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#' Mean difference from the best-performing subgroup (weighted) (MDBW)
#'
#' The Mean Difference from the Best-Performing Subgroup (MDB) is an absolute
#' measure of inequality that shows the mean difference between each population
#' subgroup and the subgroup with the best estimate. For the weighted version
#' (MDBW), subgroups are weighted according to their population share.
#'
#' The weighted version (MDBW) is calculated as the weighted average of
#' absolute differences between the subgroup estimates and the estimate for the
#' best-performing subgroup, divided by the number of subgroups. For more
#' information on this inequality measure see Schlotheuber, A., &
#' Hosseinpoor, A. R. (2022) below.
#'
#' 95% confidence intervals are calculated using a methodology of simulated
#' estimates. The dataset is simulated a large number of times (e.g., 100)
#' and MDBW is calculated for each of the simulated samples. The 95%
#' confidence intervals are based on the 2.5th and 97.5th percentiles of the
#' MDBW results.
#'
#' **Interpretation:** MDBW only has positive values, with larger values
#' indicating higher levels of inequality. MDBW is zero if there is no
#' inequality.
#'
#' **Type of summary measure:** Complex; absolute; weighted
#'
#' **Applicability:** Non-ordered; more than two subgroups
#'
#' @param pop The number of people within each subgroup.
#' Population size must be available for all subgroups.
#' @param est The subgroup estimate.
#' Estimates must be available for all subgroups.
#' @param se The standard error of the subgroup estimate.
#' If this is missing, 95% confidence intervals of MDBW cannot be calculated.
#' @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 favourable_indicator Records whether the indicator is
#' favourable (1) or non-favourable (0). Favourable indicators measure
#' desirable health events where the ultimate goal is
#' to achieve a maximum level (such as skilled birth attendance).
#' Non-favourable indicators measure undesirable health events where
#' the ultimate goal is to achieve a minimum level (such as under-five
#' mortality rate).
#' @param sim The number of simulations to estimate 95% confidence intervals
#' @param seed The random number generator (RNG) state for the 95% confidence
#' interval simulation
#' @param ... Further arguments passed to or from other methods.
#' @examples
#' # example code
#' data(NonorderedSample)
#' head(NonorderedSample)
#' with(NonorderedSample,
#' mdbw(pop = population,
#' est = estimate,
#' se,
#' scaleval = indicator_scale,
#' favourable_indicator
#' )
#' )
#' @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 MDBW value, corresponding estimated standard error,
#' and confidence interval as a `data.frame`.
#' @importFrom dplyr %>% rowwise mutate ungroup
#' @export
#'
mdbw <- function(pop,
est,
se = NULL,
favourable_indicator,
scaleval,
sim = NULL,
seed = 123456,...){
# Variable checks
## Stop
if(anyNA(est) & sum(is.na(est))/length(est)>.15){
stop('Estimates are missing in more than 15% of subgroups')
}
if(anyNA(est)){
pop <- pop[!is.na(est)]
if(!is.null(se)) se <- se[!is.na(est)]
if(!is.null(scaleval)) scaleval <- scaleval[!is.na(est)]
est <- est[!is.na(est)]
}
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(length(unique(favourable_indicator))!=1){
stop('Favourable indicator not unique across subgroups')
}
## Warning
if(any(is.na(se)) | is.null(se))
warning("Standard errors are missing in all or some subgroups, confidence
intervals will not be computed.")
# Calculate summary measure
ref_est <- ifelse(favourable_indicator == 1, max(est), min(est))
popsh <- pop/sum(pop)
mdbw <- sum(popsh * abs(est - ref_est))
# Calculate 95% confidence intervals
se.formula <- NA
boot.lcl2 <- NA
boot.ucl2 <- NA
mdbw_sim <- c()
if(!any(is.na(se)) & !is.null(se)) {
if(is.null(sim)){
sim <- 100
}
input_data <- data.frame(est,
se,
popsh,
scaleval,
favourable_indicator)
set.seed(seed)
for (j in 1:sim) {
# Simulate each estimate in the dataset
simulated_data <- input_data %>%
rowwise() %>%
mutate(simulation =
{result <- if (scaleval != 100) {
repeat {
result <- rnorm(1, mean = est, sd = se)
if (result > 0) break
}
result
} else {
repeat {
result <- rnorm(1, mean = est, sd = se)
if (result >= 0 & result <= 100) break
}
result
}
}) %>%
ungroup()
simulated_data <- simulated_data %>%
mutate(ref_estimate_sim =
ifelse(favourable_indicator == 1,
max(simulated_data$simulation),
min(simulated_data$simulation)))
# Calculate summary measure using simulated estimates
mdbw_sim[j] <- with(
simulated_data, (sum(popsh * abs(simulation - ref_estimate_sim))))
}
boot.lcl <- quantile(mdbw_sim, probs = c(0.025), na.rm = TRUE)
boot.ucl <- quantile(mdbw_sim, probs = c(0.975), na.rm = TRUE)
}
# Return data frame
return(data.frame(measure = "mdbw",
estimate = mdbw,
lowerci = boot.lcl,
upperci = boot.ucl)
)
}
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