Summary Measures of Disparity for Domains with Ordered Categories
National Center for Health Statistics Centers for Disease Control and Prevention
Elsie Pamuk
Measurement of disparity allows comparisons:
Across health indicators Between or across populations Over time
Focus of attention?
Individual groups
• Comparing single groups to a reference point
A domain
• Summarizing disparity across all groups constituting a conceptual domain
Definition of “domain”
A domain consists of the entire set of population groups that are based on one or more characteristics of persons in a population
Why focus on the domain, rather than the groups?
The groups are not inherently meaningful
The groups are inherently meaningful, but so is the defining aspect of the domain
Distinction between ordered and unordered domains –
for inherently ordered domains, the primary focus is usually on the domain itself, rather than the component groups.
Whenever the focus is on the domain, it is appropriate to combine information from the component groups and create a summary measure of disparity.
Domains with ordered categories
Socioeconomic status (SES)
• Income • Education • Wealth • Occupational status
Other
• Urbanization
Asthma rates for children <18 years of age, NHIS 1998-2003
10 9 8 7 6 5 4 3 2 1 0 <100% 100200%- 400%+ <200% <400% <100% 100200%- 400%+ <200% <400%
White
Black
9.1 7.5 6.5 7.2
7.1 5.3 5.2
4.9
White
% of population .10 .18 .36 .36
Black
% of population .35 .26 .27 .13 % with asthma episode 9.1 7.5 6.5 7.2 1.9 1.26
Income
<100% 100<200% 200<400% 400%+
% with asthma episode
7.1 5.3 5.2 4.9 2.2 1.45
Lowest
-
Highest = =
Lowest / Highest
Common characteristics of summary measures of health disparities related to SES
Use information from all of the component groups Preserve the inherent ordering of the groups Incorporate the size of the groups
Regression-based measures
10 9 8 7 6 5 4 3 2 1 0 0
Percent of White Children with Asthma by Income (as a percent of poverty)
<100%
100 < 200%
200 - <400%
400%+
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cumulative proportion of population
10 9 8 7 6 5 4 3 2 1 0 0
Percent of White Children with Asthma by Income (as a percent of poverty)
<100%
100 < 200%
200 - <400% 400%+
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cumulative proportion of population
10 9 8 7 6 5 4 3 2 1 0 0
Percent of White Children with Asthma by Income (as a percent of poverty)
<100%
100 < 200%
200 - <400% 400%+
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cumulative proportion of population
Percent of White Children with Asthma by Income (as a percent of poverty)
10 9 8 7 6 5 4 3 2 1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 100 < 200% <100%
Slope Index of Inequality SII = b = -1.7
200 - <400%
400%+
Cumulative proportion of population
Percent of White Children with Asthma by Income (as a percent of poverty)
10 9 8 7 6 5 4 3 2 1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 100 < 200% <100%
Slope Index of Inequality SII = b = -1.7 = (6.1-4.5)
200 - <400%
400%+
Cumulative proportion of population
Regression based measures of disparity
SII = b = (y at x=1) – (y at x=0)
RII (mean) = SII/mean of y
mean of y = population value of y
Or RII (ratio) = (y at x=1) / (y at x=0)
Percent of White Children with Asthma by Income (as a percent of poverty)
10 9 8 7 6 5 4 3 2 1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 100 < 200% <100%
Mean of y = 5.3 RII (mean) = -.32 = (-1.7/5.3) RII (ratio) = 1.4 = (6.1/4.5)
200 - <400%
400%+
Cumulative proportion of population
Percent of Black Children with Asthma by Income (as a percent of poverty)
10 9 8 7 6 5 4 3 2 1 0 0
SII = -3.4 RII (mean) = -.44 RII (ratio) = 1.6
<100% 100 - < 200% 200 - < 400% 400%+
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cumulative proportion of population
White
% of population .10 .18 .36 .36 -1.7 -.32 1.4
Black
% of population .35 .26 .27 .13 -3.4 -.44 1.6 % with asthma episode 9.1 7.5 6.5 7.2
Income
<100% 100<200% 200<400% 400%+
% with asthma episode
7.1 5.3 5.2 4.9
SII RII (mean) RII (ratio)
Concentration Indices
CONCENTRATION INDEX
1 0.9 0.8 0.7
Cumulative proportion of Black children with asthma
C = -.07
0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cumulative proportion of Black children by family income level
<100% 100-<200% 200-<400% 400%+
CONCENTRATION INDEX
1 0.9 0.8 0.7
Cumulative proportion of White children with asthma
C = -.05
0.6 0.5 0.4 0.3 0.2 0.1 0 0
<100% 100<200% 200-<400% 400%+
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
Cumulative proportion of White children by family income level
White
% of population .10 .18 .36 .36 -1.7 -.32 1.4
Black
% of population .35 .26 .27 .13 -3.4 -.44 1.6 % with asthma episode 9.1 7.5 6.5 7.2
Income
<100% 100<200% 200<400% 400%+
% with asthma episode
7.1 5.3 5.2 4.9
SII RII (mean) RII (ratio)
C
-.05
-.07
Conversion between C and RII
C = 2 cov(x,y)/m SII = cov(x,y)/var(x)
and,
RII = SII/m = [cov(x,y)/var(x)]/m
so,
C = 2 var(x)(RII)
Practical considerations when choosing methods to summarize SES disparities in health
Graphical presentation Ease of computation / statistics
Percent of children with no health care visit in the past year, NHIS 1990 and 2003
1990
Income <100% 100-<200% 200%+ Lowest - Highest Lowest / Highest % of population .17 .26 .57 % with no MD visit 23.2 22.0 14.9 8.3 1.56
2003
% of population .16 .22 .62 % with no MD visit 12.2 13.0 8.1 4.1 1.51
Percent of children with no health care visit in the past year, NHIS 1990 and 2003
1990
Income <100%
2003
% with no MD visit 23.2
% of population
.17
% of population
.16
% with no MD visit 12.2
100<200%
200%+ SII RII (mean) RII (ratio) C
.26
.57
22.0
14.9 -14.46 -.80 2.3 -.105
.22
.62
13.0
8.1 -8.9 -.91 2.7 -.110
Making decisions on how to measure disparity
Who is the audience?
What is the purpose and scope of the exercise?
Argument for weighting summary measures of disparity for SES domains:
The essentially arbitrary nature of the categories
Categories differ by amount, rather than type
Distributions can be influenced by policy