Multilevel models concept and application

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					Income inequality and health

               S V Subramanian
            Harvard School of Public Health
          Acknowledgements: Ichiro Kawachi

                   January 6, 2006
    PURE Steering Committee and Operation Meeting
                     Dubai, UAE
                  Income inequality: some facts

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        World inequality

                  Source: UNDP, 2005, Human Development Report
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      World inequality trend

                               Source: Milanovic B, World Apart: international and world inequality

S V Subramanian                                                                                  4
     What is driving global income inequality?

          • Largely between-country (rather than within-

          • BUT, within country contribution not trivial

                  – Of the 73 countries for which data are
                    available, 53 (80% of the world’s population)
                    have seen inequality rise, while only 9 (4%
                    of the population) have seen it narrow.

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      Income distribution in the US

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    Is this news?

                  Sources: 1947-79: Analysis of U.S. Census Bureau data in Economic Policy Institute, The State of Working America 1994-95 (M.E.
                                                        Sharpe: 1994) p. 37.; 1979-2001: U.S. Census Bureau, Historical Income Tables, Table F-3

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     So what?

          • Economic residential segregation

          • Crime and rising prison population

          • Drag on economic growth

          • Erosion of social cohesion

          • Worse health status?

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    Income and health: a typology

      • Absolute or Relative

      • Individual or Community

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  Income and health: absolute and
  individual interpretation

                          hi  f ( yi )
         • Where hi is an individual’s level of well-being (for
           example, years of life), and yi refers to that
           individual’s own level of income.

         • The relationship between individual income and
           individual health is concave, i.e., a $ increase is
           accompanied by relatively small or even no
           improvement in health, beyond a particular level
           of income.

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     Concavity effect

          Health y1

                       x1   x2      x     x3   x4

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  Income and health: relative and individual

        • Inspired by the concept of relative deprivation
          formulated by Runciman (1966). It is “the extent of
          the difference between the desired situation and
          that of the person desiring it”.

        • “…we can roughly say that A is relatively deprived
          of X when (i) he does not have X, (ii) he sees some
          other person or persons, which may include himself
          at some previous or expected time, as having X
          (whether or not this is or will be in fact the case), (iii)
          he wants X, and (iv) he sees it as feasible that he
          should have X.” (Runciman 1966) (p.10)”

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  Income and health: relative and individual

                     hi  f ( yi  y r )
        • Where health of an individual is a function of the
          term (yi-yr ) that denotes the relative gap between
          an individual’s income, yi, and the income of
          some reference population, yr . The reference
          population could be the income of co-workers,
          neighbors, or the national population.

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  Income and health: absolute and
  community interpretation

                     hij  f (Y j , yij )

        • Health of an individual i in community j is a
          function of their own income (yij) AND the
          average income levels of community (Yj) in which
          the individuals reside.

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  Income and health: relative and
  community interpretation

                      hij  f ( I j , yij )

        • Where Ij refers to a summary measure of
          income distribution (e.g., Gini coefficient) for the
          community in which the individual resides.

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          Pollution effect

             Life expectancy

                               Effect of income redistribution


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     Income inequality hypothesis:
     intrinsically multilevel

                  hij  f ( I j , yij , ( yij  yrj ), Yij )
          Health of an      Community    Individual   Individual   Community
          individual in a   Income       Absolute     Relative     Absolute
          community         inequality   income       income       income

      For substantive and technical reasons, we need a
      multilevel regression approach to estimate the above.

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       What does the evidence using multi-level
                 data-sets suggest?

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     Detectable patterns in US studies

     • Positive studies
        – US states
        – Wide range of outcomes
        – Larger samples

     • Null studies
       – US counties/metropolitan areas
       – Smaller samples

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                         Conditions                                    OR                 95%CI

     No individual income effect                                      1.32            (1.19-1.46)
     Linear effect of income                                          1.31            (1.18-1.46)
     Income transformed into log                                      1.30            (1.17-1.45)
     Non-linear (2nd order polynomial)                                1.31            (1.17-1.45)

     Income as deciles                                                1.29            (1.15-1.43)
     Income as quintiles                                              1.29            (1.16-1.44)
     Income as categories                                             1.30            (1.17-1.45)

      OR for Gini based on 0.05 (5%) change in Gini;
      Note: All models additionally controlled for individual age, sex, marital status, race, years of
      education, covered by health insurance and state median income.
      *The equivalized household income categories were as follows: above $75,000: reference,
      $50,000-75,000, $30,000-50,000, $15,000-30,000, below $15,000.

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                            Conditions                    OR       95%CI

          Baseline                                        1.57   (1.39-1.78)
          + State median income                           1.50   (1.34-1.67)
          + Age                                           1.53   (1.37-1.71)
          + Sex                                           1.52   (1.36-1.70)
          + Marital Status                                1.51   (1.35-1.69)
          + Race                                          1.42   (1.27-1.57)
          + Years of Education                            1.34   (1.21-1.48)
          + Equivalized household income                  1.30   (1.17-1.45)
          + Health insurance                              1.30   (1.17-1.45)

          OR for Gini based on 0.05 (5%) change in Gini

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     Detectable patterns in non-US studies

     • Mostly null, BUT

             – ALL countries studied thus far are FAR more egalitarian
               (Sweden, Denmark, Japan, UK) than the US

             – ALL countries studied are also centralized states, thus raising
               the issue related to the relevance of a chosen unit of aggregation

     • Is US an exception; what about societies more unequal
       than the US?

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    Income inequality and health in Chile


           Odds Ratio fo r poor h ealth


                                                                                   1.22                         1.21


                                           1                  1

                                                less than 0.4 (Reference)   0.4 to 0.45               0.45 to 0.50        0.50 and above
                                                                                Com m unity Gini Coefficients

                                                                                                                       Source: Subramanian, 2003

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    Income inequality and health in India


           OR (95% CI)

                         1.1                                                                                  1.1


                          1                   1

                               <18.5     18.5-22.9       23-24.9                  25-29.9                   ≥30
                                                     Body Mass Index

                                                                       Source: Subramanian, Kawachi, Davey Smith (Unpublished)

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      Mechanisms linking income inequality
      and health

            •     Access to material resources
            •     Relative comparisons
            •     Social cohesion and social capital

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    Evidence for RD explanation?
          • Defining reference groups using combinations of state,
            race, education, and age, Eibner and Evans (2005) found
            that high relative deprivation is associated with a higher
            probability of death, self-reported limitations, body mass
            index, risky health behaviors, and poor self-reported health.

                  – No association between state mean income and the
                    probability of death

                  – One standard deviation (0.022) increase in the Gini
                    coefficient is associated 8 percent increase in the
                    probability of death.

                  – Gini coefficient AND the relative deprivation measure
                    positively related to mortality, but RD attenuates the
                    coefficient associated with Gini.
                      Eibner CE, Evans WN. Relative deprivation, poor health habits and mortality. Journal of Human Resources. 2005;40(3):591-620.
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     For better or for worse the Gini is out of
     the bottle….

                   If recent global and national economic trends
                     provide any indication, research on income
                  inequality and its potential effects on health will
                     probably be more, and not less, important.

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      FOR (in the US)                                                                      Source: Subramanian, Kawachi, 2004

             Authors, Year              Sample population                      Method              Outcome

        Kennedy et al., 1998     205245 adults from 50 U.S.            Marginal Models      Self-rated health
        Soobader and LeClere,    9,637 white males from U.S.           Marginal models      Self-rated health
        1999                     counties and tracts (n for counties
                                 and tracts not reported)

        Blakely et al., 2000     279066 adults nested within 50        Multilevel models    Self-rated health
                                 U.S. states
        Diez-Roux et al., 2000   81,557 adults nested within 50        Multilevel models    Hypertension,
                                 U.S. states                                                smoking,
                                                                                            sedentarism, body
                                                                                            mass index
        Kahn et al., 2000        8285 women from 50 U.S. States        Marginal models      Depressive
                                                                                            symptoms, self-
                                                                                            rated health
        Lochner et al., 2001     546,888 adults from 50 U.S.           Marginal models      Mortality
        Subramanian et al.,      144692 adults nested within 39        Multilevel models    Self-rated health
        2001                     U.S. states
        Subramanian et al.,      90,000 adults aged 45 and above       Multilevel models    Self-rated health
        2003                     nested within 50 U.S. states
                                 nested within 9 census divisions

        Subramanian and          201221 adults nested within 50        Multilevel models    Self-rated health
        Kawachi, 2003            U.S. states
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      AGAINST (in the US)
              Authors, Year          Sample population                 Method                    Outcome

          Fiscella and Franks,   14407 adults from U.S.          Single-level        Mortality
          1997                   counties (n for counties not    regression
          Daly et al., 1998      About 6500 adults from U.S.     Single-level        Mortality
                                 states (n for states not        regression
          Mellor and Milyo,      309135 adults aged 25-74        Marginal models     Self-rated health
          2002                   from U.S. states and
                                 metropolitan areas (n not

          Blakely et al., 2002   18547 respondents and           Multilevel models   Self-rated health
                                 adults nested within 232 U.S.
                                 metropolitan areas; and
                                 216 counties

          Sturm and Gresenz,     8,235 adults from U.S.          Marginal models     Self-reports of 17 common
          2002                   metropolitan areas (n for                           conditions (e.g., arthritis,
                                 metropolitan areas not                              depression)

          Mellor and Milyo,      309135 adults aged 25-74        Marginal models     Self-rated health
          2003                   from U.S. states

                                                                                                 Source: Subramanian, Kawachi, 2004

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     Outside of the US
          Author, Year           Sample population               Method          Outcome            Support for
        Gerdtham and         40,000+ adults from           Marginal models     Mortality                  No
        Johannesson,         Municipalities in Sweden (n
        2001                 for municipalities not
        Jones et al., 2004   8720 adults nested within     Multilevel models   Mortality                  No
                             207 UK constituency nested
                             within 22 regions
        Osler et al., 2002   25728 adults from parishes    Single level        Mortality                  No
                             within Copenhagen city (n     regression
                             for parishes not reported)
        Shibuya et al.,      80899 adults from Japanese    Marginal models     Self-rated                 No
        2002                 prefectures (n for                                health
                             prefectures not reported)
        Blakely et al.,      1391118 adults nested         Multilevel models   All-cause and              No
        2003                 within regions within New                         cause-specific
                             Zealand (3 alternatives,                          mortality
                             n=14, n=35, n=73)
        Subramanian et       98344 adults nested within    Multilevel models   Self-rated                Yes
        al., 2003            61978 households nested                           health
                             within 285 Chilean
                             communities nested within
                             13 regions

                                                                                            Source: Subramanian, Kawachi, 2004

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     Gini coefficient
      • Most popular measure of inequality developed by the
        Italian statistician Corrado Gini (1912).

      • Typically used to measure income inequality, but can
        be used to measure distribution on any space.

      • The Gini coefficient is a number between 0 and 1,
        where 0 corresponds with perfect equality (where
        everyone has the same income) and 1 corresponds
        with perfect inequality (where one person has all the
        income, and everyone else has zero income).

      • Algebraically, the Gini is defined as half of the
        arithmetic average of the sum of the absolute
        differences between all pairs of incomes in a
        population, normalized to mean income.
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     Lorenz curve

      • Developed by Max O Lorenz (1905) as a graphical representation of
        income distribution.

      • Portrays observed income distributions and compares this to a state
        of perfect income equality.

      • Graphical expression of verbal statements such as, "the bottom
        twenty percent of all households have ten percent of the total

      • Shows, for the bottom x% of households, the percentage y% of the
        total income which they have. Typically, the percentage of
        households is plotted on the x-axis, the percentage of income on the

      • The Lorenz curve is used to calculate the Gini coefficient.

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    Lorenz & Gini

     Ratio of the area between
     the line of perfect equality
     and Lorenz curve is {A},
     and the area underneath
     the Lorenz curve {B}.

     Expressed as a
     percentage or as the
     numerical equivalent of        {A}
     that percentage, which is
     always a number
     between 0 and 1.

      Gini index =
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