Measuring Social Inequality

class: center, middle, inverse, title-slide

.title[
# Measuring Social Inequality
]
.subtitle[
## Advanced Social Epidemiology PhD Course
]
.author[
### Sam Harper
]
.institute[
### <br> </br>
]
.date[
### University of Copenhagen <br> 2024-12-02 to 2024-12-06 </br>
]

---

class: center, top, inverse
# .orange[**Measuring Inequality**]

.left[
## .orange[**1 Conceptual Issues**]
## .orange[**2 Absolute and Relative Inequality**]
## .orange[**3 Simple vs. Complex Measures**]
## .orange[**4 Weighting**]
## .orange[**5 Reference Points**]
]

---
class: center, top, inverse
# .orange[**Measuring Inequality**]

.left[
## .orange[**1 Conceptual Issues**]
## .gray[**2 Absolute and Relative Inequality**]
## .gray[**3 Simple vs. Complex Measures**]
## .gray[**4 Weighting**]
## .gray[**5 Reference Points**]
]

---
## Why monitor health inequalities?
.pull-left[
### Surveillance

- Natural complement to monitoring overall health

- Essential for detecting important changes in risk
]

.pull-right[
### Impact

- Opportunity to evaluate etiological explanations for health inequalities

- Evaluating the distributional impacts of public health interventions and medical innovations

- Crucial for measuring the responsiveness of health care systems to those most in need
]

---
## Inequalities in health are based on *observations*
.right-column[
### .red[We are relatively good at measuring inequalities.]

- Poor people die younger than rich people

- Low social class infants have lower birth weight

- Smokers get more lung cancer than non-smokers

- Women live longer than men
]

---
## Inequities in health are based on *ethical judgements*
.right-column[
### .red[Inequities are much harder to measure]

- Should poor people die younger than rich people?

- Should low social class infants have lower birth weight?

- Should smokers get more lung cancer than non-smokers?

- Should women live longer than men?
]

---
.footnote[Adapted from McGuire et al. *Health Services Research* 2006]

.left-column[
### Anatomy of an Inequality
- How much of inequality is *unfair*?

- How would you know?
]

.right-column[
.center[
<img src="../../images/mcguire-inequity.png" width="100%" height="100%" />
]]
---
# Inequality is an ambiguous concept
Different measures of inequality emphasize different concepts.

.right-column[

>“If a concept has some basic ambiguity, then a precise representation of that ambiguous concept must preserve that ambiguity…This issue is quite central to the need for descriptive accuracy in inequality measurement, which has to be distinguished from fully ranked, unambiguous assertions.”

> Amartya Sen, On Economic Inequality, 1997
]

---
## Measuring inequality: Some issues to consider
.left-column[
<img src="02-inequality_files/figure-html/unnamed-chunk-3-1.png" width="100%" height="100%" />
]

.right-column[
1. What to measure? Total vs. Social Group Inequality

1. Scale: Is inequality relative or absolute?

1. Simple or complex measures of health inequality?

1. Weighting: Who counts, and for how much?

1. Reference points for measuring inequality: Different from what?
]

---
## What should we measure?
.pull-left[
### Total Health Inequality
- complement to measurement of average health
- measured across all individuals
- avoids normative choice of social groups
- facilitates unambiguous comparisons over time/place
]

.pull-right[
### Social Group Differences in Health
- measured across normatively important social groups
- particular social groups chosen a priori
- provide insights into causal processes linking health and social position
]

---
.footnote[Asada 2002]

.left-column[
### Health Inequality Between Whom?

- Which society has more inequality?

- Which one is worse from the perspective of inequality?
]
.right-column[
<img src="../../images/asada-distribution.png" width="100%" height="100%" />
]

---
<img src="../../images/van-ralte-title.png" width="40%" height="40%" />

.right-column[
- Life-span variation reflects uncertainty in the risk (timing) of death.
- People are generally willing to pay to reduce uncertainty.

- Heterogeneity is crucial for accurate forecasts in insurance and annuity markets, and should be measured.
- Monitoring life-span variation may facilitate early detection of adverse  mortality developments and warrant social interventions at younger ages.
]

---
class: center, top, inverse
# .orange[**Measuring Inequality**]

.left[
## .gray[**1 Conceptual Issues**]
## .orange[**2 Absolute and Relative Inequality**]
## .gray[**3 Simple vs. Complex Measures**]
## .gray[**4 Weighting**]
## .gray[**5 Reference Points**]
]

---
.left-column[
### Easy case

Evidence of clear progress
]

.right-column[
.center[
Trends in infant mortality, Brazil and Colombia, 1980-2006
<img src="../../images/bra-col-trends.png" width="100%" height="100%" />
]]

---
.left-column[
### Easy case

Evidence of clear progress
]

.right-column[
.center[
Trends in infant mortality, Brazil and Colombia, 1980-2006
<img src="../../images/bra-col-ineq.png" width="100%" height="100%" />
]]

---
.footnote[Source: US NCI SEER*Stat Database]
.left-column[
### Harder case

Are black-white inequalities in prostate cancer mortality increasing or decreasing?
]

.right-column[
.center[
Black and White Prostate Cancer Mortality Rates
<img src="../../images/bw-prostate-trends.png" width="100%" height="100%" />
]]

---
.footnote[DeLancey (2008)]
.center[
<img src="../../images/delancey-prostate-figure.png" width="80%" height="80%" />
]

---
.footnote[Source: US NCI SEER*Stat Database]
.center[
<img src="../../images/bw-prostate-ineq.png" width="80%" height="80%" />
]

---
.footnote[Chapin-Bardales et al. 2017]
.left-column[
"Racial disparities rose sharply from 1984 to the early 2000s for Blacks...concerningly, we documented a significant increase from 2006 to 2013."

On what scale?
]

.right-column[
.center[
New AIDS diagnoses by race/ethnicity, USA 1984-2013
<img src="../../images/sullivan-hiv-trends.png" width="100%" height="100%" />
]]

---
.pull-left[
### Failure to consider the scale on which inequalities are measured can have dramatic impacts on study conclusions.
- Steep declines on absolute scale.
- Increases on relative scale.

### This also has broad implications for thinking about explanations for inequality trends. 
- Did the introduction of antiretrovirals exacerbate or mitigate inequalities?
]

.pull-right[
<img src="../../images/bw-hiv-ineq.png" width="90%" height="90%" />
]

---
# Inequality is an ambiguous concept

>### .black[“There is no economic theory that tells us that inequality is relative, not absolute.  It is not that one concept is right and the other wrong.  Nor are they two ways of measuring the same thing.  Rather, they are two different concepts.”]

>### .black[Martin Ravallion, World Bank Economist, 2004]

---
class: center, top, inverse
# .orange[**Measuring Inequality**]

.left[
## .gray[**1 Conceptual Issues**]
## .gray[**2 Absolute and Relative Inequality**]
## .orange[**3 Simple vs. Complex Measures**]
## .gray[**4 Weighting**]
## .gray[**5 Reference Points**]
]

---

.footnote[Source: Data2010]
.left-column[
### Pairwise comparisons work well for a few groups
]

.right-column[
.center[
<img src="../../images/two-groups.png" width="100%" height="100%" />
]]

---
## Additional groups make summary measures appealing

.footnote[Source: Persmark (2020)]
.center[
<img src="../../images/persmark-2020-ann.png" width="100%" height="100%" />
]

---

.footnote[Ezzati et al. (2008)]
.left-column[
### Summary measures definitely needed
]

.right-column[
.center[
<img src="../../images/ezzati-counties.png" width="100%" height="100%" />
]]

---
## Range-type measures: ignore the entire distribution
.left-column[
### .white[x]

- Does A or B have 'more' inequality?

- Do you have a preference for A or B?
]

.right-column[
.center[
<img src="../../images/range-measure.png" width="80%" height="80%" />
]]

---
.left-column[
### Moving beyond simple comparisons

- More complex measures look at the entire distribution.

- E.g., Lorenz curve for income, health, or any X:
]

.right-column[
.center[
<img src="../../images/lorenz.png" width="100%" height="100%" />
]]

---
# Moving Beyond Binary Comparisons

### Rank each education group by position in the population distribution

.center[
Distribution of Socioeconomic Position in a Hypothetical Population
]

Education Level |	%	| Cumulative % |	Range | 	Midpoint
------------------|---|:--------:|:--------:|-----------:
 None |	11.93	| 11.93	 | 00.00 – 11.93	| 5.97 
 <Primary school |	15.04 |	26.97 |	11.93 – 26.97 |	19.45 
 Primary school |	26.86 |	53.83 |	26.97 – 53.83 | 	40.40
 Secondary school |	16.05	| 69.88 | 53.83 – 69.88 |	61.86
 Beyond Secondary |	30.12 |	100	| 69.88 – 100.0 |	84.94

---
.left-column[
### Summarizing across SEP

- First rank the population by SEP

- Then count up the proportion of disease each group accounts for.
]

.right-column[
.center[
Relative Concentration Curve
<img src="../../images/cc-cumulative.png" width="100%" height="100%" />
]]

---
.left-column[
### Summarizing across SEP

- Diagonal = no inequality

- Curve above diagonal: ill-health concentrated among poorer.
- Curve below diagonal: ill-health concentrated among richer.
]

.right-column[
.center[
Relative Concentration Curve
<img src="../../images/cc-both.png" width="100%" height="100%" />
]]

---
.left-column[
### Summarizing across SEP

- Concentration Index measures the extent to which disease is 'concentrated' among different SEP groups.
]

.right-column[
.center[
Concentration Index
<img src="../../images/cc-index.png" width="100%" height="100%" />
]]

---
## Formula for writing the Concentration Index
.footnote[Kakwani et al. (1997)]
.pull-left[
One way of writing the CI is:
`$$RCI= \frac{2}{n\mu} \sum_{i=1}^{n}y_{i}R_{i}-1$$`
where `$\mu$` is the mean of `$y_{i}$` (e.g., smoking status), `$R_{i}$` is the fractional rank of the *i*th person in the socioeconomic (i.e., income) distribution.
]

.pull-right[
The Absolute Concentration Index multiplies *RCI* by the mean smoking rate:
`$$ACI=\mu*RCI$$`
]

---
.left-column[
### Example of Relative and Absolute CI

1965: Smoking increases with education = + RCI

2003: Smoking decreases with education = - RCI
]

.right-column[
.center[
<img src="../../images/women-smoking-ineq.png" width="100%" height="100%" />
]]

---
.left-column[
### Slope and Relative Index of Inequality

- Conceptually similar to CI

- Correlation between SEP rank and health.

- SII: Absolute difference
- RII: Relative difference (or ratio)
]

.right-column[
<img src="../../images/sii-graph.png" width="100%" height="100%" />
]

---
.footnote[Hosseinpoor (2013)]

.left-column[
## The measure may matter!
]

.right-column[
.center[
<img src="../../images/hosseinpoor-quote.png" width="100%" height="100%" />
]]

---
## Two mechanisms for changing inequality
.footnote[Renard (2019)]
Size of social groups will also change SII/RII without mortality change. Increasing the size of higher educated groups (e.g., larger share with higher education) increases inequality:

.center[
<img src="../../images/renard-sii.png" width="80%" height="80%" />
]

---
class: center, top, inverse
# .orange[**Measuring Inequality**]

.left[
## .gray[**1 Conceptual Issues**]
## .gray[**2 Absolute and Relative Inequality**]
## .gray[**3 Simple vs. Complex Measures**]
## .orange[**4 Weighting**]
## .gray[**5 Reference Points**]
]

---
.left-column[
### Is the amount of inequality the same in these two societies?
]

.right-column[
<img src="../../images/three-groups.png" width="100%" height="100%" />
]

---
.footnote[Quach et al. (2012)]
.left-column[
No way to 'rank' ethnicity

Groups differ in size

Should we account for it?
]

.right-column[
.center[
How to summarize this variation by ethnicity?
<img src="../../images/ethnicity-vaccination.png" width="100%" height="100%" />
]]

---
### Index of Disparity
.footnote[Pearcy and Keppel (1999)]

.pull-left[
Measures the mean deviation of the group rates from some reference point as a proportion of that reference point

`$$ID = \sum_{j=1}^{J}(|y_{j} - y_{ref}|/n)/y_{ref}$$`
Where `$y_{j}$` is the rate in group `$j$`, `$y_{ref}$` is the rate for the reference point, and `$J$` is the number of groups, or the number of groups minus 1 if one of the groups is the reference point.
]

.pull-right[
Note that ID has a few important but potentially modifiable characteristics:
- Measures relative inequality
- Does not account for population size of groups
- Uses best observed health as reference level

Interpretation is also a little awkward: the average deviation across social groups as a proportion of the reference level

Are there alternatives?
]

---
.left-column[
### Inequality as 'Disproportionality'

Compares shares of health or disease with shares of the population.

Perfect equality: 
%pop = %health
]

.right-column[
.center[
<img src="../../images/disproportionality-figure.png" width="90%" height="90%" />
]]

---
.left-column[
Alternative: Mean Log Deviation
- weights by pop
- measures difference in log shares

Sensitive to 'transfers' at different points of health distribution.
]

.right-column[
<img src="../../images/mld-idisp.png" width="100%" height="100%" />
]

---
.left-column[
Does it matter?

Ezzati et al.: "There was a .red[steady increase in mortality inequality] across the US counties between 1983 and 1999, resulting from stagnation or increase in mortality among the worst-off segment of the population."
]

.right-column[
.center[Geographic inequalities in life expectancy
<img src="../../images/ezzati-trends.png" width="80%" height="80%" />
]]

---
.footnote[Harper et al. (2010)]
.left-column[
Compared weighted to unweighted inequality measures

Across:
 - counties
 - states
 - regions
 
]

.right-column[
.center[
<img src="../../images/weighting-milbank.png" width="90%" height="90%" />
]]

---
class: center, top, inverse
# .orange[**Measuring Inequality**]

.left[
## .gray[**1 Conceptual Issues**]
## .gray[**2 Absolute and Relative Inequality**]
## .gray[**3 Simple vs. Complex Measures**]
## .gray[**4 Weighting**]
## .orange[**5 Reference Points**]
]

---
.center[
<img src="../../images/diff-reference.png" width="75%" height="75%" />
]

---
.center[
<img src="../../images/obesity-trends.png" width="100%" height="100%" />
]

---
.center[
<img src="../../images/obesity-ineq.png" width="100%" height="100%" />
]

---
## Conclusions
.left-column[
<img src="02-inequality_files/figure-html/unnamed-chunk-34-1.png" width="100%" height="100%" />
]
.right-column[
Measures of health inequality are not value neutral.
- Scale of measurement (absolute/relative)
- Weighting: how much and to whom?
- Reference points: different from what standard?

The choices above have an important impact on our judgments of both the magnitude of health inequality and whether health inequalities are worsening or improving.

Monitoring health inequalities requires both precise measurement and value judgments—they are inseparable.

A suite of health inequality measures is likely necessary to provide a complete description of the magnitude of inequality.
]

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