Measuring and monitoring inequalities in health is important for informing policies and programs that aim to tackle health inequities. Broadly defined, inequalities in health are measurable differences in health across population subgroups defined by dimensions of inequality (demographic, socioeconomic or geographic characteristics). Summary measures of inequality summarise the amount of inequality across subgroups in a single number – which facilitates the comparison of inequalities over time and across different settings and indicators.

Summary measures of health inequality use either disaggregated data or individual-level data as inputs.

Disaggregated data refers to health indicator data recorded for different subgroups of a population that are defined according to dimensions of inequality, such as demographic, socioeconomic or geographic characteristics (such as wealth quintiles or subnational regions). Each record in the dataset contains data for a population subgroup.

Individual-level data refers to data where each record in the dataset contains data pertaining to an individual.

Simple summary measures (difference and ratio) compare two population subgroups. They can be calculated for all dimensions of inequality (with two subgroups or more). Complex measures are calculated for inequality dimensions with more than two population subgroups and consider the situation in all subgroups. They can only be calculated for dimensions with more than two subgroups.

Selecting appropriate measures for analysing and reporting inequality involves considering several methodological issues. There are considerations relating to the characteristics of the underlying data, which determines the types of measures that can be calculated and how they are calculated:

**Whether the dimension of inequality is ordered or non-ordered**. Ordered dimensions have subgroups with an inherent ordering (such as education level or wealth quintiles), while non-ordered and binary dimensions have subgroups that cannot logically be ranked (such as subnational regions, ethnicity or sex).**Whether the dimension of inequality has two or more than two subgroups**. Simple measures can be calculated for all inequality dimensions, but complex measures can only be calculated for dimensions with more than two subgroups.**The optimum level that is to be achieved for the health indicator**. For favourable indicators, the goal is to attain a maximum level; for adverse indicators, the goal is to attain a minimum level. Note that for some indicators there is no optimum level. The optimum level impacts the calculation of certain summary measures.

There are also considerations relating to the properties of the different measures and the desired purpose of the analysis:

**Whether inequality is measured in absolute or relative terms**. Absolute measures indicate the magnitude of inequality between population subgroups, while relative measures show proportional inequality between subgroups.**Whether subgroups should be weighted according to their population size or not**. This involves a value judgement depending on the purpose of the analysis.**The selection of a reference point for non-ordered measures**. For instance, this may be the mean, the best-performing subgroup or a user-selected reference group.

The paper Summary measures of health inequality: a review of existing measures and their application provides further information about these considerations.

The following summary measures of health inequality are included in the `healthequal`

library:

- Simple measures
- Difference (
`d`

) - Ratio (
`r`

)

- Difference (
- Disproportionality measures (ordered dimensions)
- Absolute concentration index (
`aci`

) - Relative concentration index (
`rci`

)

- Absolute concentration index (
- Regression-based measures (ordered dimensions)
- Slope index of inequality (
`sii`

) - Relative index of inequality (
`rii`

)

- Slope index of inequality (
- Variance measures (non-ordered dimensions)
- Between-group variance (
`bgv`

) - Between-group standard deviation (
`bgsd`

) - Coefficient of variation (
`covar`

)

- Between-group variance (
- Mean difference measures (non-ordered dimensions)
- Mean difference from mean - unweighted and weighted (
`mdmu`

and`mdmw`

) - Mean difference from best-performing subgroup - unweighted and weighted (
`mdbu`

and`mdbw`

) - Mean difference from reference subgroup - unweighted and weighted (
`mdru`

and`mdrw`

) - Index of disparity - unweighted and weighted (
`idisu`

and`idisw`

)

- Mean difference from mean - unweighted and weighted (
- Disproportionality measures (non-ordered dimensions)
- Theil index (
`ti`

) - Mean log deviation (
`mld`

)

- Theil index (
- Impact measures
- Population attributable risk (
`parisk`

) - Population attributable fraction (
`paf`

)

- Population attributable risk (

`healthequal`

libraryFirst, load the `healthequal`

library in your R session. This requires the `dplyr`

package.

```
library(healthequal)
require(dplyr)
```

`healthequal`

packageThe `healthequal`

package comes with sample data for users to be able to test the package functions. The `OrderedSample`

and `NonorderedSample`

data contain data disaggregated by economic status and subnational region, respectively, for a single indicator.

```
data(OrderedSample)
head(OrderedSample)
```

```
indicator
1 Births attended by skilled health personnel (%)
2 Births attended by skilled health personnel (%)
3 Births attended by skilled health personnel (%)
4 Births attended by skilled health personnel (%)
5 Births attended by skilled health personnel (%)
dimension subgroup subgroup_order
1 Economic status (wealth quintile) Quintile 1 (poorest) 1
2 Economic status (wealth quintile) Quintile 2 2
3 Economic status (wealth quintile) Quintile 3 3
4 Economic status (wealth quintile) Quintile 4 4
5 Economic status (wealth quintile) Quintile 5 (richest) 5
estimate se population setting_average favourable_indicator
1 75.60530 1.5996131 2072.436 91.59669 1
2 91.01997 1.1351504 2112.204 91.59669 1
3 96.03959 0.6461946 1983.059 91.59669 1
4 97.04223 0.5676206 2052.124 91.59669 1
5 99.22405 0.2237683 1884.510 91.59669 1
ordered_dimension indicator_scale
1 1 100
2 1 100
3 1 100
4 1 100
5 1 100
```

```
data(NonorderedSample)
head(NonorderedSample)
```

```
# A tibble: 6 × 11
indicator dimension subgroup estimate se population setting_average
<chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl>
1 Births attended … Subnatio… aceh 95.1 1.54 230. 91.6
2 Births attended … Subnatio… bali 100 0 149. 91.6
3 Births attended … Subnatio… bangka … 97.4 1.27 55.7 91.6
4 Births attended … Subnatio… banten 80.4 3.54 451. 91.6
5 Births attended … Subnatio… bengkulu 94.3 2.77 70.2 91.6
6 Births attended … Subnatio… central… 98.6 0.648 1222. 91.6
# ℹ 4 more variables: favourable_indicator <dbl>, ordered_dimension <dbl>,
# indicator_scale <dbl>, reference_subgroup <dbl>
```

The `OrderedSampleMultipleind`

and `OrderedSampleMultipleind`

data contain disaggregated data by economic status and subnational region, respectively, for two indicators.

```
data(OrderedSampleMultipleind)
head(OrderedSampleMultipleind)
```

```
indicator
1 Births attended by skilled health personnel (%)
2 Births attended by skilled health personnel (%)
3 Births attended by skilled health personnel (%)
4 Births attended by skilled health personnel (%)
5 Births attended by skilled health personnel (%)
6 Under-five mortality rate (deaths per 1000 live births)
dimension subgroup subgroup_order
1 Economic status (wealth quintile) Quintile 1 (poorest) 1
2 Economic status (wealth quintile) Quintile 2 2
3 Economic status (wealth quintile) Quintile 3 3
4 Economic status (wealth quintile) Quintile 4 4
5 Economic status (wealth quintile) Quintile 5 (richest) 5
6 Economic status (wealth quintile) Quintile 1 (poorest) 1
estimate se population setting_average favourable_indicator
1 75.60530 1.5996131 2072.436 91.59669 1
2 91.01997 1.1351504 2112.204 91.59669 1
3 96.03959 0.6461946 1983.059 91.59669 1
4 97.04223 0.5676206 2052.124 91.59669 1
5 99.22405 0.2237683 1884.510 91.59669 1
6 52.46997 3.1404064 7119.732 340.38391 0
ordered_dimension indicator_scale
1 1 100
2 1 100
3 1 100
4 1 100
5 1 100
6 1 1000
```

```
data(NonorderedSampleMultipleind)
head(NonorderedSampleMultipleind)
```

```
# A tibble: 6 × 11
indicator dimension subgroup estimate se population setting_average
<chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl>
1 Births attended … Subnatio… aceh 95.1 1.54 230. 91.6
2 Births attended … Subnatio… bali 100 0 149. 91.6
3 Births attended … Subnatio… bangka … 97.4 1.27 55.7 91.6
4 Births attended … Subnatio… banten 80.4 3.54 451. 91.6
5 Births attended … Subnatio… bengkulu 94.3 2.77 70.2 91.6
6 Births attended … Subnatio… central… 98.6 0.648 1222. 91.6
# ℹ 4 more variables: favourable_indicator <dbl>, ordered_dimension <dbl>,
# indicator_scale <dbl>, reference_subgroup <dbl>
```

For information about the datasets, type the following commands, which will display the corresponding dataset help file:

```
?healthequal::OrderedSample
?healthequal::NonorderedSample
?healthequal::OrderedSampleMultipleind
?healthequal::NonorderedSampleMultipleind
?healthequal::IndividualSample
```

The Absolute Concentration Index (ACI) is a summary measure of health inequality that can be used with **ordered dimensions**. For information about the ACI function type the following command, which will display the corresponding help file:

`?aci`

The `OrderedSample`

dataset can be used to calculate ACI. Two arguments are required: `est`

(the subgroup estimate, recorded as `estimate`

in the same dataset), and `subgroup_order`

(the order of subgroups in an increasing sequence). Other arguments, such as `pop`

(the number of people within each subgroup, recorded as `population`

in the sample dataset) or `weight`

(the sampling weight for survey data), are optional. Lastly, the `force`

argument can be used to estimate ACI when some estimates are missing.

```
with(OrderedSample,
aci(est = estimate,
subgroup_order = subgroup_order,
pop = population
)
)
```

```
measure estimate se lowerci upperci
1 aci 4.30052 1.284031 1.783865 6.817174
```

The Slope Index of Inequality (SII) is a summary measure of health inequality that can be used with **ordered dimensions**. The slope index of inequality (SII) is an absolute measure of inequality that represents the difference in estimated indicator values between the most-advantaged and most-disadvantaged, while taking into consideration the situation in all other subgroups/individuals – using an appropriate regression model.

For information about the SII function type the following command, which will display the corresponding help file:

`?sii`

SII can be calculated using disaggregated or individual data. In this example, the `IndividualSample`

dataset, a survey weighted dataset, is used. For this type of data, five arguments are required: `est`

(the individual estimate, recorded as `sba`

in the same dataset), `subgroup_order`

(the order of subgroups in an increasing sequence), `weight`

(the sampling weight), `psu`

(the primary sampling unit) and `strata`

(the variable identifying the strata).

```
with(IndividualSample,
aci(est = sba,
subgroup_order = subgroup_order,
weight = weight,
psu = psu,
strata = strata
)
)
```

```
measure estimate se lowerci upperci
1 aci 0.07801353 0.002950566 0.07223053 0.08379654
```

Between-group variance (BGV) is a summary measure of health inequality that it can be used to measure inequality across **non-ordered dimensions** of inequality. It is calculated as the weighted average of squared differences between subgroup estimates and the weighted mean. Type `?bgv`

to view the corresponding help file.

The `NonorderedSample`

dataset can be used to calculate BGV, which requires two arguments: `pop`

(the number of people within each subgroup, recorded as `population`

in the sample dataset), and `est`

(the subgroup estimate, recorded as `estimate`

in the same dataset). The argument `se`

(the standard error of the subgroup estimate) is required only to compute the corresponding 95% confidence intervals.

```
with(NonorderedSample,
bgv(pop = population,
est = estimate,
se = se
)
)
```

```
measure estimate se lowerci upperci
1 bgv 50.42023 9.560196 31.68259 69.15787
```

The previous examples showed the calculation of a single measure of inequality for a single indicator-dimension combination. These next examples use the dataset `NonorderedSampleMultipleind`

, which contains disaggregated data by subnational region for two indicators:

- Births attended by skilled health personnel (%) and
- Under-five mortality rate (deaths per 1000 live births)

The data can be inspected as follows:

`head(NonorderedSampleMultipleind)`

```
# A tibble: 6 × 11
indicator dimension subgroup estimate se population setting_average
<chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl>
1 Births attended … Subnatio… aceh 95.1 1.54 230. 91.6
2 Births attended … Subnatio… bali 100 0 149. 91.6
3 Births attended … Subnatio… bangka … 97.4 1.27 55.7 91.6
4 Births attended … Subnatio… banten 80.4 3.54 451. 91.6
5 Births attended … Subnatio… bengkulu 94.3 2.77 70.2 91.6
6 Births attended … Subnatio… central… 98.6 0.648 1222. 91.6
# ℹ 4 more variables: favourable_indicator <dbl>, ordered_dimension <dbl>,
# indicator_scale <dbl>, reference_subgroup <dbl>
```

`unique(NonorderedSampleMultipleind$indicator)`

```
[1] "Births attended by skilled health personnel (%)"
[2] "Under-five mortality rate (deaths per 1000 live births)"
```

The Coefficient of Variation (COV) is a summary measure of health inequality that it can be used to measure inequality across **non-ordered dimensions** of inequality. COV is a relative measure of inequality that considers all population subgroups. Type `?covar`

to view the corresponding help file. The `NonorderedSampleMultipleind`

dataset can be used to calculate COV for two different dimensions.

```
library(dplyr)
measures <- NonorderedSampleMultipleind %>%
dplyr::group_by(indicator) %>%
dplyr::summarize(covar(pop = population,
est = estimate,
scaleval = indicator_scale
)
)
measures
```

```
# A tibble: 2 × 5
indicator measure estimate lowerci upperci
<chr> <chr> <dbl> <lgl> <lgl>
1 Births attended by skilled health personnel … cov 7.75 NA NA
2 Under-five mortality rate (deaths per 1000 l… cov 41.5 NA NA
```

The `NonorderedSampleMultipleind`

dataset can also be used to calculate two or more different summary measures (in the example below COV and BGV) for multiple dimensions.

```
multiplemeasures <- NonorderedSampleMultipleind %>%
dplyr::group_by(indicator,
dimension) %>%
dplyr::summarize(
covar = covar(pop = population,
est = estimate,
scaleval = indicator_scale),
bgv = bgv(pop = population,
est = estimate,
se = se
)
)
multiplemeasures
```

```
# A tibble: 2 × 4
# Groups: indicator [2]
indicator dimension covar$measure bgv$measure
<chr> <chr> <chr> <chr>
1 Births attended by skilled health personn… Subnatio… cov bgv
2 Under-five mortality rate (deaths per 100… Subnatio… cov bgv
# ℹ 7 more variables: covar$estimate <dbl>, $lowerci <lgl>, $upperci <lgl>,
# bgv$estimate <dbl>, $se <dbl>, $lowerci <dbl>, $upperci <dbl>
```

```
# It is possible to extract the measures separetly
multiplemeasures$covar
```

```
measure estimate lowerci upperci
1 cov 7.752158 NA NA
2 cov 41.500365 NA NA
```

`multiplemeasures$bgv`

```
measure estimate se lowerci upperci
1 bgv 50.42023 9.560196 31.68259 69.15787
2 bgv 2468.70951 273.155091 1933.33537 3004.08365
```

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