic Origin, 1980–2000

Total

250

200

150

100

50

0

Percent Change in Population

Black API* Hispanic Non- HispanicWhite AI/AN** Other Non- Minority Hispanic

White

30.8

12.3

24.2

204.0

74.3

127.3

141.7

16.1

7.9

87.7

Figure 9. Percent Change in Population Size by Race and Hispanic Origin, 1980-2000

* Asian/Pacific Islander

** American Indian/Alaska Native

Source: Hobbs F. Stoops N. Demographic Trends of the 20th Century, 2002.

*Asian/Pacific Islander

**American Indian/Alaska Native

Source: Hobbs F, Stoops N. Demographic Trends of the 20th Century, 2002.

28
Monitoring Over Time

Inherent in the goals of Healthy People 2010 is the

idea that we monitor progress toward the

elimination of health disparities. That means it is

desirable that measures of disparity are

interpretable over time. This represents important

challenges for the use of simple pairwise relative

disparity indicators and indicators that are not

population-weighted. Because both the health

status within different social groups and the

population distribution of social groups change

over time, which together reflects the overall

public health burden of health disparities,

measures that are sensitive to both dimensions of

change may be more suitable for monitoring

disparities over time. 

Transfers

The issue of how measures of disparity respond to

hypothetical transfers between individuals has

been an important part of evaluating the

performance of income disparity measures in

economics. The major test in economics is the

principle of transfers—sometimes called the

Pigou-Dalton condition (61,62)—which maintains

that a transfer of income from a richer to a poorer

person should result in a decrease in the measure

of disparity (assuming that everyone else’s income

remains unchanged and the transfer is not large

enough to reverse anyone’s relative positions).

This is an intuitively powerful and desirable

notion that corresponds well with what we

believe disparity measures should be able to

capture. Yet, theoretically, this is a somewhat

difficult concept to employ for judgments about

health disparity. Is “health” a fungible good like

income that can be redistributed in different

ways? It is hard to imagine social mechanisms

(perhaps apart from organ donation) through

which a “healthy” person can directly transfer

some of her health to someone who is less

healthy, though it is possible to conceive of

redistributing health resources. The task, however,

is to measure disparities in health, not health

resources. 

We have noted that measuring disparity in

health versus income differs in at least one

important respect, namely that goods such as

income or wealth are, in fact, transferable from

one individual to another. One potential way to

avoid this difficulty is to think of comparing

disparity in two different populations (e.g., in two

repeated observations of a cohort). One might

then think of a transfer-like principle according to

which we evaluate a measure of health disparity.

If the health of every individual remains the

same, but a single “healthier” person becomes less

healthy and a previously “less healthy” person’s

health improves, the measure of health disparity

should decrease (25). This seems a plausibleenough principle to warrant evaluating a measure

of health disparity, but health disparities and

income distributions are dissimilar in another

way. Even if we are willing to put aside the issue

of the literal inability to “transfer” health, it is not

at all clear in the previous example that we would

be willing to accept the decreased health of one

person for the sake of increasing the health of

another. For income, this is not a problem

because it is the distribution of the good itself that

is under question. Most people generally believe

that it is unfair that some have enormous

incomes while others live in extreme poverty. Do

29
we truly believe, however, that some individuals

possess more than their fair share of health? As

was emphasized earlier, one of the major reasons

for the increasing focus on health inequalities is

not simply that some are healthy while others are

sick. It is that some kinds of individuals or the

members of some social groups are healthy while

other kinds are sick. It is the normative

distinction between the kinds of healthy or

unhealthy individuals that drives our concern

that health differs so markedly by social group.

The concern over health disparities then, at least

in the current historical period, is not that there

are health differences in society but that these

health differences systematically covary with

membership in particular social groups. 

Subgroup Consistency

Generally, this criterion says that if the measure of

overall disparity includes, for example, three

groups, and disparity within two groups remains

unchanged while increasing within the third, the

measure of disparity should increase. This is of

most relevance when we are interested in

measuring the overall disparity (i.e., across the

entire population). For instance, suppose we were

examining alcohol consumption at two points in

time in a population composed of two social

groups (rich and poor). At each time, both the

size of these groups and their average alcohol

consumption remain constant, but the disparity

in consumption increases within the poor and

remains constant within the rich. Subgroup

consistency requires that any measure of overall

disparity also should register an increase in this

scenario. This is not likely to be an important

criterion for health disparity measures in the

context of Healthy People 2010 because it does not

focus on health disparities within subgroups of a

social group (e.g., within the poor).

Decomposability

Decomposition as a property of statistical

measures is common in both economics and

epidemiology. In economics, it typically refers to

the ability to decompose a measure of disparity by

sources of income or into between-group and

within-group partitions (40). Decomposable

disparity measures are seen as advantageous as

they can offer information about the sources of

increasing or decreasing disparity as indicated in a

summary statistic. In public health,

decomposition often is used to capture differences

in summary rates. For example, a difference in

age-adjusted mortality rates between two

populations can be “decomposed” into differences

between mortality rates and differences in age

structure. 

Scale Independence

Scale independence (or invariance) often is seen

as a desirable property of disparity measures. It

often is argued that, all else being equal, if

everyone’s health “doubles,” the disparity

measure should remain unchanged. It is arguable,

however, whether for public health, where we also

are concerned about the absolute level of ill

health, this is a desirable property. 

30
Transparency/Interpretability for

Policy Makers

Finally, it seems salient that an interpretability

criterion be included as a factor in decisions about

measures of disparity. For instance, despite other

desirable properties, the actual value of more

sophisticated summary measures such as the

Concentration Index have no obvious

interpretation and thus may make

communicating health disparity indices to the

community and policy makers potentially more

difficult. Thus, the extent to which different

measures of disparity can be captured graphically

to aid communication might be important in

deciding which measures are most appropriate for

monitoring cancer-related health disparities.

Perhaps the use of real-time graphical displays of

changes in outcomes of interest may aid the

understanding of health disparity. This dimension

of health disparity monitoring should not be

underestimated, as evidenced by the lack of

general application of more sophisticated disparity

measures in health disparity research.

31
33

Measures of Health Disparity

This section reviews most of the statistics that are

available to measure health disparities. The goal is

to provide a brief overview of each measure,

followed by the method of calculation and

statistical interpretation and, often, an example of

its actual or potential use for measuring disparities

in cancer-related health objectives. 

Note that there are methods to calculate

indicators of precision (e.g., 95% confidence

interval) for all of the measures reviewed here.

These can be found in the source publications

detailed in the references. Although issues of

variability and precision are important, they are

not germane to the choice of disparity measure

because they ultimately derive from the precision

of the underlying rates, prevalence, and

proportions that are used to generate a particular

disparity measure.

Measures of Total Disparity

A measure of “total disparity” in health is a

summary index of health differences across a

population of individuals. Generally, measures of

total disparity do not account for social grouping

and have been used chiefly by health economists

(see, for example, 25,49). They are an important

first step in understanding the scope of health

variation in a population and have advantageous

properties for monitoring trends, particularly for

cross-country comparisons. They do not, however,

inform about systematic variation in health

among population subgroups, which is inherent

in the Healthy People 2010 health disparity

initiatives. The measurement of health disparity

as total disparity is associated most closely with

and endorsed by the WHO as a component of its

general framework for routinely assessing the

performance of health systems in different

countries. The WHO, however, is not the only

advocate of measuring total disparity. Some

health economists also advocate for the

measurement of total health disparity (25,63,64)

as the primary form of assessing health

inequalities.

A number of criticisms have been levied at

this kind of measure, primarily because it does not

distinguish among individuals from different

social groups (51,53,54,65). In addition, empirical

investigations using measures of total disparity

appear difficult to interpret (54,66,67). Those who

endorse this measure often cite as their primary

justification the weighty normative choices that

must be made to measure health differences

between social groups and note that the absence

of such a priori choices makes disparity between

individuals a more “objective” measure of health

disparity. We recognize that Healthy People 2010

specifically calls for social-group monitoring and

not total variation, but we include measures of

total group disparity because they are prominent

in the overall framework of efforts to monitor

global health disparity and because they provide

an essential context for understanding the
“decomposition” of health disparity measures, as

described below. 

Individual-Mean Differences

Individual-mean difference (IMD) measures of

health disparity calculate the difference between

the health of every individual in the population

and the population average. The general formula

for the class of individual/mean difference

measures is given by Gakidou and colleagues (49)

as: 

[1]

where an individual i’s health is yi

, μ is the mean

health of the population, and n is the number of

individuals in the population. The parameters α

and β specify, respectively, the significance

attached to health differences at the ends of the

distribution relative to the mean and whether the

individual-mean difference is absolute or relative

to the mean health of the population. For

instance, large values of α emphasize greater

deviations from the mean, and larger values of β

emphasize relative disparity because of heavier

weighting of the mean. Those familiar with basic

statistics will note that, when α = 2 and β = 0, the

IMD simply is the variance; and when α = 2 and

β = 1, the IMD is the coefficient of variation (49).

Similar to many other disparity measures, the IMD

is a “dimensionless” index that is not measured in

units because it always is relative to the mean in

the population.

Inter-Individual Differences (IID)

The IID measures health differences between all

individuals in the population and is consistent

with the Gini coefficient but may be weighted in

accordance with differential aversion to disparity

(i.e., the value chosen for α). These measures are

different from the IMD class because they

compare every individual in the population with

every other individual in the population, whereas

the IMD measures disparity relative to the

population average. It should be clear that

different measures of disparity implicitly express

different perspectives on which aspects of

disparity should be emphasized in the measure.

The class of inter-individual difference measures is

(49):

[2]

where yi is individual i’s health, yj is individual j’s

health, μ is the mean health of the population,

and n is the number of individuals in the

population. The parameters α and β are defined as

for the IMD above, and it is worth noting that,

when α = 2 and β = 1, the IID is equal to the more

well-known Gini coefficient. Gakidou and King

have used this disparity measure (with α = 3 and

β = 1) to compare total disparity in child survival

among 50 countries (68). Weighting α = 3 implies

that the measure should be more sensitive to

larger than smaller pairwise deviations between

individuals and thus reflects additional concern

about larger health differences between

individuals. To our knowledge, there is only one

study of total disparity that uses data from the

United States (69).

IID( ) = 

yi – yj 

2n2

μ α, β

α

Σj = 1

n

Σi = 1

n

β

I MD ( ) = 

yi – μ

nμ α, β

α

Σi = 1

n

β

34
Measures of Social-Group Disparity

The measures of total variation described above

have a number of merits, including their ability to

make unambiguous health disparity comparisons

between populations and over time. In defining

health disparity as disparity between individuals

instead of between social groups, such measures

avoid the difficulty of comparability of groups

between populations or over time (50). This

makes them particularly attractive for crosscountry comparisons, in which defining

comparable social groups is challenging because

of differences in how social groups are classified

in different countries (70).

The disparity goals of Healthy People 2010,

however, explicitly are goals that relate to socialgroup differences in health. It is an open question

as to whether measures of total disparity and

social-group disparity are “better” or “worse”

disparity measures, but the concern among health

policy makers in the United States specifically is

expressed in terms of social-group differences in

health. Measures of total disparity therefore are

insufficient for monitoring progress toward

eliminating cancer-related health differences

among social groups in the United States.

Pairwise Comparisons

Simple comparisons of some health indicator

between two groups in a population (so-called

pairwise comparisons) clearly are one of the most

straightforward ways to measure progress toward

eliminating disparities between groups. For

example, age-adjusted incidence rates of lung

cancer for black and white females in 1973 were,

respectively, 23.6 and 20.4 per 100,000. By 1999,

rates for both groups had increased, to 57.0 for

blacks and 52.3 for whites (71). It would seem

easy enough to answer the question: Did blackwhite disparity grow from 1973 to 1999?

Unfortunately, however, the answer depends on

the measure of disparity. If the disparity measure

is the absolute difference between the black and

white rates, then we would conclude that the

black-white disparity increased from 3.2 to 4.7.

If the disparity measure is the relative difference

between the black and white rates (i.e., black

rate ÷ white rate), however, we would conclude

the opposite because the relative disparity

decreased from 1.16 to 1.09. Both answers are

correct. This has been a source of continuing

confusion and sometimes unresolved debate in

the health disparities literature (72,73) and,

although most of the empirical work in health

disparities has been in terms of “relative

disparity,” it should always be kept in mind that

large relative differences can mask very small

differences in absolute terms, which can be

misleading with respect to the disparity’s

population-health impact. Conversely, there may

be situations where large relative disparities may

be viewed as grossly unjust, despite the fact that

they reflect small absolute differences.

Absolute Disparity

The absolute disparity between two health-status

indicators is the simple arithmetic difference. It is

calculated as:

[3]

where r1 and r2 are indicators of health status in

two social groups. In this case, r2 serves as the

reference population, and the AD is expressed in

A D = r1 – r2

35
the same units as r1 and r2. A typical disparity

measure that uses the absolute difference between

two rates for an entire population is the range,

where case r1 above corresponds to the leasthealthy group and r2 to the most-healthy group. 

Relative Disparity

For the same pairwise group comparison in

equation [3], we also can divide r1 into r2 to

calculate the relative disparity as:

[4]

where, again, r2 is the reference population. This

rate ratio can be transformed easily into a

percentage difference by multiplying the ratio by

100. Figure 10 shows the absolute and relative

black-white disparity for prostate and stomach

cancer incidence from 1992–1999. Clearly, there is

a much larger absolute disparity in prostate cancer

incidence because the rates for both groups are

relatively high compared to the stomach cancer

rates; however, the relative disparity is larger for

stomach cancer.

Regression-Based Measures

One drawback of the pairwise comparison

measures of disparity is that, when a social group

has more than two subgroups (as most do),

information on the other groups is ignored.

Normally it is desirable to use as much of the

information present in the data as possible. If we

R D = r1/r2

36

Figure 10. Absolute and Relative Black-White Disparities in Prostate and Stomach Cancer Incidence,

1992–1999

Prostate

300

250

200

150

100

50

Rate pe 100 000

Stomach

Black

White

Figure 10. Absolute and Relative Black-White Disparities in Prostate and Stomach Cancer Incidence, 1992-1999 

Absolute Disparity

Relative Disparity

Prostate Stomach

102.4

1.6

6.0

1.8
compare the “best” group to the “worst” group,

we effectively ignore the information on the

health status of all the groups in between, aside

from knowing that they fall somewhere between

the best and worst groups. One possible solution

would be to calculate a series of (j–1) pairwise

comparisons for j groups using one group as the

reference point, or j pairwise comparisons using

an external reference point. Although feasible, as

the number of groups, time periods, or both

increases, attempting to evaluate the disparity

trend may become complicated in terms of

summarizing the many pairwise comparisons. To

overcome this limitation and make use of the

information for all groups, one might consider

calculating a summary measure of disparity. This

choice, however, undoubtedly involves additional

complexity and assumptions that must be traded

off against the insights about disparity gleaned

from the use of a summary measure (74).

Simple Linear Regression

If one is willing to assume that the relationship

between social group and health status is linear

(i.e., that each step up the social-group scale

results in an equivalent health gain/loss), then a

potential way to include information on all of the

groups is to calculate a summary measure of

disparity using regression. One way of writing this

is:

[5]

where yi is a measure of health status for

individual i, β0 is the value of the health variable

when Xi is 0 (e.g., if Xi is a continuous measure of

income, then β0 is the health status of an

individual with zero income), Xi indexes social

group, and β1 is the summary measure of

disparity. In general terms, β1 is equal to the

covariation of Xi and yi expressed in terms of the

variance of Xi

. The specific interpretation of β1

depends on the particular health status measure

used and the specification of the model. If yi is an

untransformed health status measure—for

example, BMI—then β1 is the absolute increase in

BMI associated with a one-unit change in social

group and is referred to as a Regression-Based

Absolute Effect or RAE (70). It is an absolute

measure because it is expressed in the same units

as the quantity of health measured in yi

.

Continuous types of health outcomes, however,

are relatively less common in the area of cancerrelated data. More likely are noncontinuous types

of health data (e.g., the presence or absence of

cancer, receipt or nonreceipt of screening), where

the linear relationship in equation [5] applies to

some transformation of the dependent variable yi

.

For transformations of the dependent variable yi

(e.g., the logarithmic or logit transformation),

β1 then becomes a relative-risk (logarithmic

transformation) or odds-ratio (logit

transformation) and is interpreted as the

proportional increase in health status for a one-unit

change in social group and referred to as a

Regression-Based Relative Effect or RRE (70).

Figure 11 (page 38) graphically shows a simple

regression-based disparity measure, applied in this

case by Steenland et al. to the risk of lung cancer

among men of different education groups

(grammar, some high school, high-school

graduate, some college, college graduate) in the

1982–1996 Cancer Prevention Study II (36). The

y-axis is the risk of mortality relative to those

completing graduate school (whose relative risk is

by definition equal to 1.0), the x-axis is the

approximate number of years of education for

each education group (Xi in equation [5]), and the

fitted line indicates the linear decrease in relative

yi = β0 + β1Xi

37
risk—which Steenland and colleagues reported as

about 10%—for each 1-year increase in the

number of years of education. (It is important to

note that, for ease of presentation, the plotted

points in Figure 11 show only the average relative

risk for each education group. The actual

regression equation is performed on all 500,000 or

so individuals in the CPS-II.) Relative-effect

measures also may be transformed into absolute

effect measures by applying them to the rates of

health in the referent social group. An additional

drawback to the RAE and RRE is that the

assumption of linearity between health and social

group may be problematic. For example, while

Kunst and colleagues find linear associations

between education and self-rated health (75),

Manor et al. report nonlinearity between

education and a number of chronic conditions

(76), and Backlund and colleagues report a

nonlinear association between income and

mortality (77).

Slope Index of Inequality

The regression-based methods outlined above,

subject to the assumptions of the model, work

well for calculating a summary measure of health

disparity at a single point in time. As noted above,

however, over time the distribution of the

population in various social groups may change

38

Figure 11. Example of a Simple Regression-Based Disparity Measure

3.0

2.8

2.6

2.4

2.2

2.0

1.8

1.6

1.4

1.2

1.0

Relative Risk of Mortality

4 6 8 10 12 14 16 18

Years of Education

Systematic 

Association 

Between 

Education and 

Lung Cancer 

Mortality Risk

Figure 11. Example of a Simple Regression-Based Disparity Measure

Source: Adapted from Steenland et al. Am J Epidemiol 2002;156:11-21. Source: Adapted from Steenland et al. Am J Epidemiol 2002;156:11–21. 
drastically, and it would be advantageous for a

measure of health disparity to be sensitive to such

changes. One measure that does so is the Slope

Index of Inequality (SII). To calculate the SII, the

social groups first are ordered from lowest to

highest. The population of each social-group

category covers a range in the cumulative

distribution of the population and is given a score

based on the midpoint of its range in the

cumulative distribution in the population. For

example, in the 2001 NHIS those with an incometo-poverty ratio of less than 0.5 (approximately

<$9,000 for a family of four) were 3.45% of the

population, and those in the next highest income

group—with an income-to-poverty ratio of 0.5 to

0.74—comprised 3.02%, in which case the lowest

group is assigned a score of [0 + (.0345 – 0)/2] =

.0173, and the next lowest group is assigned a

score of [.0345 + (.0647 – .0345)/2] = .0496. 

Health status then is plotted against this

midpoint socioeconomic category variable, and a

regression line is fitted to the data. The SII thus is

similar to the regression-based methods above,

but differs because it uses the midpoint of the

cumulative social group distribution and because

it (usually) is based on grouped data and is a

weighted index, where the weights are based on

the size of the social groups. By weighting social

groups by their population share, the SII is able to

incorporate changes in the distribution of social

groups over time that affect the population health

burden of health disparities. Figure 12 (page 40)

shows the predicted slope for the income disparity

(based on income-to-poverty ratio) in current

smoking for the United States in 2001. Note that,

in Figure 11, the location of the data points on

the x-axis is based on the estimated number of

years of education, whereas in Figure 12, the

location is based on the group’s share of the

population. This reflects the fact that the

education groups actually comprise different

proportions of the population distribution.

Formally, the SII, which was introduced by

Preston, Haines, and Pamuk (78), may be obtained via regression of the mean health variable

on the mean relative rank variable:

[6]

where j indexes social group, is the average

health status, is the average relative ranking of

social group j, β0 is the estimated health status of a

hypothetical person at the bottom of the social

group hierarchy (i.e., a person whose relative rank

Rj in the social group distribution is zero), and β1

is the difference in average health status between

the hypothetical person at the bottom of the

social group distribution and the hypothetical

person at the top (i.e., Rj = 0 vs. Rj = 1). Because

the relative rank variable is based on the

cumulative proportions of the population (from

0 to 1), a “one-unit” change in relative rank is

equivalent to moving from the bottom to the top

of the social group distribution. Because this

regression is run on grouped data (as opposed to

individual data as in equation [5]), it is estimated

via weighted least squares, with the weights equal

to the population size nj of group j (60). The

coefficient β1 in equation [6] is the SII, which is

interpreted as the absolute difference in health

status between the bottom and top of the socialgroup distribution. Thus, the regression equation

in Figure 12 shows that the absolute difference in

the prevalence of smoking across the entire

Rj

yj

yj = β0 + β1Rj

39
distribution of income is –18.1 percentage points.

The same regression also may be run on

individual data (as in equation [5]), but replacing

Xi with Ri, with Ri being an individual’s relative

rank in the social-group distribution. In this case,

the data would be self-weighting and could be

estimated by ordinary least squares. 

Relative Index of Inequality

The SII discussed above is a measure of absolute

disparity. Dividing this estimated slope by the

mean population health, however, provides a

relative disparity measure, the Relative Index of

Inequality or RII (79):

[7]

where μ is mean population health and the SII is

the estimate of β1 from equation [6]. Its

interpretation is similar to the SII, but it now

measures the proportionate (in regard to the

average population level) rather than the absolute

increase or decrease in health between the highest

and lowest socioeconomic groups. In the income

and smoking example seen in Figure 12, the RII is

calculated as –18.1/24.6 = –0.74, indicating that a

RII = SI I / 1 μ = β/ μ

40

Figure 12. Income-Based Slope Index of Inequality for Current Smoking, NHIS, 2002

0.0

40

35

30

25

20

15

10

5

0

Percent of Current Smokers

0.2 0.4 0.6 0.8 1.0

Cumulative Percent of Population, Ranked by Income-to-Poverty Ratio (X)

Observed

Predicted

Figure 12. Income-Based Slope Index of Inequality for Current Smoking, NHIS, 2002

Average Smoking Rate = 24.6

SII = –18.1

RII = –0.74

y = 33.7 - 18.1x
move from the bottom to the top of the income

distribution is associated with a 74% decline in

the prevalence of smoking. Kunst and

Mackenbach (70) modified this definition of the

RII slightly by dividing the estimated health of the

hypothetical person at the bottom of the socialgroup distribution by the estimated health of the

hypothetical person at the top of the social-group

distribution:

[8]

where β0 and β1 are defined as in equation [6].

From Figure 12, this is calculated as 33.7/(33.7 –

18.1) = 2.16, indicating that the rate of smoking is

2.16 times higher at the bottom of the income

distribution than at the top. Thus, the KunstMackenbach RII is more like a traditional relative

risk measure in that it compares the health of the

extremes of the social distribution, but it is

estimated using the data on all social groups and

is weighted to account for social-group sizes. As

noted above, the use of the SII and RII indices (as

well as the Health Concentration Index discussed

below) depends on having a social-group

classification scheme that is hierarchical. This

seems straightforward with respect to education

and income, but social-group classifications based

on occupation may be somewhat more

challenging because there inherently is more

ambiguity in the ranking of occupations (80). In

their international study of occupational

mortality differences, Kunst and Mackenbach (81)

note this difficulty as a possible explanation for

the lack of consistency of their results with those

of Wagstaff for the size of disparity in Finland

versus England and Wales (60).

Population Impact Measures

Population Attributable Risk

The Population Attributable Risk (PAR) and its

relative analogue, the PAR%, are longstanding

epidemiologic measures of the population burden

that is associated with differential health between

groups. Although typically applied to groups

defined by their exposure status (e.g., comparing

smokers with nonsmokers), it also may be applied

in the context of health differences between social

groups (poor vs. nonpoor). It is a summary of

differences between each social group’s health and

the health of the “best” group. For example, it

indicates the absolute (or relative, in the case of

the PAR%) aggregate health improvement that

would be obtained if all education groups had the

health of the healthiest education group. The

basic formulas for PAR and PAR% as health

disparity indicators (70) are:

[9]

[10]

where r

pop is the rate in the total population and

rref is the rate of health or disease in the reference

group, typically the best-off social group. While

not immediately clear from the above formula,

the PAR% in fact is a population-weighted (by

social-group size) sum of the relative risks (RRs) for

each group (13) and also may be written as:

[11]

where pj is the group’s population share and RRj is

the relative rate of group j compared to the

reference group. To see this, note that we could

PAR% = pj (RRj Σ – 1)

pj (RRj Σ – 1) + 1

PAR% = rpo p – rre f

rpo p

PA R = rpo p – rre f RIIK M = = β0 + SI I β1

β0

β0 + 

β0

41
substitute rj

/rref for RRj and rref /rref for 1 in equation

[11] and multiply through by rref to get:

[12]

Because and , equation

[12] reduces to equation [10]. The PAR% varies

from 0 to 100 and is interpreted as the percent

improvement in the health of the total

population that would be achieved if all social

groups had the rates of health in the best-off

social group, a commonly used metric for

describing the impact of health disparities. For

example, Navarro argues that “the intervention

that would add the most years of life to the

populations of Spain or the USA (or, for that

matter, any other country) would be one that

would lead to all social classes having the same

mortality rates as those at the top” (65, page

1701). In the example in Figure 13, the

population average rate of cervical cancer would

be improved by 28% if all social groups had the

rate experienced by American Indians and Alaska

Natives.

Σ pj rref = r Σ re f pj rj = rpop

PAR% = pj (rj – rref Σ )

pj (rj – rref) + r Σ ref

42

Figure 13. Example of the Population-Attributable Risk Percent

Total

18

16

14

12

10

8

6

4

2

0

Incidence Rate per 100 000

Non-Hispanic API**

White

Black Hispanic AI/AN*

9.6

6.9

Figure 13. Example of the Population-Attributable Risk Percent

Cervical Cancer Incidence by Race and Hispanic Origin, 1996–2000

PAR% = (9.6 – 6.9) / 9.6 = 28.1%

Observed Rates

If All Groups Had Best Rate

* American Indian/Alaska Native

** Asian/Pacific Islander

Source: SEER Cancer Statistics Review, 1975–2000.

*American Indian/Alaska Native

**Asian/Pacific Islander

Source: SEER Cancer Statistics Review, 1975–2000.
Index of Dissimilarity

The Index of Dissimilarity (ID) originally was

developed as a measure of residential segregation

of population groups (82). For example, in the

context of black-white segregation among

neighborhoods within a city, the ID measures the

proportion (using the relative version) or number

(using the absolute version) of blacks (or whites)

that would have to move to a different

neighborhood to achieve a racial distribution in

each neighborhood that was similar to that of the

city as a whole. As such, the ID is a summary

measure of the disparity between each

neighborhood’s racial composition and the racial

composition of the city as a whole. Similarly, in

the context of health disparity measurement, we

can think of the ID as a summary measure of the

disparity between, for example, each racial group’s

cancer rate and the cancer rate of the whole

population. In this case, the ID would be

interpreted as the number or proportion of cancer

cases that would have to be redistributed across

racial groups for each group’s cancer rate to be the

same as the rate in the whole population. The

formula for the relative ID with respect to health

is given in Wagstaff and colleagues (60) as:

[13]

where j indexes social groups, sjh is the jth group’s

share of health (e.g., share of all cancer cases), and

sjp is the jth group’s share of the total population.

According to Kunst and Mackenbach (70),

equation [13] is the relative version of the ID. The

relative ID compares how each social group’s

share of the population’s health compares with its

share of the total population and represents the

proportion of all cases (e.g., the proportion of all

cancer cases) that would have to be redistributed

across social groups so that each group has the

same rate as the total population. The absolute

version of the ID is calculated as:

[14]

where dj and pj are, respectively, the observed

number of cancer cases and the population of the

jth social group, r

pop is the cancer rate in the total

population, so that pj

r

pop is the expected number

of cancer cases that would be observed if group j

had the same cancer rate as the total population.

One could also derive the absolute version of the

ID by multiplying the relative ID by the total

number of cases to determine the absolute

number of cases that need to be redistributed

across groups.

Table 1 on page 44 shows how one might

calculate the absolute and relative ID for

esophageal cancer incidence among working-age

(ages 25–64) racial groups during 1992–2000. A

comparison of columns (3) and (5) shows that the

share of cancer cases is lower than the share of

the SEER population for all groups except blacks,

who represent 13.5% of all esophageal cancer

cases but only 10.5% of the population. Similarly

for the absolute ID, a comparison of columns (2)

and (6) shows that if all groups experienced the

population rate of esophageal cancer, more cases

would be observed for all groups except for blacks.

The relative ID in this case is 3.4, which means

that 3.4% of the 17,186 cases of esophageal

cancer need to be redistributed across racial

groups to eliminate the racial disparity. In

absolute terms, this means redistributing 592

cases of esophageal cancer.

Absolute I D = dj – pj rpop 2

1 Σj = 1

J

Relative I D = sjh – sjp 2

1 Σj = 1

J

43
Index of Disparity

The Index of Disparity, which we will abbreviate

as IDisp to distinguish it from the Index of

Dissimilarity (ID), summarizes the difference

between several group rates and a reference rate

and expresses the summed differences as a

proportion of the reference rate. This measure was

formally introduced by Pearcy and Keppel (30)

and is calculated as:

[15]

where rj indicates the measure of health status in

the jth group, rref is the health status indicator in

the reference population, and J is the number of

groups compared. Although in principle any

reference group may be chosen, the authors

recommend using the best group rate as the

comparison because that represents the rate

desirable for all groups to achieve. In this case, it

is not necessary to take the absolute value of the

rate differences because they all will be positive.

Other potential reference rates include the total

population rate, the average of group rates, or

some external target rate. A similar disparity

measure was developed by Gaswirth (83), but it

weights each group’s deviation from the best rate

by its population size, so that the disparity index

(U) becomes:

[16]

where pj is each group’s population size. In this

case, U is calculated as the weighted sum of the

health difference between each group and the

reference group. Similar to the Index of Disparity,

above, this value also can be expressed relative to

the health status of the total population, which

Gaswirth defines as G = U ÷ r

pop. For example,

Gaswirth applied this disparity measure to rates of

mammography screening among non-Hispanic

white, non-Hispanic black, Hispanic, and Other

women ages 50–65 in the 2000 NHIS (83). The

overall screening rate was 78.6%, and Figure 14

(page 45) shows that white women had the

highest rates of screening (81%). The fraction of

the entire population that is “underserved” (U,

the shaded area in Figure 14) in this case is 2.04%,

and if the population screening rate were

increased by G = 2.6% and targeted to minority

women, the screening disparity would have been

eliminated. This measure has the additional

desirable feature of intuitive graphical

representation. Although not immediately clear

from equation [16], however, it should be noted

U = pj (rj – rref Σ ) j = 1

J – 1

I Disp = rj – rref | / J /r Σ ref x100 j = 1

J – 1

( (

44

Table 1. Incidence of Esophageal Cancer, Ages 25–64 by Race, 12 SEER Registries, 1992–2000

% of % of Cases if

T otal T otal No ID ID

Race Rate Cases Cases Population Population Disparity Relative Absolute

(1) (2) (3) (4) (5) (6) | (3) – (5) | | (2) – (6) |

American Indian/Alaska Native 5.7 133 0.8 2,316,609 1.3 226 0.5 93

Asian/Pacific Islander 8.7 1,648 9.6 18,850,492 10.7 1,835 1.1 187

Black 12.9 2,395 13.9 18,518,113 10.5 1,803 3.5 592

White 9.5 13,010 75.5 136,864,686 77.5 13,323 1.8 313

T otal 9.7 17,186 100.0 176,549,900 100.0 17,186 3.4% 592
that, in practice, when the reference group is the

group with the best rate, Gaswirth’s measure U is

equivalent to the PAR described above, and G is

equivalent to the PAR% because their calculations

are identical to the PAR and PAR%.

The Between-Group Variance

The variance is a commonly used statistic that

summarizes all squared deviations from a

population average. In the case of grouped data,

this is the Between-Group Variance (BGV), and it

is calculated according to the following formula

that squares the differences in group rates from

the population average and weights by their

population sizes:

[17]

where pj is group j’s population size, yj is group j’s

average health status, and μ is the average health

status of the population. The Between-Group

Variance may be a useful indicator of absolute

disparity for unordered group data because it

weights by population group size and is sensitive

to the magnitude of larger deviations from the

BG V = pj ( yj – μ)

2

Σj = 1

J

45

Figure 14. Disparity in Mammography Screening Among Racial/Ethnic Groups, NHIS, 2000

0.0

1.0

0.8

0.6

0.4

0.2

0.0

Proportion Having a Mammogram in the Previous 2 Years

0.2 0.4 0.6 0.8 1.0

OH B W

U = Fraction of the Entire Population

“Under-treated” Relative to the Best Group

Subpopulations in Order of Their

Mammogram Screening Rates

Figure 14. Disparity in Mammography Screening Among Racial/Ethnic Groups, NHIS, 2000

Source: Gastwirth JL. Prev Med (forthcoming).

U

Source: Gastwirth JL. Prev Med (forthcoming). 
population average. As an example, Figure 15

shows trends in age-adjusted lung cancer

mortality among U.S. Census divisions. 

The between-region variance in lung cancer

mortality in 1968 was 7.1 deaths per 100,000, but

in 1998 the BGV was 22.8 deaths per 100,000.

This larger absolute disparity in regional mortality

indicates divergent regional trends in lung cancer

over time (see Figure 15). The use of the variance

as a measure of disparity in economics sometimes

is discouraged because it is not “scale invariant.”

In other words, it is sensitive to absolute changes,

such as when everyone’s income doubles over

time. In this case, economists sometimes feel that

it is not desirable for the disparity measure also to

double, because relative inequality is maintained.

Although this may be an undesirable property

when dealing with income disparity, however, we

believe it is not necessarily a limitation for

discussing health disparity, in which we are

interested in absolute disparity burdens (84). From

a population health perspective, in which we may

be concerned with the health care implications of

increasing absolute disparity, we may care about

situations in which the absolute disparity

increases, and it is appropriate that the disparity

indicator reflect this increased concern. In this

case, then, using the variance (which squares the

absolute deviations from the population average)

46

Figure 15. Age-Adjusted Lung Cancer Mortality by U.S. Census Division, 1968–1998

1968

80

70

60

50

40

30

20

10

0

Rate per 100 000

972 1976 1980 1984 1988 1992 1996 2000

Figure 15. Age-Adjusted Lung Cancer Mortality by U.S. Census Division, 1968-1998

Source: NCHS. Compressed Mortality Files 1968-1998

East North Central

East South Central

Middle Atlantic

Mountain

New England

Pacific

South Atlantic

West North Central

West South Central

Source: NCHS. Compressed Mortality Files 1968–1998.
is consistent with a population health perspective.

In the example above of changes in regional lung

cancer disparity, the overall rates increase by 70%,

the coefficient of variation (the variance divided

by the mean) increases by 89% (indicating that

relative disparity increases as well), but the

variance increases by 320%. Thus, choosing this

as the measure of disparity reflects our concerns

with widening absolute differences among the

regions.

Measures of Average

Disproportionality

When describing health inequalities, public

health researchers and policy makers often use

what might be called the “language of

disproportionality.” For example, in the context of

arguing for the importance of measuring health

inequalities between socially meaningful

population groups, Braveman and colleagues

stated that “a disproportionate share of ill-health

and premature mortality is borne by the socially

disadvantaged” (51, page 233). Similarly, in

discussing health disparity trends, the Secretary of

Health and Human Services recently noted that

various racial/ethnic groups in the United States

“suffer an unequal burden of death and disease,

despite improvements in the overall health of the

general population over the past decade” (85).

The terms “disproportionate share” and “unequal

burden” are important descriptors because they

communicate the ethical notions inherent in the

collective concerns over health disparities. That is,

they capture the notion that it is unfair that some

groups experience more ill health than others; a

just distribution of health implies that ill health

should be experienced proportionately by

different social groups. A more explicit example

can be found in the Guidance for the U.S. National

Healthcare Disparities Report in which, in discussing

the disparity in cardiac catheterization rates

between blacks and whites, LaVeist states that the

“degree to which the predicted percentage of

catheterization deviates from the observed

percentage indicates the degree of disparity,” and

concludes that “African Americans received 67%

of the catheterizations that they should have

received, and whites received 14% more than

their share” (86, page 90). 

The quotations above make clear that health

disparity often is equated with the concept of

disproportionality. What is perhaps less clear is

that, in the context of the commonly used

“language of disproportionality,” there usually is

an implied reference group, which is the general

population. In fact, in the catheterization

example, LaVeist was arguing explicitly against

measuring health disparity using a relative

measure such as a risk ratio or odds ratio, because

doing so means using a particular social group (in

this case, whites) as the reference group, which

necessarily assumes that the rate in the reference

group is “most desirable.” Thus, he argued that

disparity measures that use whites as the reference

group would not be able to identify their “overutilization” of cardiac catheterization. The

intuitive ethical notion expressed in the

quotations above is that the amount of ill health

in social group j is far greater than would be

expected if ill health were evenly distributed with

respect to all J social groups. An even distribution

of ill health across J social groups implies that the

47
number of individuals of social group j with

condition y is proportionate to group j’s share of

the total population, so that the rate of ill health,

Yj, in each of the j groups is exactly the same,

which would necessarily equal the rate in the

total population. Thus, the proportional

distribution of y among J groups implies that

(the mean of y) for all groups. 

This is an important point because many

commonly used measures of income disparity

(e.g., the Gini coefficient) and residential

segregation (e.g., the Index of Dissimilarity), some

of which currently are employed to measure

health disparities, may be expressed conveniently

as measures of average disproportionality (87–89).

For each social group j, we can define a health (or

ill health) ratio as the ratio of measure y in the jth

group to that of the mean of y for the whole

population, so that for each group. Note

that this makes such measures relative rather than

absolute disparity indicators. In this framework,

measures of disparity take the general form

[18]

where pj is group j’s proportion of the total

population and f(rj

) is some disproportionality

function of the ratio . It should be clear

that equation [18] is a weighted disparity measure

because each group’s disproportionality function

f(rj) is multiplied by its population share pj.

Measures of this type of disparity indicator differ

because they implement different disproportionality functions. Perhaps one of the appealing

features of such measures is that they provide a

rather direct correspondence between the

commonly used languages of health disparity in

terms of “disproportionality” with the

operationalization of the measurement. 

Figure 16 (page 49) depicts the concept of

“disproportionality” using data on all deaths in

the United States, by gender and education, for

the year 2000. Among males, those with less than

12 years of education bear a disproportionate

burden of all deaths, as they account for 24% of

all male deaths but account for only 12% of the

male population. Conversely, males with greater

than 12 years of education account for 55% of the

total population but only 32% of all deaths. The

level of disproportionality for females with less

than 12 years of education is slightly smaller.

Table 2 (page 49) shows some commonly

used statistical measures and their

disproportionality functions. Readers should note

that the measures differ only in how they express

the difference between shares of health and shares

of population. 

Entropy Indices

One class of disproportionality measures that

often is favored by economists are measures of

general entropy, developed by Henri Theil (90).

The example described below is for measuring the

disparity in BMI, which is a risk factor for a

number of cancer sites (91,92). Theil’s index gives

relatively more weight to the concentration in the

upper end of the health distribution and is

calculated (with grouped data) by summing the

product of each group’s BMI share of the

population’s total BMI and the natural log of each

rj = Yj / Y

I = pj f (rj Σ ) j

rj = Yj / Y

Yj = Y

48
49

Figure 16. Example of the “Disproportionality” of Deaths and Population, by Gender and Education,

2000

Deaths Population Deaths Population

Figure 16. Example of the “Disproportionality” of Deaths and Population, by Gender and Education, 2000

Source: NCHS. Deaths: Final Data for 2000, Natl Vit Stat Rep 2002;50(15).

Shares of All Deaths and Population, by Gender and Education, 2000

Males Females

>12 yrs >12 yrs

12 yrs 12 yrs

<12 yrs <12 yrs

32%

45%

24%

55%

32%

13%

33%

46%

21%

55%

32%

12%

Source: NCHS. Deaths: Final Data for 2000, Natl Vit Stat Rep 2002;50(15). 

Table 2. Commonly Used Disproportionality Functions

Index Name Disproportionality Function

Squared coefficient of variation (CV2) (rj – 1)2

Gini index (G) Individual-level data: | ri – rj | / 2

Grouped data: rj(qj – Qj), where qj is the proportion of the total population in groups less healthy than group j, and

Qj is the proportion of the total population in groups healthier than group j (i.e., pj + qj + Qj = 1)

Relative concentration index (RCI) Same as for G, but groups are ranked by social group position instead of by health, so that qj is the proportion of

the total population in groups less advantaged than group j, and Qj is the proportion of the total population in

groups more advantaged than group j (i.e., pj + qj + Qj = 1) 

Theil index (T ) rjln(rj)

Mean logarithmic deviation (MLD) ln(1/rj) = –ln(rj)

Variance of log-health (VarLog) [ln rj – ∑(ln rj)]2

Note: Adapted from Firebaugh, 2003 (88).
group’s BMI share. For individual-level data, total

disparity in BMI measured by Theil’s index can be

written as

[19]

where pi is an individual’s population share

(which in the case of individual data will be 1/n,

so that pi

= 1) and ri is the ratio of the

individual’s BMI to the population average BMI

(i.e., ). When the population of

individuals is arranged into J groups, Theil

showed that equation [19] is the exact sum of two

parts: between-group disparity and a weighted

average of within-group disparity:

[20]

where Tj is the disparity in BMI within group j.

The within-group component (the second term

on the right side of equation [20] is weighted by,

in this case, group j’s share of the total BMI,

because (where sj is the share of total

BMI) when the denominator for rj is the mean

BMI for the total population. More importantly,

the above decomposition also makes it clear that

it is possible to calculate between-group disparity

in BMI—the primary quantity of interest with

respect to social disparities in health—in the

absence of data on each individual. The only data

needed are the group proportions and the ratio of

the group’s BMI to the population average BMI.

Between-group disparity, however, may increase

because total disparity is increasing (i.e., both

between-group and within-group disparity are

increasing simultaneously). The primary

advantage of using additively decomposable

inequality measures is that they allow us to

determine not just whether between-group

disparity is increasing, but whether the share of

total disparity that is due to disparity between

groups is increasing or decreasing. Although this

measure has attractive qualities, the betweengroup/within-group decomposition requires

continuous outcome data measurable in

individuals, so it is not clear whether this can be

applied to many relevant cancer outcomes that

are based on events (e.g., incidence, mortality, or

screening). Even for noncontinuous outcomes,

however, entropy indices easily can be used to

calculate between-group disparities in the absence

of individual-level data. For example, suppose that

instead of BMI we wanted to measure the

between-group disparity in obesity rates. We could

do this by calculating the first term on the right

side of equation [20] using only the data on each

group’s proportion in the population (pj

) and the

group’s rate of obesity relative to the overall

population rate (rj

)—data that are more likely to

be readily available. 

Measuring between-group inequality in BMI

in the above manner makes clear that changes in

the value of disparity over time are a function of

two quantities: changing group proportions and

changing social group BMI ratios. This is

important— in the case of obesity, for example—

because differentiating between these two

components of change has different implications

for obesity as a public health problem and may be

the result of very different social policies. If we

find that disparity is increasing but that the main

reason for the observed change is that the share of

the population among social groups at the tails of

the BMI distribution has increased, it simply

demonstrates that the inequality increase is due

primarily to the movement into and out of

pj x rj = sj

T = pjrjln(rj) + pjr Σ j

Tj j = 1

J

Σj = 1

J

ri = yi / Y1n pj

sj

s Σ j ( (

T = pi ri ln(ri Σ ) i = 1

N

50
different social groups—not to differentially

increasing rates of BMI within subgroups of a

social group. However, if we find that population

shares have remained relatively constant over

time but BMI disparity has increased because BMI

ratios are increasing, this implicates differential

sources of BMI change among particular groups—

which may then become the target of public

health intervention.

Atkinson’s Measure

Atkinson’s index actually is not a single index of

disparity but depends on specifying the relative

sensitivity of the index to different parts of the

distribution. One way of writing Atkinson’s index

is:

[21]

where pj and rj are again, respectively, the share of

population and the health ratio (relative to the

total population rate), as defined above. Clearly

with this index, the extent of disparity hinges on

specifying the parameter ε, which indicates the

degree of “aversion to disparity.” Larger values of ε

indicate stronger aversion to disparity, which also

may be interpreted as placing increased weight on

the least healthy groups. For example, if we are

particularly concerned about improving the

health of least-healthy individuals, we could make

the measure of disparity more sensitive to changes

in the bottom of the health distribution.

Gini Coefficient

The Gini coefficient summarizes social group

differences in, for example, BMI for the entire

population and can be thought of as a measure of

association between each social group’s share of

population, ranked by the group’s health and its

share of health. Its formula for individual data is

given above for the IID in equation [2], when

α = 2 and β = 1. Formally, the Gini coefficient is

the ratio of the area between the line of equality

in Figure 17 (page 52) and the Lorenz curve to the

total area of the triangle beneath the line of

equality (40). Because the Gini coefficient is a

function of the disproportionality between shares

of population and shares of health, one can see

from Figure 17 that health disparity increases as

the Lorenz curve moves further away from the

line of equality (i.e., as the disproportionality

between shares of population and shares of health

increases).

Concentration Index

The Concentration Index (CI) is calculated

similarly to the Gini index, but it results from a

bivariate distribution of health and social-group

ranking. In the same way that the Gini coefficient

is derived from the Lorenz curve, the CI is derived

from a concentration curve, where the population

is ordered first by social-group status (rather than

by health status, as for the Gini), and the

cumulative percent of the population then is

plotted against the group’s share of total ill

health. When the y-axis is the share of ill health,

this results in the Relative Concentration Index

(RCI); however, an Absolute Concentration Index

(ACI) also may be derived by plotting the

cumulative share of the population against the

cumulative amount of ill health (i.e., the

cumulative contribution of each subgroup to the

mean level of health in the population). Figure 18

(page 53) gives a graphical representation of a

relative concentration curve. Note the similarity

with the Lorenz curve drawn in Figure 17 to

illustrate the Gini coefficient. The two curves and

A = 1 – [ pjrj

1 – ] , > 0 1 / 1 – Σj = 1

J ε

ε ε

51
thus the Gini coefficient and the RCI are

calculated similarly, the only difference being the

way in which social groups are ordered. In the

case of the Gini coefficient, social groups are

ordered by their health status (lowest to highest),

regardless of their socioeconomic group ranking;

for the RCI, social groups are ordered by their

ranking in terms of, for example, years of

education, regardless of their health status. It is

important to note that, because the

Concentration Index incorporates information

on both health and social-group status, the

concentration curve may lie either above or 

below the line of equality. The general formula for

the Relative Concentration Index (RCI) for

grouped data is given by Kakwani and colleagues

(93) as:

[22]

where pj is the group’s population share, μj is the

group’s mean health, and Rj is the relative rank of

the jth socioeconomic group, which is defined as:

[23]

where pγ

is the cumulative share of the population

up to and including group j, and pj is the share of

the population in group j. Rj essentially indicates

the cumulative share of the population up to the

midpoint of each group interval, similar to the

categorization of the Slope and Relative Index of

Rj = pγ– p Σ j j = 1

J

2

1

RCI = [ pj Σ j Rj]– 1 j = 1

J

μ μ 2

52

Figure 17. Representation of the Gini Coefficient of Disparity

0 100

100

0

Cumulative Percent of Health

Cumulative Percent of Population, Ranked by Health

Figure 17. Representation of the Gini Coefficient of Disparity

Line of Equality

Lorenz Curve
Inequality above. In fact, the RCI has a specific

mathematical relationship with the RII (60):

[24]

where R is the relative rank variable identified in

equation [23]. Thus, the SII/RII and the ACI/RCI

will produce the same rank ordering of health

inequality over time but will differ in scale. The

absolute version of the Concentration Index (ACI)

is calculated by multiplying the RCI by the mean

rate of the health variable:

[25]

where μ is the mean level of health in the

population. It also is worth pointing out that,

when using continuous health outcomes, the RCI

is unbounded and takes minimum and maximum

values of –1 and +1, but when using binary health

outcomes, the possible values of the RCI are

limited by the mean (e.g., the prevalence) of the

distribution (94). Adam Wagstaff shows that, for a

given nonzero mean of a binary variable (μ), the

minimum of the RCI is [ ] and the

maximum is [ ], with n being the

sample size. This of course has implications for

analyses that compare the extent of

socioeconomic inequality in health between areas

or outcomes with very different levels of average

health, and one potential strategy for facilitating

comparisons is to normalize the Concentration

Index by dividing it by its bound (95). 

1 – μ + (1/n)

μ – 1 + (1 /n)

ACI = μRC I RCI = 2var(R)RII

53

Figure 18. Representation of the Health Concentration Curve

0 100

100

0

Cumulative Percent of Ill Health

Cumulative Percent of Population, Ranked by Socioeconomic Position

Figure 18. Representation of the Health Concentration Curve

Disparities Favor

the “Worse-off”

No Social Disparity

Disparities Favor

the “Better-off”
Table 3 shows a simple example of how the

RCI and ACI are calculated using equations [22]

and [25] with grouped data using lung cancer

mortality rates by educational attainment. One

can see that lung cancer mortality rates decrease

with increasing education, and the negative value

of both indices shows that the disparity in lung

cancer mortality favors the better educated.

One of the reasons the ACI and RCI (and, by

extension, the SII/RII indices) are favored by some

is that they “reflect the socioeconomic dimension

to inequalities in health” (60, page 548). That is, a

downward health gradient (such that health

worsens with increasing social-group rank) results

in a positive index, whereas an upward health

gradient results in a negative index. For example,

if the data in Table 3 were reversed so that lung

cancer mortality rates for those with <12 years of

education were 16.9 and the rates were 49.8 for

those with >12 years of education, the RCI then

would be calculated as 0.114 and the ACI as

4.873, indicating that lung cancer mortality

actually favors the less educated. This sensitivity

to the direction of the health gradient is not a

property of other disproportionality measures,

such as the Gini coefficient and the Index of

Dissimilarity, because they do not depend on the

strict ordering of social groups.

This undoubtedly is an advantage of the RCI,

but, as with all disparity measures, it also may be

seen as a disadvantage. Because of its sensitivity to

socioeconomic gradients in health, the RCI may

not register any disparity when health is not

ranked directly by social group. Thus, when a

social group ranked in the middle of a hierarchy

bears a disproportionate burden of ill health, the

RCI well may register this as zero disparity. This is

not just a theoretical limitation of the RCI. For

instance, age-adjusted rates of breast cancer deaths

(per 100,000) in the United States in 1998 were

20.0 among those with less than a high-school

education, 28.4 among those with a high-school

education, and 22.0 among those with at least

some college education (9). If the respective shares

of the population in each of the education groups

were approximately 38.8%, 20%, and 41.2%, the

RCI would be virtually zero, indicating no

educational mortality disparity; yet those with a

high-school education will contribute roughly

40.3% of breast cancer deaths. A reasonable case

could be made that a disproportionate burden of

breast cancer falls on the high-school-educated

54

Table 3. Educational Disparity in Lung Cancer Mortality, 1999

Education Rate per 100,000 Population Share Midpoint (%) CI

<12 years 49.8 0.128 0.064 0.408

12 years 41.0 0.327 0.292 3.913

>12 years 16.9 0.545 0.728 6.699

T otal 29.0 1.0 1 1.020

Relative Concentration Index → –0.240

Absolute Concentration Index → –6.959

Note: Rates are for persons aged 25–64 years and exclude the following states: Georgia, Kentucky, Rhode Island, and South Dakota. Rate data are from

DATA2010...the Healthy People 2010 Database, April 2004 edition, and SEER*Stat. Population data are from NCHS, Deaths: Final Data for 1999: Table VII.
(using this categorization of education), but the

RCI would not reveal this pattern. This pattern of

the worst health among those in the middle social

group is not simply an artifact of breast cancer as

an unusual cause of death. This pattern also is

seen for colorectal and prostate cancers and

melanoma as well where rates across ordered

social groups are not simple gradients. 

We use the breast cancer example not

necessarily to suggest that the RCI is a poor index

for measuring social-group disparities in health,

but rather to emphasize that all disparity

measures have advantages and disadvantages that

should be considered when selecting and

interpreting a disparity index; no summary

disparity measure should be used as a substitute

for detailed inspection of the health status

indicators for each social group via tables and

graphs.

Wagstaff also derived a method for

incorporating a society’s degree of aversion to

disparity into the RCI, which he calls the

“extended” Concentration Index (96). The

aversion parameter changes the weight attached

to the health of different socioeconomic groups in

a manner similar to the Atkinson Index described

above. The formula for this extended version of

the RCI for grouped data is: 

[26]

where ν is the “aversion parameter,” and the other

quantities are defined as in the RCI in equation

[22] above. Setting ν = 1 weights every group’s

health equally (i.e., complete indifference to

inequality), and setting ν = 2 gives the standard

RCI defined above. As ν increases, the weight

attached to the health of lower socioeconomic

groups increases, and the weight attached to the

health of higher socioeconomic groups decreases.

Table 4 (page 56) shows the effect of varying the

weight placed on the health of the less-educated

groups for the disparity in current smoking in the

state of Michigan in 1990 and 2002. The two

rightmost columns are the calculated RCIs, with

differing aversions to disparity. Setting ν = 2 gives

the standard RCI of –0.129, indicating that the

disparity in current smoking favors the better

educated. Increasing the weight placed on the

health of the less-educated groups in 1990 results

in only a marginal increase in the measure of

disparity to –0.178, most likely because the rate of

smoking among those with <8 years of education

actually is quite low. The major effect of the

differential weighting of the RCI can be seen in

the disparity change from 1990 to 2002; in 2002,

the standard RCI(2) was –0.19, a disparity increase

of 48.5%, and the more bottom-sensitive RCI(4)

was –0.32, indicating a much larger 81% increase

in the relative education disparity in smoking.

The reason the increase in disparity is so much

larger for RCI(4) is that, although rates of smoking

decreased overall and in every other education

category, the estimated rate of current smoking

actually increased among the least-educated

group. This example shows how we can

incorporate an ethical judgment (particular

concern about the health status of the least

educated) into a measure of health disparity.

RCI(v) = p μ (1 – R )

v –

Σ= 

J

μ

v p (1 – R )

v –

Σ= 

J

v –

55
Combining Health Disparity and Average

Health

As we emphasized in the above discussion of

relative and absolute health disparities, the goals

of Healthy People 2010 are couched specifically in

terms of both health disparities and average levels

of population health. Thus, we also may be

interested in investigating potential ways to

incorporate both average health and health

disparity into a single summary measure. One

potential measure, created by Adam Wagstaff, is

called the Health Achievement Index or HAI (96).

The Health Achievement Index

The HAI in some respects is similar to the ACI

described above, but combines disparity and

average health by essentially subtracting the

Absolute Concentration Index from the

population’s average health, creating a “disparitydiscounted” level of average health. The formula

for the HAI is (96):

[27]

where μ is the population’s average health and

RCI(ν) is the extended Relative Concentration

Index defined above. Thus, applying equation

[27] to the data on the average rate and

educational disparity (using RCI[2]) in smoking

in Michigan, the HAI(2) for Michigan in 1990

is 0.29 x (1 – [–0.129]) = 0.33, and is 0.24 x

(1 – [–0.191]) = 0.29 in 2002. Clearly, if RCI = 0,

then the HAI is equal to the population average

rate of health, and the larger the RCI, the further

away the HAI is from the population average—a

kind of “disparity penalty” applied to the

population average rate. In this sense, the HAI is

HA I(v) = μ 1 – R CI(v)

= μ – ACI(v)

56

Table 4. Example of Extended Relative and Absolute Concentration Index Applied to the Change in

Educational Disparity in Current Smoking, Michigan, 1990 and 2002

Education Population (%) % Smokers Midpoint (%) RCI ( ν = 2) RCI ( ν = 4)

1990

<8 years 4.5 27.2 2.3 0.006 0.011

9–11 years 12.4 39.9 10.7 –0.082 –0.131

12 years 36.9 33.3 35.4 –0.068 –0.057

13–15 years 27.3 29.6 67.5 –0.003 –0.001

16+ years 18.9 13.6 90.6 0.019 0.000

T otal 100.0 29.1 –0.129 –0.178

ACI = –3.75 ACI = –5.16

2002

<8 years 2.0 36.6 1.0 –0.021 –0.041

9–11 years 7.8 36.3 5.9 –0.073 –0.130

12 years 31.4 31.3 25.5 –0.137 –0.152

13–15 years 29.6 24.5 56.0 –0.003 –0.001

16+ years 29.2 12.2 85.4 0.042 0.002

T otal 100.0 24.2 –0.191 –0.321

ACI = –4.63 ACI = –7.77

Note: Data is for current smoking and is drawn from the 1990 and 2002 Behavioral Risk Factor Surveillance System (BRFSS).
not exactly a measure of health disparity but a

potentially useful way of capturing both

aggregative (Healthy People 2010 Goal 1) and

disparity (Healthy People 2010 Goal 2) concerns in

a single summary measure, at least with respect to

ordered social groups. For example, while both

relative and absolute education disparity in

smoking increased in Michigan over the 12-year

period (i.e., education disparity unambiguously

increased, see Table 4), health achievement

actually improved because almost all education

groups experienced a decrease in the rate of

smoking (in this case, health “achievement”

increases as the population rate of smoking

decreases). 

Two populations (or time periods) therefore

might have the same value on the Achievement

Index but differ greatly on both average health

and the extent of health disparity. For example, in

Figure 19 (page 58) the relative concentration

curves for education disparity in obesity in New

York State are plotted for 1990 and 2002. Because

the 2002 curve is beneath the 1990 curve for every

education group, we can unambiguously declare

that relative education inequality in obesity in

New York decreased from 1990 to 2002. The

standard RCIs summarizing the two curves also

reflect the decrease in disparity, going from –0.284

in 1990 to –0.125 in 2002. As was mentioned at

the outset, however, we do not believe that

disparity is all that matters. We also are concerned

with the average health of the population, and

the estimated obesity rate in New York more than

doubled over this period, from 9.8% in 1990 to

20.6% in 2002. Figure 20 (page 59) shows the

absolute concentration curves, which clearly

reflect the increase in obesity among all groups.

Inspection of the education-group-specific obesity

rates reveals that, in general, the education

disparity in obesity declined because of increasing

obesity rates, particularly among the middle- and

better-educated groups. When we incorporate the

adverse changes in overall population rates of

obesity with the changes in disparity, the change

in the Health Achievement Index (for which

larger values are worse because the health

outcome, obesity, is negative) indicates that

things became worse, having increased from 0.13

in 1990 to 0.23 in 2002.

57
58

100

Cumulative Percent of Population, Ranked by Education

Figure 19. Relative Concentration Curves for Educational Disparity in Obesity in New York State, BRFSS, 1990 and 2002

80

100

80

60

40

20

C l ti P t f Ob P (BMI 30)

Equality

1990

2002

Figure 19. Relative Concentration Curves for Educational Disparity in Obesity in New York State, BRFSS,

1990 and 2002
59

100

Cumulative Percent of Population, Ranked by Education

Figure 20. Absolute Concentration Curves for Educational Disparity in Obesity in New York State, BRFSS, 1990 and 2002

80

25

20

15

10

C l ti P t f T t l Ob ity R t

Equality

1990

2002

Figure 20. Absolute Concentration Curves for Educational Disparity in Obesity in New York State, BRFSS,

1990 and 2002
61

Choosing a Suite of Health Disparity Indicators

Monitoring progress toward the elimination of

disparities in cancer-related health objectives

involves a number of ethical, conceptual, and

methodological issues that must be given careful

consideration to answer the question of which

measure or measures should be employed to

monitor progress toward the elimination of health

disparities between social groups. 

One possibly useful way to approach the

measurement of health disparity is to consider a

sequence of methodological approaches. 

• First, we cannot emphasize enough the close

inspection of the underlying subgroup-specific

health outcomes (rate or prevalence, etc), either

via tabular or graphical inspection. This is likely

to reveal important population health patterns,

highlight the situation of specific subgroups of

interest, and lend an understanding of any

underlying heterogeneity that a summary

measure of health disparity may not emphasize. 

• Next, consider the relevant question that is to

be answered. If one is interested in the health

disparity between two particular groups—for

example, the trend in the disparity between black

and white males in lung cancer mortality—then

the use of a pairwise comparison of trends is

sufficient. 

• Even for assessing health-disparity trends

between two groups using a pairwise comparison,

we recommend using both an absolute and a

relative disparity measure. This is especially

warranted when making long-term comparisons

that may involve steep declines or increases for all

social groups. Although the relative disparity

measure gives some indication of the progress (or

lack thereof) one group is making, regardless of

the actual level of health, absolute disparity

measures provide a context in which to judge the

public health impact of relative health disparities.

Thus, we would argue for the primacy of the

absolute indicator of disparity. Efforts to improve

public health often rely on the absolute burden of

disease; thus, the absolute disproportionality in

health disparity also should have priority. This is

the case especially when comparing the size of

social-group disparity across different cancer

outcomes and risk factors. We also understand,

however, that this in no way excludes particular

cases in which the relative inequality may be

judged—for other equally good reasons—to be of

high priority despite low levels of disproportionate absolute burden. For instance, the twofold relative disparity in cervical cancer between

black and white women may be judged to be

especially important because it is a health

disparity that is almost entirely avoidable through

the routine use of screening, even though the

absolute disparity involves only about 5 deaths

per 100,000.

• If one is interested in monitoring the health

disparity trend across the entire range of
62

subgroups within a social-group category—for

example, across all racial/ethnic groups rather

than comparing, say, blacks and whites—or if the

social-group category has many subgroups—such

as the disparity across the 50 U.S. states—then

summary measures of health disparity are

warranted. The first decision involved in choosing

a summary measure is dictated by whether or not

the social groups in question have a natural

ordering.

Summary Indicators

Ordered Social Groups

If the social group does have a natural ordering, as

with education and income groups, then we

recommend using either the Absolute

Concentration Index (ACI) or Slope Index of

Inequality (SII) as a measure of absolute health

disparity, and the Relative Concentration Index

(RCI) or the Relative Index of Inequality (RII) as a

measure of relative disparity. The major reasons

for choosing these particular measures are that

• they account for changes in the underlying

population distributions in the social groups over

time and use information across the entire range

of social groups;

• they are flexible enough to allow different

levels of aversion to disparity to be incorporated;

and 

• they are sensitive to the direction of the social

gradient in health.

Although this last criterion mainly is what

distinguishes these measures from other summary

measures of inequality, such as the Gini

coefficient or the Index of Dissimilarity, we would

also reemphasize that, if the social groups in the

middle of the distribution (e.g., those with a highschool education as opposed to those with less or

more education) experience a disproportionate

burden of ill health, our selected measures may

indicate that no disparity exists when it in fact

could be argued otherwise. Of course, if the

sequence laid out above is adhered to, then Step

1—a simple and careful inspection of the basic

subgroup data—should reveal this. 

This is part of the “cost” of using summary

measures of disparity, but in this case a

comparison of the RCI or RII with another

measure of disproportionality that is not strictly

sensitive to health gradients, such as the Gini

coefficient or Theil index, may reveal important

information about the social distribution of

health. Lastly, because the RCI has a mathematical

relationship to the RII, and the ACI has such a

relationship to the SII, they always will result in

the same rank ordering of health distributions.

That being said, one additional desirable feature

of the ACI and RCI is the ability to graph their

associated health concentration curves. Although

the ability of any summary measure of health

disparity to communicate important information

about disparity trends to health policy makers

may be limited, the ACI and RCI may serve this

purpose better than the RII and SII.
63

Unordered Social Groups 

Our recommendations for health disparity

measures for ordered groups restate the

recommendations of earlier reviews of health

disparity measures (60,70). In the context of the

Healthy People 2010 goals, however, groups with a

natural ordering represent only a small number of

the social groups across which we want to

eliminate disparities in cancer-related health

outcomes. Therefore, we also need to think about

disparity measures that can be applied to

unordered social groups. Again, we would

emphasize choosing a summary measure of health

disparity only when one is interested in

monitoring the extent of disparity across more

than two or three social groups. For comparisons

of two specific groups, there is no substitute for

simple pairwise measures of absolute and relative

disparity. 

If comparisons across multiple unordered

groups are needed, we recommend the BetweenGroup Variance (BGV) as a summary of absolute

disparity and the general entropy class of

measures developed by Henri Theil as summary

measures of relative disparity (more specifically,

the Theil index and the Mean Log Deviation). An

important reason for choosing the Between-Group

Variance and the entropy-based measures is that

they are disparity measures that can be

decomposed perfectly into between-social-group

and within-social-group components, given a

continuous health outcome. This cannot be said

of other measures, such as the Gini coefficient

and Atkinson’s measure (97,98). The ability of the

variance and the entropy class of disparity

measures to decompose disparity is important

because it allows one to look at any number of

cross-classified social groups, whether ordered or

not. For example, race and income, or gender and

education, can be examined jointly to assess the

trend in disparity between certain dimensions of

society. We could look first, for example, at the

trend in between-race disparity in cancer survival

time and see whether the disparity is increasing or

decreasing. We then could look at the disparity

between race-education groups over time. It may

be that, while the between-race disparity is

decreasing, educational disparities within race

groups actually are increasing. In addition, the

entropy-based measures also can be decomposed

to investigate the relative effects of changing

social group distributions versus changing health

distributions. This is important because both of

these aspects of the population constantly are

changing over time. Understanding the relative

impact of health changes versus compositional

changes in social groups is important for

understanding the prospects for intervening to

eliminate health disparities. Thus, because of their

decomposition properties, the entropy measures

may be useful tools for describing and

understanding the stratification of cancer-related

health outcomes across time.

Our recommendation for measures of health

disparity, for both ordered and unordered social

groups, come from explicitly adopting the

population health perspective toward monitoring

health disparities. By taking a population health

perspective, we emphasize using the total

population as the reference group for measuring

health disparity, weighting social groups

according to the number of individuals they

represent, and examining both absolute and

relative disparities in health. By doing so, we are

able to account for changes in the distribution of
individuals across social groups over time, a fact

that has clear population health consequences,

and we also are able to express health disparities

in a way that emphasizes their overall burden on

population health.

64

Table 5. Summary Table of Advantages and Disadvantages of Potential Health Disparity Measures

Absolute All Reflect Social Inequality

or Reference Social SES Group A version Graphical

Disparity Measure Symbol Relative Group Groups Gradient W eighting Parameter Analogue

T otal Disparity

Inter-Individual Difference IID Variable ATBOa No No No Yes No

Individual-Mean Difference IMD Variable Average No No No Yes No

Social Group Disparity

Absolute Difference AD Absolute Best No Yes No No Yes

Relative Difference RD Relative Best No Yes No No Yes

Regression-Based Relative Effect RRE Relative Best Yes Yes Nob No Yes

Regression-Based Absolute Effect RAE Absolute Best Yes Yes Nob No Yes

Slope Index of Inequality SII Absolute Average Yes Yes Yes No Yes

Relative Index of Inequality RII Relative Average Yes Yes Yes No Yes

Index of Disparity IDisp Relative Best Yes No No No No

Population Attributable Risk PAR Absolute Best Yes No Yes No Yes

Population Attributable Risk% PAR% Relative Best Yes No Yes No No

Index of Dissimilarity ID Absolute Average Yes No Yes No Yes

Index of Dissimilarity% ID% Relative Average Yes No Yes No No

Relative Concentration Index RCI Relative Average Yes Yes Yes Yes Yes

Absolute Concentration Index ACI Absolute Average Yes Yes Yes Yes Yes

Between-Group Variance BGV Absolute Average Yes No Yes Yes No

Squared Coefficient of Variation CV2 Relative Average Yes No Yes No No

Atkinson’s Measure A Relative Average Yes No Yes Yes No

Gini Coefficient Gini Relative Average Yes No Yes No Yes

Theil Index T Relative Average Yes No Yes Yes No

Mean Log Deviation MLD Relative Average Yes No Yes Yes No

Variance of Logarithms VarLog Relative Average Yes No Yes No No

aAll those better off.

bIn the case of regression-with grouped data.
65

Appendix: Example Analyses

This appendix presents two examples of how to

measure and monitor cancer-related disparity

trends using the suite of indicators and

measurement strategy outlined in the

recommendations above. The examples are taken

from the cancer-related objectives outlined in

Healthy People 2010 and are illustrative rather than

substantive analyses. The first example assesses

the trend in the prevalence of mammography

screening among education groups and

emphasizes disparity measures for ordered social

groups. The second example assesses the trend in

colorectal cancer mortality among racial groups

and highlights the use of disparity measures for

unordered social groups.

Example 1: Educational Disparity in

Mammography Screening, 1990–2002

This example is based on self-reported data on the

use of mammography screening from the Centers

for Disease Control and Prevention’s (CDC)

Behavioral Risk Factor Surveillance Survey

(BRFSS), an annual state-based telephone survey

of adults. Although perhaps not the optimal

source of data on routine cancer screening

because of its high rate of nonresponse, the BRFSS

may be used to approximate a nationally

representative sample (99), and its annual

administration and timely reporting of results

make it useful for illustrating disparity trends.

Method

• Step 1: Inspect the underlying subgroup data.

Figure A1 (page 66) shows the prevalence of

women over age 40 who reported having not

received a mammogram in the past 2 years for

five education groups. From the chart, two things

are immediately clear. First, all groups are

improving over time (i.e., the proportion of

women not having mammograms is declining),

and some groups have actually achieved the

Healthy People 2010 target rate of 30%. Second,

there is a graded relationship between the

proportion of women not having a mammogram

in the past 2 years and years of education—

women with fewer years of education are less

likely to have received a mammogram in the past

2 years.

• Step 2: Determine the disparity question to be

answered. For this example, we are concerned

about whether the extent of disparity in

mammography screening across all education

groups is increasing or decreasing. As a result, we

will use a summary measure of health disparity.

Suppose, however, that there had been a

dedicated effort to increase the rate of screening

among women with a high-school education. We

then might be more interested in the question of

whether the effort had narrowed the gap in

screening between women with the highest 
screening rates (college-educated) and highschool-educated women. In this case, a summary

measure might mask an important change in this

particular subgroup, so we would use a simple

pairwise comparison of the absolute and relative

difference in screening. 

• Step 3: Choose a summary measure of health

disparity. Having decided to use a summary

measure, the choice of a measurement tool

hinges on whether the social groups in question

have a natural ordering. In the case of years of

education, there clearly is a natural ordering, so

we will choose the Relative Concentration Index

(RCI) as a measure of relative disparity and the

Absolute Concentration Index (ACI) as a measure

of absolute disparity. Both measures are

calculated for two levels of disparity aversion,

ν = 2, which gives the standard RCI and ACI (96),

and ν = 4, which gives additional weight to the

health of the lower-educated groups. 

Results 

For the beginning and end of the period

1990–2002, Table A1 (page 68) shows the

prevalence of not having a mammogram in the

past 2 years (μj

) and the population proportion

66

Figure A1. Proportion of Women Age 40 and Over Who Did Not Receive a Mammogram in the Past

2 Years by Educational Attainment, 1990–2002

1990

60

50

40

30

20

10

0

Percent

991 1993 1995 1997 1999 2000 2001 2002

Figure A1. Proportion of Women Age 40 and Over Who Did Not Receive a Mammogram in 

 the Past 2 Years by Educational Attainment, 1990-2002

Source: CDC, Behavioral Risk Factor Surveillance Surveys 1990–2002.

1992 1994 1996 1998

<8y 9–12y 12y 13–15y 16+y 2010 Target

Source: CDC, Behavioral Risk Factor Surveillance Surveys 1990–2002.
(pj

) for each group. The relative ranking of each

interval (Rj

), based on the midpoint of the

cumulative population distribution, is derived by

applying equation [23] above; thus, for the group

with 9–11 years of education, the relative ranking

is 0.09 + (0.5 x 0.14) = 0.17. This particular

group’s contribution to the RCI(2) is calculated

using equation [26] above as [2 x 0.14 x

(1 – 0.17)(2–1)] – [(2/41.0) x 51.6 x 0.14 x

(1 – 0.17)(2–1)] = –0.0618. Applying equation [26]

across all education groups gives the overall

RCI(2), which for 1990 = –0.1045. To give this

value some perspective, Zhang and Wang, using

income as a measure of socioeconomic position

and using data from the National Health and

Nutrition Examination Survey (NHANES III) (100),

report a relative Concentration Index of –0.055

for obesity. Because in this case the outcome is the

proportion of women not having a mammogram,

the negative sign of RCI(2) indicates that the

disparity favors better-educated women. A positive

RCI(2) in this case would have indicated that

disparity actually favors less-educated women.

Additionally, the effect of increasing the aversion

to disparity becomes readily apparent as the value

of the RCI in 1990 increases (from –0.10 to –0.19)

when the aversion to disparity increases twofold.

Our preferred measure of absolute disparity for

ordered social groups, the Absolute Concentration

Index (ACI), also is displayed in Table A1 and is

calculated from equation [27] above; for 1990

ACI(2) = 41.0 x (–0.1045) = –4.2. 

Comparing 1990 and 2002 it appears that, as

measured by the standard ACI (i.e., with ν = 2),

absolute disparity in mammography screening

declined substantially over those 12 years—a

43.9% reduction. Relative disparity showed only

slight improvement, with the HCI(2) declining

only 2.6%. Note that, with an increased aversion

to disparity (ν = 4), relative disparity actually

shows a slight increase (from –0.191 to –0.201),

while absolute disparity still declines (from –7.8 to

–4.7). Although this indicates virtually no change

in relative disparity, Figure A2 (page 69) shows

that, when calculated annually, relative disparity

was not consistent over the entire period. As the

prevalence of not having a mammogram fell

faster for the less-educated groups in the first half

of the 1990s, both absolute and relative disparity

declined (i.e., the best possible scenario). As

screening rates tapered off among the lesseducated groups, however, relative disparity

increased in the latter half of the 1990s,

eventually returning to the 1990 level by 2002.

Note also that two components of the RCI and

ACI were changing over the period of observation:

the prevalence rates and the population shares in

each education group. Most notably, the share of

the population with less than 12 years of

education—the groups with the highest

prevalence rates—declined from 24% (0.09 among

those with <8 years plus 0.14 for those with 9–11

years) to 14% (0.06 + 0.08). Because the RCI is a

population-weighted index, this change alone

(i.e., in the absence of any change in prevalence

rates) would serve to decrease the level of

disparity. Thus, a logical next step in analyzing

the disparity trend might be to decompose the

change in disparity to determine how much of

the change is due to declining prevalence rates

and how much is due to upward shifting of the

education distribution. We will not go through

the decomposition steps here, but we would reemphasize that such decomposition techniques

are likely to be useful in understanding the

sources of changes in health disparities.

67
68

Thus, by using two summary measures of

disparity, we can make some generalization about

the trend in the education-related disparity in

mammography screening. Between 1990 and

2002, the relative disparity between education

groups remained essentially the same, but the

absolute disparity declined because the prevalence

of not having a mammogram declined in all

education groups, with the largest absolute

declines having occurred among the less-educated

groups. Thus, we would argue that the population

health burden associated with the educationrelated disparity in mammography screening has

decreased. This, of course, is not the best possible

scenario, but we would argue that the disparity

situation is better in 2002 than it was in 1990. 

Lastly, we would re-emphasize that our

conclusion about the socioeconomic disparity

trend in mammography reflects a population

health perspective on health disparities. Because

we were concerned about the disparity across all

education groups, we chose two populationweighted summary disparity measures. The results

obtained by the application of these measures

may or may not be consistent with other disparity

measures that reflect concern about a different

dimension of disparity.

Table A1. Example of Relative and Absolute Concentration Index Applied to the Change in Educational

Disparity in Mammography, 1990 and 2002

Population Cumulative

Y ears of Rate Share Share Midpoint RCI ( ν = 2) RCI ( ν = 4)

Education [μj] [pj] [pγ] [Rj] ( ν) Σ [pj(1 – Rj) ( ν – 1) ] – ( ν/ μ) Σ [pjμj(1 – Rj) ( ν – 1) ]

1990

<8 years 54.2 0.09 0.09 0.05 –0.0583 –0.1059

9–11 years 51.6 0.14 0.24 0.17 –0.0618 –0.0860

12 years 41.1 0.36 0.60 0.42 –0.0012 –0.0008

13–15 years 38.0 0.22 0.82 0.71 0.0093 0.0016

16+ years 29.0 0.18 1.00 0.91 0.0095 0.0002

T otal 41.0

Relative Concentration Index → –0.1025 –0.1910

Absolute Concentration Index → –4.1963 –7.8229

2002

<8 years 33.3 0.06 0.06 0.03 –0.0452 –0.0854

9–11 years 33.7 0.08 0.14 0.10 –0.0610 –0.0998

12 years 24.7 0.34 0.47 0.30 –0.0214 –0.0208

13–15 years 22.1 0.27 0.74 0.61 0.0134 0.0042

16+ years 18.6 0.26 1.00 0.87 0.0144 0.0005

T otal 23.6

Relative Concentration Index → –0.0998 –0.2014

Absolute Concentration Index → –2.3549 –4.7493

Note: Data is for the proportion of women over 40 who did not have a mammogram within the past 2 years and is drawn from the 1990–2002 Behavioral Risk

Factor Surveillance System.
Example 2: Racial Disparity in Colorectal

Cancer Mortality, 1990–2002

Our second example concerns rates of colorectal

cancer mortality from 1990 to 2002 among four

racial groups: American Indian/Alaska Natives,

Asian/Pacific Islanders, blacks, and whites. The

data for this example come from NCI’s SEER

Program (www.seer.cancer.gov). There are several

limitations to this example that should be

recognized. First, it is not possible with current

data to analyze longer trends for mutually

exclusive detailed racial/ethnic groups because

many states did not have complete information

on ethnicity in death certificate data. Second,

there is great heterogeneity of cancer risk among

subgroups of American Indian/Alaska Natives and

Asian/Pacific Islanders that is not reflected in this

simple example because we are forced to combine

these groups. Similar issues of lack of

homogeneity arise in comparing groups defined

by ethnicity and by various social, economic, and

geographic factors.

69

Figure A2. Trends in Education-Related Disparity and Prevalence for the Proportion of Women Age 40

and Over Who Did Not Receive a Mammogram in the Past 2 Years, 1990–2002

1990

50

40

30

20

10

P e ale ce Rate

991 1993 1995 1997 1999 2000 2001* 2002

Figure A2. Trends in Education-Related Disparity and Prevalence for the Proportion of Women Age 40 and

 Over Who Did Not Receive a Mammogram in the Past 2 Years, 1990-2002

Source: CDC, Behavioral Risk Factor Surveillance Surveys 1990–2002. 

*Note: Question not asked in 2001.

1992 1994 1996 1998

-2

-4

-6

-8

-10

-12

-14

Co ce t atio I de

<8y 9–12y 12y 13–15y 16+y RCIx100 ACI

Absolute Disparity [ACI]

Relative Disparity [RCIx100]

Source: CDC, Behavioral Risk Factor Surveillance Surveys 1990–2002.

*Note: Question not asked in 2001.
70

Method

• Step 1: Inspect the underlying subgroup data.

Figure A3 (page 71) shows trends among those

aged 45–64 years for colorectal cancer mortality

for the four racial groups. Blacks have the highest

rates of colorectal cancer mortality, followed by

whites, and then by American Indian/Alaska

Natives and Asian/Pacific Islanders, both of whom

have similar mortality rates that actually are near

the 2010 age-adjusted target rate. Both blacks and

whites experienced relatively steady declines in

colorectal cancer mortality rates during the 1990s

(although the decline in black rates seems to slow

down after the mid-1990s), but the rates among

other groups remained somewhat steady,

hovering near the 2010 target rate. 

• Step 2: Determine the disparity question to be

answered. Although a number of interesting

pairwise comparisons could be made, in the spirit

of the Healthy People 2010 goals we are interested

in the extent to which progress is being made

toward the elimination of racial disparities in

colon cancer mortality. This would be achieved

when all groups have the same mortality rate, so

we will use a summary measure of health

disparity to determine if racial disparities in

working-age colorectal cancer mortality are

increasing or decreasing.

• Step 3: Choose a summary measure of health

disparity. Clearly, there is no natural ordering

among racial groups, so having decided to use a

summary measure of health disparity, we will use

the Between-Group Variance (BGV) to measure

the absolute level of disparity and two entropybased measures of relative disparity—the Theil

index (T) and the Mean Log Deviation (MLD).

Although it is not necessary to use both T and

MLD to measure relative health disparity, it may

be instructive to do so for reasons outlined below.

Results 

Table A2 (page 72) shows the colorectal cancer

mortality rate (μj

), the rate relative to the

population average rate (i.e., the mortality ratio

rj), and the population share (pj) for each racial

group in 1990 and 2001. Recall that both T and

MLD are measures of average disproportionality—

that is, they take the general form and

measure the extent to which shares of population

and shares of health differ—but they use different

disproportionality functions (i.e., different specifications of f(rj

)). The disproportionality function

for T is rj

ln(rj) and for MLD is –ln(rj) or, equivalently, ln(1/rj

). It may not seem immediately clear

why it might be helpful to use both measures, but

it may be more clear if we use some simple

algebra to rewrite the equations. First, note that

when the denominator for the mortality ratio rj is

the total population rate, , where sj is the

share of mortality for racial group j. We can then

rewrite the disproportionality function f(rj

) for T

as and MLD as . When we apply

the general formula for measures of

average disproportionality, the formula for T

becomes and MLD becomes .

Expressed in this fashion, it is clear that both T

and MLD measure the difference in (log) shares of

health (or ill health) and population, but T is

1n sj

pj

p Σ j ( ( 1n pj

sj

s Σ j ( (

pj f(rj Σ ) j

1n sj

pj

( ( 1n pj

sj

pj

sj

( (

rj x pj = sj

pj f(rj Σ ) j
weighted by shares of health (or ill health, i.e., sj

),

whereas MLD is weighted by population shares

(pj

). Thus, in the context of our example T will be

somewhat more influenced by groups with high

mortality ratios, whereas MLD will be somewhat

more influenced by groups with large population

shares. 

Applying the disproportionality functions for

T and MLD listed in Table 2, in 1990 the

American Indian/Alaska Native segment of T is

calculated as 0.006 x 0.375 x ln(0.375) = 

–0.0023, and the segment of MLD is 0.006 x

[–ln(0.375)] = 0.062. The Between-Group Variance

(BGV) is calculated using equation [17] above and,

for the American Indian/Alaska Native segment in

1990, is calculated as 0.006 (9.5 – 25.5)2 = 1.607.

The racial disparity in 1990 as measured by the

Theil index is 0.0124. We might then immediately

ask whether this disparity is large or small.

Because there has been little use of entropy-based

measures in health disparities research, this is a

difficult question to answer. We may get some

leverage, perhaps, from the recent work by

Goesling and Firebaugh (101), who used T and

MLD to investigate trends in international health

71

Figure A3. Trends in Mortality from Colorectal Cancer by Race, Ages 45–64, 1990–2001

1990

40

35

30

25

20

15

10

Rate per 100 000

991 1993 1995 1997 1999 2000 2001

Figure A3. Trends in Mortality from Colorectal cancer by Race, Ages 45-64, 1990-2001

* AI/AN = American Indian/Alaska Native

** API = Asian/Pacific Islander

Source: Surveillance, Epidemiology, and End Results (SEER) Program. SEER*Stat Database, National Cancer Institute,

DCCPS, Surveillance Research Program, Cancer Statistics Branch, released December 2003.

1992 1994 1996 1998

AI/AN* API** Black White 2010 Target

*AI/AN = American Indian/Alaska Native

**API = Asian/Pacific Islander

Source: Surveillance, Epidemiology, and End Results (SEER) Program (www.seer.cancer.gov) SEER*Stat Database, National Cancer Institute,

DCCPS, Surveillance Research Program, Cancer Statistics Branch, released December 2003.
disparity in life expectancy among 169 countries.

They report that in 2000 T for global disparity in

life expectancy was 0.0099 and MLD was 0.0106.

We find a T of 0.0198 and MLD of 0.0186 in

2002. Thus, it would appear that U.S. racial

disparities in colorectal cancer among those 45–64

are similar in magnitude to cross-national

disparities in life expectancy, but the extent to

which the number of groups compared (4 race

groups vs. 169 countries) and the health outcome

(colorectal cancer mortality rates vs. life

expectancy) may affect the level of disparity is an

open question. As additional analyses applying

entropy-based disparity measures within the

United States are conducted (102), a clearer sense

of how to interpret their magnitude should

develop. 

The results in Table A2 suggest that the

absolute racial disparity (BGV) in colorectal cancer

mortality rates remained approximately constant

over the period in question, but the relative

disparity increased and to a slightly greater extent

when measured with T than with MLD. The slight

difference between T and MLD results from the

fact that T is somewhat more affected by high

mortality ratios, and MLD is somewhat more

affected by large population shares (88). Thus, in

the case of colorectal cancer mortality, the Theil

will be more sensitive to mortality change in

blacks, and the MLD will be more sensitive to

mortality change in whites. The black mortality

ratio increased from 1.41 to 1.59 from 1990 to

2001, but the white ratio declined only slightly,

72

Table A2. Example of Theil Index and the Between-Group Variance Applied to the Change in Racial

Disparity in Colorectal Cancer Mortality, 1990 and 2001

Rate per Population Rate Relative

100,000 Share to T otal T MLD BGV 

Race [μj] [pj] [rj] [pj x rj x ln( rj)] [pj x – ln( rj)] pj [( μj – ∑μj) 2]

1990

American Indian/

Alaska Native 9.5 0.006 0.375 –0.0023 0.0062 1.607

Asian/Pacific Islander 14.5 0.026 0.570 –0.0084 0.0147 3.130

Black 35.9 0.100 1.412 0.0486 –0.0344 10.979

White 24.7 0.868 0.970 –0.0255 0.0263 0.502

T otal 25.5 0.0124 0.0128 16.219

2001

American Indian/

Alaska Native 10.4 0.009 0.541 –0.0029 0.0053 0.672

Asian/Pacific Islander 12.1 0.040 0.629 –0.0116 0.0184 2.018

Black 30.0 0.109 1.559 0.0751 –0.0482 12.561

White 18.3 0.843 0.950 –0.0410 0.0431 0.776

T otal 19.2 0.0198 0.0186 16.027

Note: Rates are age adjusted to the year 2000 population distribution and were generated by the National Cancer Institute’s SEER*Stat software, version 5.2.2.
from 0.97 to 0.95, thus favoring a relatively larger

increase in the Theil index.

Figure A4 shows the absolute and relative

disparity trends across the entire 11-year period,

which indicate that the change in racial disparity

was not constant over time. Both absolute and

relative disparity declined from 1990 to 1992,

after which absolute disparity rose to remain at

roughly its 1990 level for the rest of the period,

while relative disparity continued to increase

steadily as mortality rates declined for all racial

groups. On the whole, then, we would take a less

favorable view of the trend in racial disparities in

colorectal cancer compared to that of educationrelated disparities in mammography. There

virtually was no decline in absolute disparity, and

relative disparity increased markedly from 1990 to

2002 despite an overall decline in the population

mortality rate.

73

Figure A4. Racial Disparity Trends in Working Age (45–64) Mortality from Colorectal Cancer by Race,

1990–2001

1990

40

35

30

25

20

15

10

R t p 100 000 d BGV

1991 1993 1995 1997 1999 2000

Figure A4. Racial Disparity Trends in Working-Age (45-64) Mortality from Colorectal Cancer

 by Race, 1990-2001

* AI/AN = American Indian/Alaska Native

** API = Asian/Pacific Islander

Source: Surveillance, Epidemiology, and End Results (SEER) Program. SEER*Stat Database, National Cancer Institute,

DCCPS, Surveillance Research Program, Cancer Statistics Branch, released December 2003.

1992 1994 1996 1998

AI/AN* API** Black White BGV

2001

0.025

0.020

0.015

0.010

0.005

0.000

Th il d MLD

Theil MLD

Relative Disparity (T, MLD

Absolute Disparity (BGV

*AI/AN = American Indian/Alaska Native

**API = Asian/Pacific Islander

Source: Surveillance, Epidemiology, and End Results (SEER) Program (www.seer.cancer.gov) SEER*Stat Database: Mortality—All COD, Total

U.S. for Expanded Races (1990–2001), National Cancer Institute, DCCPS, Surveillance Research Program, Cancer Statistics Branch,

released December 2003. Underlying mortality data provided by NCHS (www.cdc.gov/nchs).
75

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