Population attributable fraction (PAR) is a relative measure of inequality that shows the potential improvement in the average of an indicator, in absolute terms, that could be achieved if all population subgroups had the same level of the indicator as a reference point. The reference point refers to the most advantaged subgroup for ordered dimensions and the best-performing subgroup for non-ordered dimensions (i.e. the subgroup with the highest value for favourable indicators and the subgroup with the lowest value for adverse indicators).
Usage
paf(
est,
pop = NULL,
favourable_indicator,
ordered_dimension,
subgroup_order = NULL,
setting_average = NULL,
scaleval,
conf.level = 0.95,
force = FALSE,
...
)Arguments
- est
The subgroup estimate. Estimates must be available for the two subgroups being compared.
- pop
The number of people within each subgroup.Population size must be available for all subgroups.
- 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).
- setting_average
The overall indicator average for the setting of interest. Setting average must be unique for each setting, year and indicator combination. If population (pop) is not specified for all subgroups, the setting average is used for the calculation.
- 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.
- conf.level
Confidence level of the interval. Default is 0.95 (95%).
- force
TRUE/FALSE statement to force calculation when subgroup estimates are missing.
- ...
Further arguments passed to or from other methods.
Value
The estimated PAF value, corresponding estimated standard error,
and confidence interval as a data.frame.
Details
PAF is calculated as the difference between the estimate for the reference subgroup and the mean (e.g. the national average), divided by the mean and multiplied by 100. For more information on this inequality measure see Schlotheuber (2022) below.
If the indicator is favourable and PAF < 0, then PAF is replaced with 0. If the indicator is adverse and PAF > 0, then PAF is replaced with 0.
Interpretation: PAF assumes positive values for favourable indicators and negative values for non-favourable (adverse) indicators. The larger the absolute value of PAF, the higher the level of inequality. PAF is 0 if no further improvement can be achieved (i.e., if all subgroups have reached the same level of the indicator as the reference subgroup or surpassed that level).
Type of summary measure: Complex; relative; weighted
Applicability: Any dimension of inequality with more than two subgroups
Warning: The confidence intervals are approximate and might be biased. See Walter S.D. (1978) below for further information on 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.
Walter, SD. Calculation of attributable risks from epidemiological data. Int J Epidemiol. 1978 Jun 1;7(2):175-82. doi:10.1093/ije/7.2.175.
Examples
# example code
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
with(OrderedSample,
paf(est = estimate,
pop = population,
favourable_indicator = favourable_indicator,
ordered_dimension = ordered_dimension,
subgroup_order = subgroup_order,
scaleval = indicator_scale))
#> measure estimate se lowerci upperci
#> 1 paf 8.327116 0.003681919 8.319899 8.334332