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#' Slope index of inequality (SII)
#'
#' 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. SII can be calculated using both disaggregated data and
#' individual-level data. Subgroups in disaggregated data are weighted
#' according to their population share, while individuals are weighted by
#' sample weight in the case of data from surveys.
#'
#' To calculate SII, a weighted sample of the whole population is ranked from
#' the most-disadvantaged subgroup (at rank 0) to the most-advantaged subgroup
#' (at rank 1). This ranking is weighted, accounting for the proportional
#' distribution of the population within each subgroup. The indicator of
#' interest is then regressed against this relative rank using an appropriate
#' regression model (e.g., a generalized linear model with logit link), and the
#' predicted values of the indicator are calculated for the two extremes (rank
#' 1 and rank 0). The difference between the predicted values at rank 1 and
#' rank 0 (covering the entire distribution) generates the SII value. For more
#' information on this inequality measure see Schlotheuber, A., & Hosseinpoor,
#' A. R. (2022) below.
#'
#' **Interpretation:** SII is zero if there is no inequality. Greater absolute
#' values indicate higher levels of inequality. For favourable indicators,
#' positive values indicate a concentration of the indicator among the
#' advantaged, while negative values indicate a concentration of the indicator
#' among the disadvantaged. For adverse indicators, it is the reverse: positive
#' values indicate a concentration of the indicator among the disadvantaged,
#' while negative values indicate a concentration of the indicator among the
#' advantaged.
#'
#' **Type of summary measure:** Complex; absolute; weighted
#'
#' **Applicability:** Ordered; more than two subgroups
#'
#' **Warning:** The confidence intervals are approximate
#' and might be biased.
#'
#' @param est The subgroup estimate.
#' Estimates must be available for all subgroups.
#' @param subgroup_order The order of subgroups in an increasing sequence.
#' @param pop The number of people within each subgroup.
#' Population size must be available for all subgroups.
#' @param 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.
#' @param weight Individual sampling weight (required if data come from a
#' survey)
#' @param psu Primary sampling unit (required if data come from a survey)
#' @param strata Strata (required if data come from a survey)
#' @param fpc Finite population correction
#' @param conf.level confidence level of the interval.
#' @param linear TRUE/FALSE statement to specify the use of a linear
#' regression model for SII estimation (default is logistic regression)
#' @param force TRUE/FALSE statement to force calculation with missing
#' indicator estimate values.
#' @param ... Further arguments passed to or from other methods.
#' @examples
#' # example code
#' data(IndividualSample)
#' head(IndividualSample)
#' with(IndividualSample,
#' sii(est = sba,
#' subgroup_order = subgroup_order,
#' weight = weight,
#' psu = psu,
#' strata = strata
#' )
#' )
#' @references Schlotheuber, A., & Hosseinpoor, A. R. (2022).
#' Summary measures of health inequality: A review of existing
#' measures and their application. International journal of
#' environmental research and public health, 19 (6), 3697.
#' @return The estimated SII value, corresponding estimated standard error,
#' and confidence interval as a `data.frame`.
#' @importFrom stats binomial gaussian glm predict qnorm quantile rnorm vcov
#' quasibinomial
#' @importFrom utils data
#' @importFrom srvyr as_survey
#' @importFrom survey svyglm svymean svyvar svydesign
#' @importFrom dplyr lag group_by select
#' @importFrom emmeans emmeans regrid contrast
#' @importFrom rlang .data
#' @importFrom marginaleffects avg_comparisons
#' @export
#' @rdname sii
#'
sii <- function(est,
subgroup_order,
pop = NULL,
scaleval = NULL,
weight = NULL,
psu = NULL,
strata = NULL,
fpc = NULL,
conf.level = 0.95,
linear = FALSE,
force = FALSE, ...) {
# Variable checks
## Stop
if(!force){
if(anyNA(est)) stop('Estimates are missing in some subgroups')
} else {
pop <- pop[!is.na(est)]
subgroup_order <- subgroup_order[!is.na(est)]
if(!is.null(psu)) psu <- psu[!is.na(est)]
if(!is.null(strata)) strata <- strata[!is.na(est)]
if(!is.null(weight)) weight <- weight[!is.na(est)]
if(!is.null(fpc)) fpc <- fpc[!is.na(est)]
if(!is.null(scaleval)) scaleval <- scaleval[!is.na(est)]
est <- est[!is.na(est)]
}
if(length(unique(est)) == 1)
stop("SII not calculated - all estimates have the same value.")
if(!is.null(pop)) {
if(anyNA(pop)){
stop('Population is missing in some subgroups')
}
if(!is.numeric(pop)){
stop('Population needs to be numeric')
}
if(all(pop == 0)){
stop('The population is of size 0 in all cells')
}
}
if(is.null(subgroup_order)){
stop('Subgroup order needs to be declared')
}
if(!is.null(weight) & !is.numeric(weight)){
stop('Weights needs to be numeric')
}
#Warning
if(is.null(pop) & is.null(weight)) {
message("Data not aggregated nor weighted")
}
# Options
options(survey.lonely.psu = "adjust")
options(survey.adjust.domain.lonely = TRUE)
# Calculate summary measure
# Assign scale
if(!is.null(scaleval)){
scale <- max(scaleval)
} else {
scale <- ifelse(est <= 1, 1,
ifelse(est > 1 & est <= 100, 100,
ifelse(est > 100 & est <= 1000, 1000,
ifelse(est > 1000 & est <= 10000, 10000,
ifelse(est > 10000 & est <= 100000,
100000,
1000000
)
)
)
))
scale<-max(scale)
}
# Create pop if NULL
y <- NULL
ny <- NULL
if(is.null(pop) & is.null(weight)){
pop <- rep(1, length(est))
}
if(is.null(pop) & !is.null(weight)){
pop <- weight
} else {
pop <- ceiling(pop)
y <- round((est/scale) * pop)
ny <- pop - y
if(any(ny < 0 | y > pop | y < 0))
return(data.frame(measure = "sii",
estimate = NA,
se = NA,
lowerci = NA,
upperci = NA))
}
# Rank subgroups from the most-disadvantaged to the most-advantaged
reorder <- order(subgroup_order)
pop <- pop[reorder]
subgroup_order <- subgroup_order[reorder]
if(!is.null(weight)) weight <- weight[reorder]
if(!is.null(strata)) strata <- strata[reorder]
if(!is.null(psu)) psu <- psu[reorder]
if(!is.null(fpc)) fpc <- fpc[reorder]
if(!is.null(y)) y <- y[reorder]
if(!is.null(ny)) ny <- ny[reorder]
est <- est[reorder]
est_sc <- est / scale
sumw <- sum(pop, na.rm = TRUE)
cumw <- cumsum(pop)
cumw1 <- lag(cumw)
cumw1[is.na(cumw1)] <- 0
newdat_sii <- as.data.frame(cbind(est_sc,
pop,
psu,
strata,
weight,
subgroup_order,
sumw,
cumw,
cumw1,
fpc,
y,
ny))
newdat_sii <- newdat_sii %>% group_by(subgroup_order) %>%
mutate(cumwr = max(.data$cumw, na.rm = TRUE),
cumwr1 = min(.data$cumw1, na.rm = TRUE)) %>%
ungroup() %>%
mutate(rank = (.data$cumwr1 + 0.5*
(.data$cumwr-.data$cumwr1)) / .data$sumw)
newdat_sii <- newdat_sii %>%
select(est_sc, rank,
pop,
weight,
psu,
strata,
fpc,
y,
ny)
# Calculate SII
if(is.null(weight)){ #For non survey
if(!linear){
mod <- glm(formula = cbind(y, ny) ~ rank,
weights = pop,
data = newdat_sii,
family = binomial("logit"))
} else {
mod <- glm(est_sc ~ rank,
data = newdat_sii,
family = gaussian,
weights = pop)
}
siie <- marginaleffects::avg_comparisons(mod, comparison="difference",
variables = list(rank = c(0,1)),
vcov = "HC1")
sii <- siie$estimate
# Calculate 95% confidence intervals
se.formula <- siie$std.error
lowerci <- sii - se.formula * qnorm(0.975)
upperci <- sii + se.formula * qnorm(0.975)
} else{ #For survey
tids <- if(is.null(psu)) {
~1
} else {
~psu
}
tstrata <- if(is.null(strata)) {
NULL
} else {
~strata
}
tfpc <- if(is.null(fpc)) {
NULL
} else {
~fpc
}
newdat_sii_s <- svydesign(ids = tids,
probs = NULL,
strata = tstrata,
weights = ~weight,
fpc = tfpc,
data = newdat_sii)
if(!linear){
mod <- svyglm(est_sc ~ rank,
design = newdat_sii_s,
family = quasibinomial(link="logit"))
} else{
mod <- svyglm(est_sc ~ rank,
design = newdat_sii_s,
family = gaussian)
}
siie_emmeans <- contrast(regrid(emmeans(mod, specs = ~ rank,
at = list(rank = c(1, 0)))),
method = "pairwise")
siie_sum <- summary(siie_emmeans)
sii <- siie_sum$estimate
# Calculate 95% confidence intervals
se.formula <- siie_sum$SE
cilevel <- 1-((1-conf.level)/2)
lowerci <- sii - se.formula * qnorm(cilevel)
upperci <- sii + se.formula * qnorm(cilevel)
}
# Return data frame
return(data.frame(measure = "sii",
estimate = sii * scale,
se = se.formula * scale,
lowerci = lowerci * scale,
upperci = upperci * scale)
)
}
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