The ratio (R) is a relative measure of inequality that shows the ratio of an indicator between two population subgroups. For more information on this inequality measure see Schlotheuber (2022) below.
Usage
r(
est,
se = NULL,
favourable_indicator,
ordered_dimension,
subgroup_order = NULL,
reference_subgroup = NULL,
conf.level = 0.95,
...
)Arguments
- est
The subgroup estimate. Estimates must be available for the two subgroups being compared.
- se
The standard error of the subgroup estimate. If this is missing, confidence intervals of D cannot be calculated.
- favourable_indicator
Records whether the indicator is favourable (1) or adverse (0). Favourable indicators measure desirable health events where the ultimate goal is to achieve a maximum level (such as skilled birth attendance). Adverse indicators measure undesirable health events where the ultimate goal is to achieve a minimum level (such as under-five mortality rate).
- ordered_dimension
Records whether the dimension is ordered (1) or non-ordered (0). Ordered dimensions have subgroup with a natural order (such as economic status). Non-ordered or binary dimensions do not have a natural order (such as subnational region or sex).
- subgroup_order
The order of subgroups in an increasing sequence. Required if the dimension is ordered (ordered_dimension=1).
- reference_subgroup
Identifies a reference subgroup with the value of 1, if the dimension is non-ordered or binary.
- conf.level
Confidence level of the interval. Default is 0.95 (95%).
- ...
Further arguments passed to or from other methods.
Value
The estimated D value, corresponding estimated standard error,
and confidence interval as a data.frame.
Details
R is calculated as R = y1 / y2 where y1 and y2 indicate the
estimates for subgroups 1 and 2. The selection of the two subgroups depends
on the characteristics of the inequality dimension and the purpose of the
analysis. In addition, the direction of the calculation may depend on the
indicator type (favourable or adverse). Please see specifications of how
y1 and y2 are identified below.
Ordered dimension: Favourable indicator: Most-advantaged subgroup / Least-advantaged subgroup Adverse indicator: Least-advantaged subgroup / Most-advantaged subgroup
Non-ordered dimension: No reference group & favourable indicator: Highest estimate / Lowest estimate No reference group & adverse indicator: Lowest estimate / Highest estimate Reference group & favourable indicator: Reference estimate / Lowest estimate Reference group & adverse indicator: Lowest estimate / Reference estimate
Interpretation: R only assumes positive values. The further the value of R from 1, the higher the level of inequality. R is 1 if there is no inequality. R is a multiplicative measure and therefore results should be displayed on a logarithmic scale. Values larger than 1 are equivalent in magnitude to their reciprocal values smaller than 1 (e.g. a value of 2 is equivalent in magnitude to a value of 0.5).
Type of summary measure: Simple; relative; unweighted
Applicability: Any dimension of inequality
Warning: The confidence intervals are approximate and might be biased. See Ahn et al. (2018) below for further information about the standard error formula.
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, Luta G. Variance estimation and confidence intervals for 11 commonly used health disparity measures. JCO Clin Cancer Inform. 2018;2:1-19. doi:10.1200/CCI.18.00031.
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,
r(est = estimate,
se = se,
favourable_indicator = favourable_indicator,
ordered_dimension = ordered_dimension,
reference_subgroup = reference_subgroup))
#> measure estimate se lowerci upperci
#> 1 r 1.481696 0.1110345 1.191918 1.841924