The mean difference from a reference point (MDR) is an absolute measure of inequality that shows the mean difference between each population subgroup and a defined reference subgroup (e.g. the capital city or region for data disaggregated by subnational regions).
Usage
mdrw(
est,
se = NULL,
pop,
scaleval = NULL,
reference_subgroup,
sim = NULL,
seed = 123456,
force = FALSE,
...
)Arguments
- est
The subgroup estimate. Estimates must be available for at least 85% of subgroups.
- se
The standard error of the subgroup estimate. If this is missing, 95% confidence intervals cannot be calculated.
- pop
The number of people within each subgroup.Population size must be available for all subgroups.
- scaleval
The scale of the indicator. 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. If this is missing, 95% confidence intervals cannot be calculated.
- reference_subgroup
Identifies a reference subgroup with the value of 1.
- sim
The number of simulations to estimate 95% confidence intervals. Default is 100.
- seed
The random number generator (RNG) state for the 95% confidence interval simulation. Default is 123456.
- force
TRUE/FALSE statement to force calculation when more than 85% of subgroup estimates are missing.
- ...
Further arguments passed to or from other methods.
Value
The estimated MDRW value, corresponding estimated standard error,
and confidence interval as a data.frame.
Details
The weighted version (MDRW) is calculated as the weighted average of absolute differences between the subgroup estimates and the estimate for the reference subgroup. Absolute differences are weighted by each subgroup’s population share. For more information on this inequality measure see Schlotheuber (2022) below.
95% confidence intervals are calculated using a Monte Carlo simulation-based method. The dataset is simulated a large number of times (e.g. 100), with the mean and standard error of each simulated dataset being the same as the original dataset. MDRW is calculated for each of the simulated sample datasets. The 95% confidence intervals are based on the 2.5th and 97.5th percentiles of the MDRW results. See Ahn (2019) below for further information.
Interpretation: MDRW only has positive values, with larger values indicating higher levels of inequality. MDRW is 0 if there is no inequality. MDRW has the same unit as the indicator.
Type of summary measure: Complex; absolute; weighted
Applicability: Non-ordered dimensions of inequality with more than two subgroups
References
Schlotheuber, A, Hosseinpoor, AR. Summary measures of health inequality: A review of existing measures and their application. Int J Environ Res Public Health. 2022;19(6):3697. doi:10.3390/ijerph19063697.
Ahn J, Harper S, Yu M, Feuer EJ, Liu B. Improved Monte Carlo methods for estimating confidence intervals for eleven commonly used health disparity measures. PLoS One. 2019 Jul 1;14(7).
Examples
# example code
data(NonorderedSample)
head(NonorderedSample)
#> indicator dimension
#> 1 Births attended by skilled health personnel (%) Subnational region
#> 2 Births attended by skilled health personnel (%) Subnational region
#> 3 Births attended by skilled health personnel (%) Subnational region
#> 4 Births attended by skilled health personnel (%) Subnational region
#> 5 Births attended by skilled health personnel (%) Subnational region
#> 6 Births attended by skilled health personnel (%) Subnational region
#> subgroup estimate se population setting_average
#> 1 aceh 95.11784 1.5384434 230.20508 91.59669
#> 2 bali 100.00000 0.0000000 149.46272 91.59669
#> 3 bangka balitung 97.41001 1.2676437 55.66533 91.59669
#> 4 banten 80.35694 3.5440531 451.26550 91.59669
#> 5 bengkulu 94.25756 2.7740061 70.17540 91.59669
#> 6 central java 98.56168 0.6476116 1221.94446 91.59669
#> favourable_indicator ordered_dimension indicator_scale reference_subgroup
#> 1 1 0 100 1
#> 2 1 0 100 0
#> 3 1 0 100 0
#> 4 1 0 100 0
#> 5 1 0 100 0
#> 6 1 0 100 0
with(NonorderedSample,
mdrw(est = estimate,
se = se,
pop = population,
scaleval = indicator_scale,
reference_subgroup = reference_subgroup))
#> measure estimate se lowerci upperci
#> 1 mdrw 5.64322 NA 4.66525 7.056331