Title

healthequal -- calculates summary measures of health inequality

Syntax

healthequal varname [if] [weight], measure(string) [options]

varname specifies the variable containing the indicator estimates. Apart from the calculation of simple measures (d and r), estimates must be available for all subgroups for ordered dimensions of inequality and must be available for at least 85% of subgroups for non-ordered dimensions of inequality. The force option can force calculations when estimates are missing.

weight specifies the variable containing population or sampling weights. Only pweights are allowed; see weight. For disaggregated data, this is the number of people within each subgroup (or the weighted population in the case of disaggregated estimates from a survey). For individual-level (micro) data from a survey, this is the individual sampling weight. This option is required for the calculation of aci, rci, sii and rii (unless weights are specified using svyset and the svy option), and are required for bgv, bgsd, cov, idisw, mdbw, mdmw, mdrw, ti and mld. It is also required for the calculation of idisu, mdmu, paf and par in the absence of the average option and for the calculation of 95% confidence intervals of these measures.

Required
measure(varname) summary measure(s) to calculate; multiple measures may be entered, separated by spaces

Main
average(varname) indicator average for the setting

se(varname) standard error of the subgroup estimates

dimension(varname) whether the dimension is ordered (0) or non-ordered / binary (0)

order(varname) ranking order of subgroups or individuals

fav(varname) whether the indicator is favourable (1) or not (0)

scale(varname) scale/unit of the indicator

reference(varname) reference subgroup indicated with 1

svy can be specified when using complex survey designs if svyset has been used to identify the survey design characteristics prior to running healthequal

linear specifies the use of a linear regression model for the calculation of SII and RII (default is logistic regression)

limits(#1 #2) used to specify the theoretical minimum (#1) and maximum (#2) for bounded variables

erreygers in conjunction with RCI and limits requests the Erreygers correction of the concentration index

wagstaff in conjunction with RCI and limits requests the Wagstaff correction of the concentration index

sim(#) specifies the number of simulations (default is 100)

format($fmt) format for summary measures output

noprint supresses summary measure output (default is print)

force force calculation with missing indicator estimate values

by is allowed; see [D] by.

Description

healthequal calculates a range of summary measures of health inequality. Summary measures of health inequality summarize the amount of inequality across population subgroups using a single number - which facilitates the comparison of inequalities over time and across different settings and indicators.

Health inequalities are observed differences in health between population subgroups that are formed on the basis of dimensions of inequality. Dimensions of inequality encompass demographic, socioeconomic and geographic characteristics (e.g., age, economic status, education, and subnational region). Dimensions of inequality can be categorised as binary (with only two subgroups, such as male/female or urban/rural place of residence), ordered (with subgroups that have a natural or inherent ordering, such as education level or wealth quintiles), or non-ordered (with subgroups that cannot be inherently ranked, such as subnational regions or ethnicity).

Note that the primary indended use of healthequal is to calculate summary measures of health inequality using disaggregated data (i.e., data that are broken down by population subgroups). However, the measures aci, rci, sii and rii used with ordered dimensions of inequality can also be calculated using individual-level (micro) data.

There is no default summary measure; the measure option specifies the summary measure(s) to be calculated. For further information about the summary measures, calculation methods, and methodological considerations see Schlotheuber and Hosseinpoor (2022).

Options

measure(string) identifies the summary measure(s) to calculate. Multiple measures may be entered, separated by spaces. Inequality can be measured in either absolute or relative terms. Two measures (d and r) measure inequality between two population subgroups within a dimension of inequality, while the other measures calculated by healthequal require data for more than two population subgroups. Four measures (aci, rci, rii and sii) measure inequality in ordered dimensions (e.g., education level, economic status). Thirteen measures (bgsd, bgv, cov, idisu, idisw, mdbu, mdbw, mdmu, mdmw, mdru, mdrw, mld, ti) measure inequality in non-ordered dimensions (e.g., subnational region, ethnicity). Two measures (paf and par) measure inequality in both ordered and non-ordered dimensions.

measures

Simple measures
d Difference

r Ratio

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

rii Relative index of inequality

Disproportionality measures (ordered dimensions)
aci Absolute concentration index

rci Relative concentration index

Variance measures (non-ordered dimensions)
bgv Between-group variance

bgsd Between-group standard deviation

cov Coefficient of variation

Mean difference measures (non-ordered dimensions)
mdmu Mean difference from mean (unweighted)

mdmw Mean difference from mean (weighted)

mdbu Mean difference from best-performing subgroup (unweighted)

mdbw Mean difference from best-performing subgroup (weighted)

mdru Mean difference from a reference subgroup (unweighted)

mdrw Mean difference from a reference subgroup (weighted)

idisu Index of Disparity (unweighted)

idisw Index of Disparity (weighted)

Disproportionality measures (non-ordered dimensions)
ti Theil Index

mld Mean log deviation

Impact measures
paf Population attributable fraction

par Population attributable risk

average(varname) specifies the indicator average for the setting. This option can be used for the calculation of idisu, mdmu, paf and par in the absence of specifying a weight variable (however 95% confidence intervals will not be calculated).

se(varname) specifies the standard error of the subgroup estimates. This option is required for the calculation of 95% confidence intervals of d, r, bgv, bgsd, cov, idisu, idisw, mdbu, mdbw, mdmu, mdmw, mdru, mdrw, ti and mld.

dimension(varname) specifies whether the dimension is ordered (e.g., economic status, education level), non-ordered (e.g., subnational region, ethnicity) or binary (e.g., sex, urban/rural place of residence). The variable varname must have the value of 1 for ordered dimensions and 0 for non-ordered and binary dimensions. This option is required for the calculation of d, r, par and paf.

order(varname) specifies the ranking order of subgroups or individuals for ordered dimensions of inequality (e.g., economic status, education). The variable varname must be at least an ordinal variable. This option is required for the calculation of aci, rci, rii and sii and is required for the calculation of d, r, par and paf if the dimension is ordered.

fav(varname) specifies whether the indicator being measured is favourable or not. The variable varname must have the value of 1 for favourable indicators (which measure desirable health events where the ultimate goal is to achieve a maximum level, such as skilled birth attendance) and 0 for non-favourable indicators (which measure undesirable health events where the ultimate goal is to achieve a minimum level, such as under-five mortality rate). This option is required for the calculation of d, r, mdbu, mdbw, par and paf.

scale(varname) specifies the scale of the indicator being measured. For example, the scale of an indicator measured as a percentage is 100; the scale of an indicator measured as a rate per 1000 population is 1000. This option is required for the calculation of 95% confidence intervals of idisu, idisw, mdbu, mdbw, mdmu, mdmw, mdru, mdrw, par and paf.

reference(varname) specifies a reference subgroup. The variable varname must indicate only one reference subgroup with the value 1 and must contain the value 0 for all other subgroups. This is required for the calculation of mdru and mdrw and can be used with d and r to override the default selection of the reference subgroup.

svy can be specified when using complex survey designs if svyset has been used to identify the survey design characteristics prior to running healthequal, for the calculation of aci, rci, sii and rii.

linear specifies the use of a linear regression model for the calculation of sii and rii (the default is logistic regression). Linear regression is recommended when using individual-level data and the indicator estimate is recorded as a continuous variable (e.g., weight or height).

limits(#1 #2) specifies the theoretical minimum (#1) and maximum (#2) of bounded variables for the calculation of aci and rci. Bounded variables have a finite upper limit, such as any binary variable (0,1), an index, or number of years of schooling.

erreygers in conjunction with rci and limits(#1 #2) requests the Erreygers correction of the concentration index.

wagstaff in conjunction with rci and limits(#1 #2) requests the Wagstaff correction of the concentration index.

sim(#) specifies the number of simulations for the calculation of confidence intervals of bgsd, cov, idisu, idisw, mdbu, mdbw, mdmu, mdmw, mdru and mdrw. The default if sim is not specified is 100.

format(%fmt) specifies a format other than the default for the summary measures output.

noprint supresses summary measure output (the default is print).

force forces the calculation of summary measures even if indicator estimates are missing.

Example 1: Disaggregated data

Load example disaggregated data

. use sample_rmnch, clear

Calculate the slope index of inequality (sii) for the ordered dimension of inequality (ordered_dimension==1) using subgroup estimates (est), subgroup population sizes (pop), and the ranking of subgroups identified in the variable subgroup_order:

. healthequal est [pw=pop] if ordered_dimension==1, measure(sii) order(subgroup_order)

Calculate between-group variance (bgv) for the non-ordered dimension of inequality (ordered_dimension==0) using subgroup estimates (est), subgroup population sizes (pop) and the standard error of subgroup estimates (se):

. healthequal est [pw=pop] if ordered_dimension==0, measure(bgv) se(se)

For each dimension of inequality, calculate the population attributable risk (par) and the population attributable fraction (paf) using subgroup estimates (est) and subgroup population sizes (pop), with the variable favourable_indicator indicating whether the indicator is favourable or not, the variable ordered_dimension indicating whether the dimension is ordered or not, and the variable subgroup_order indicating the order of subgroups (required if ordered_dimension==1). The output is formatted to 2 decimal places:

. bysort dimension: healthequal est [pw=pop], measure(par paf) fav(favourable_indicator) dim(ordered_dimension) order(subgroup_order) format(%4.2f)

Example 2: Individual-level data

Load example individual-level survey data

. use sample_dhs, clear

Calculate the absolute concentration index (aci) and relative concentration index (rci) taking survey design into account, using the indicator result (sba) and the ranking of individuals (subgroup_order):

. svyset psu [pw=weight], strata(strata)

. healthequal sba, measure(aci rci) order(subgroup_order) svy

Stored results

healthequal stores the following in r(), where measure is the summary measure that has been calculated:

Scalars

r(measure) summary measure value

r(measure_se) standard error

r(measure_ll) lower 95% confidence interval

r(measure_ul) upper 95% confidence interval

Acknowledgements

The authors would like to acknowledge Sam Harper (McGill University), George Luta (Georgetown University) and Zev Ross (ZevRoss Spatial Analysis) for their support in developing the summary measure calculations used in the Health Equity Assessment Toolkit (HEAT and HEAT Plus), and Patricia Menéndez (University of Melbourne) for review of the R version of the summary measure codes.

Authors

Katherine Kirkby, Department of Data and Analytics, World Health Organization, Switzerland.

Daniel A. Antiporta, Department of Data and Analytics, World Health Organization, Switzerland.

Anne Schlotheuber, Department of Data and Analytics, World Health Organization, Switzerland.

Ahmad Reza Hosseinpoor (corresponding author), Department of Data and Analytics, World Health Organization, Switzerland <hosseinpoora@who.int>

Citation

World Health Organization. 2024. healthequal: Stata module for calculating summary measures of health inequality.

References

Ahn J, Harper S, Yu M, Feuer EJ, Liu B, Luta G. Variance Estimation and Confidence Intervals for 11 Commonly Used Health Disparity Measures. JCO Clin Cancer Inform. 2018 Dec;2:1-19.
https://doi.org/10.1200/CCI.18.00031

Erreygers G. Correcting the Concentration Index. Journal of Health Economics. 2009;28:504–515.
https://doi.org/10.1016/j.jhealeco.2008.02.003

O'Donnell O, van Doorslaer E, Wagstaff A, Lindelow M. Analyzing Health Equity Using Household Survey Data: A Guide to Techniques and Their Implementation. World Bank Institute; Washington, D.C: 2008.
https://hdl.handle.net/10986/6896

Schlotheuber A, Hosseinpoor AR. Summary Measures of Health Inequality: A Review of Existing Measures and Their Application. Int J Environ Res Public Health. 2022 Mar 20;19(6):3697.
https://doi.org/10.3390/ijerph19063697

Wagstaff A. The bounds of the concentration index when the variable of interest is binary, with an application to immunization inequality. Health Economics. 2005;14:429–432.
https://doi.org/10.1002/hec.953

World Health Organization. Handbook on health inequality monitoring: with a special focus on low- and middle-income countries. Geneva: World Health Organization; 2013.
https://www.who.int/publications/i/item/9789241548632

Also see

conindex, concindc, dstat, ainequal, siilogit and cixr if installed.