Summary Measures of Disparity for Domains with Ordered Categories by Sfusaro

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									  Summary Measures of
Disparity for Domains with
   Ordered Categories
               Elsie Pamuk
    National Center for Health Statistics
 Centers for Disease Control and Prevention
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     White                                    Black
                                  9.1
 8
 7                                        7.5
      7.1                                               7.2
 6                                                6.5
 5
              5.3   5.2   4.9
 4

 3
 2

 1

 0
     <100%    100- 200%- 400%+   <100%    100- 200%- 400%+
             <200% <400%                 <200% <400%
                        White                   Black
                            % with                  % with
                 % of       asthma       % of       asthma
Income         population   episode    population   episode
<100%             .10           7.1       .35           9.1
100-              .18           5.3       .26           7.5
<200%
200-              .36           5.2       .27           6.5
<400%
400%+             .36           4.9       .13           7.2


 Lowest   -   Highest =         2.2                     1.9
 Lowest / Highest       =       1.45                    1.26
      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
         Percent of White Children with Asthma by
                          Income
10                (as a percent of poverty)
 9
 8
 7              <100%
 6
 5
 4             100 -
 3             < 200%         200 - <400%
                                                        400%+
 2
 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 population
         Percent of White Children with Asthma by
                          Income
10                (as a percent of poverty)
 9
 8
 7
                <100%
 6
 5
 4             100 -
 3             < 200%
                              200 - <400%
 2                                                      400%+

 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 population
         Percent of White Children with Asthma by
                          Income
10                (as a percent of poverty)
 9
 8
 7
                <100%
 6
 5
 4             100 -
 3             < 200%
                              200 - <400%
 2                                                      400%+

 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 population
         Percent of White Children with Asthma by
                          Income
                  (as a percent of poverty)
10
 9                                      Slope Index of Inequality
 8                                      SII = b = -1.7
 7
                  <100%
 6
 5
 4               100 -
 3               < 200%
                                200 - <400%
 2                                                        400%+
 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 population
         Percent of White Children with Asthma by
                          Income
                  (as a percent of poverty)
10
 9                                      Slope Index of Inequality
 8                                      SII = b = -1.7 = (6.1-4.5)
 7
                  <100%
 6
 5
 4               100 -
 3               < 200%
                                200 - <400%
 2                                                        400%+
 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 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
                                      Mean of y = 5.3
 8
                                      RII (mean) = -.32 = (-1.7/5.3)
 7
                  <100%               RII (ratio) = 1.4 = (6.1/4.5)
 6
 5
 4               100 -
 3               < 200%
                                200 - <400%
 2                                                        400%+
 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 population
         Percent of Black Children with Asthma by
                          Income
                  (as a percent of poverty)
                                                  SII = -3.4
10                                                RII (mean) = -.44
 9                                                RII (ratio) = 1.6
 8
 7
             <100%
 6
 5
                             100 - < 200%
 4                                             200 - < 400%
 3                                                            400%+
 2
 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 population
                       White                  Black
                           % with                 % with
                % of       asthma      % of       asthma
Income        population   episode   population   episode
<100%            .10           7.1      .35           9.1
100-             .18           5.3      .26           7.5
<200%
200-             .36           5.2      .27           6.5
<400%
400%+            .36           4.9      .13           7.2


SII             -1.7                   -3.4
RII (mean)      -.32                   -.44
RII (ratio)      1.4                    1.6
Concentration Indices
                           CONCENTRATION INDEX

                  1
                 0.9
                 0.8
                 0.7
                                 C = -.07
Cumulative       0.6
proportion of
Black children
                 0.5
with asthma      0.4
                 0.3
                 0.2
                                 <100%    100-<200%       200-<400%     400%+
                 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
                           CONCENTRATION INDEX

                  1
                 0.9
                 0.8
                 0.7
                                   C = -.05
Cumulative       0.6
proportion of
White children
                 0.5
with asthma      0.4
                 0.3
                           <100%
                 0.2
                 0.1           100-      200-<400%               400%+
                               <200%
                  0
                       0    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                  Black
                           % with                 % with
                % of       asthma      % of       asthma
Income        population   episode   population   episode
<100%            .10           7.1      .35           9.1
100-             .18           5.3      .26           7.5
<200%
200-             .36           5.2      .27           6.5
<400%
400%+            .36           4.9      .13           7.2


SII             -1.7                   -3.4
RII (mean)      -.32                   -.44
RII (ratio)      1.4                    1.6
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                     2003
                                % with                   % with
               % of             no MD      % of          no MD
Income       population          visit   population       visit
<100%              .17           23.2       .16           12.2
100-<200%          .26           22.0       .22           13.0
200%+              .57           14.9       .62           8.1


Lowest - Highest                   8.3                      4.1
Lowest / Highest                  1.56                     1.51
Percent of children with no health care visit
in the past year, NHIS 1990 and 2003
                       1990                      2003
                              % with                    % with
                % of          no MD       % of          no MD
Income        population       visit    population       visit
<100%            .17           23.2        .16           12.2
100-             .26           22.0        .22           13.0
<200%
200%+            .57           14.9        .62           8.1


SII                           -14.46                      -8.9
RII (mean)                       -.80                     -.91
RII (ratio)                      2.3                       2.7
C                              -.105                     -.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

								
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