R/d.R

In healthequal: Compute Summary Measures of Health Inequality

#'  Difference (D)
#'
#'  The difference (D) is an absolute measure of inequality that shows the
#'  difference in an indicator between two population subgroups. For more
#'  information on this inequality measure see Schlotheuber (2022) below.
#'
#'  D is calculated as `D = 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:** Greater absolute values indicate higher levels of
#'  inequality. D is 0 if there is no inequality.
#'
#'  **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.
#'
#' @param est The subgroup estimate. Estimates must be available for the two
#' subgroups being compared.
#' @param se The standard error of the subgroup estimate. If this is missing,
#' confidence intervals of D cannot be calculated.
#' @param 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).
#' @param 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).
#' @param subgroup_order The order of subgroups in an increasing sequence.
#' Required if the dimension is ordered (ordered_dimension=1).
#' @param reference_subgroup Identifies a reference subgroup with the value of
#' 1, if the dimension is non-ordered or binary.
#' @param conf.level Confidence level of the interval. Default is 0.95 (95%).
#' @param ... Further arguments passed to or from other methods.
#' @examples
#' # example code
#' data(NonorderedSample)
#' head(NonorderedSample)
#' with(NonorderedSample,
#'      d(est = estimate,
#'        se = se,
#'        favourable_indicator = favourable_indicator,
#'        ordered_dimension = ordered_dimension,
#'        reference_subgroup = reference_subgroup))
#' @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.
#' @references 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.
#' @return The estimated D value, corresponding estimated standard error,
#' and confidence interval as a `data.frame`.
#' @export
#'
d <- function(est,
              se = NULL,
              favourable_indicator,
              ordered_dimension,
              subgroup_order = NULL,
              reference_subgroup = NULL,
              conf.level = 0.95,
              ...) {

  # Variable checks
  ## Stop
  if (all(is.na(est))) {
    stop('Estimates are missing for all subgroups')
  }
  if (!is.null(est)) {
    if (!is.numeric(est))
      stop('Estimates need to be numeric')
  }
  if (!all(favourable_indicator %in% c(0,1))) {
    stop('Favourable indicator variable must contain 0 or 1')
  }
  if (length(unique(favourable_indicator)) != 1) {
    stop('Favourable indicator variable must be consistent across subgroups,
         for the same indicator')
  }
  if (!all(ordered_dimension %in% c(0,1))) {
    stop('Ordered dimension variable must contain 0 or 1')
  }
  if (length(unique(ordered_dimension)) != 1) {
    stop('Ordered dimension variable must be consistent across subgroups,
         for the same indicator')
  }
  if (!is.null(se)) {
    if (!is.numeric(se))
      stop('Standard errors need to be numeric')
  }
  if (!is.null(ordered_dimension) & any(ordered_dimension != 0)) {
    if (is.null(subgroup_order)) {
      stop('Subgroup order variable needs to be declared')
    }
    sorted_order <- sort(subgroup_order)
    if (any(diff(sorted_order) != 1) || any(sorted_order %% 1 != 0)) {
      stop('Subgroup order variable must contain integers in increasing order')
    }
  }
  if (!is.null(reference_subgroup)) {
    if (sum(reference_subgroup) > 1) {
      stop('Reference subgroup variable must identify one reference subgroup
         with the value 1')
    }
  }
  ## 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')
  }

  # Identify reference estimates for y1 and y2
  y1_ref <- rep(0, length(est))
  y2_ref <- rep(0, length(est))

  if (sum(ordered_dimension, na.rm = TRUE) != 0) {
    ## Ordered dimension
    y1_ref[((subgroup_order == min(subgroup_order, na.rm = TRUE) &
               favourable_indicator[1] == 0) |
              (subgroup_order == max(subgroup_order, na.rm = TRUE) &
                 favourable_indicator[1] == 1))] <- 1
    y2_ref[((subgroup_order == max(subgroup_order, na.rm = TRUE) &
               favourable_indicator[1] == 0) |
              (subgroup_order == min(subgroup_order, na.rm = TRUE) &
                 favourable_indicator[1] == 1))] <- 1
  }

  if (sum(ordered_dimension, na.rm = TRUE) == 0) {
    ## Non-ordered dimension
    if (sum(reference_subgroup, na.rm = TRUE) == 0) {
      ### No reference subgroup
      y1_ref[which(est ==  max(est, na.rm = TRUE))[1]] <- 1
      y2_ref[which(est ==  min(est, na.rm = TRUE))[1]] <- 1
    } else {
      ### Reference subgroup
      y1_ref[((reference_subgroup == 1 & favourable_indicator[1] == 1) |
                (reference_subgroup != 1 & favourable_indicator[1] == 0 &
                   est ==  max(est[reference_subgroup != 1], na.rm = TRUE)))] <- 1
      y2_ref[((reference_subgroup == 1 & favourable_indicator[1] == 0) |
                (reference_subgroup != 1 & favourable_indicator[1] == 1 &
                   est ==  min(est[reference_subgroup != 1], na.rm = TRUE)))] <- 1
    }
  }

  # Calculate summary measure
  y1 <- est[y1_ref == 1 & !is.na(y1_ref)]
  y2 <- est[y2_ref == 1 & !is.na(y2_ref)]
  y1_se <- se[y1_ref == 1 & !is.na(y1_ref)]
  y2_se <- se[y2_ref == 1 & !is.na(y2_ref)]

  d <- y1 - y2

  # Calculate 95% confidence intervals
  d_se <- NA
  lowerci <- NA
  upperci <- NA
  cilevel <- 1 - ((1 - conf.level) / 2)

  if (sum(is.na(se) == 0)) {
    d_se <- sqrt(y1_se^2 + y2_se^2)
    lowerci <- d - d_se * qnorm(cilevel)
    upperci <- d + d_se * qnorm(cilevel)
  }

  # Return data frame
  return(data.frame(measure = "d",
                    estimate = d,
                    se = d_se,
                    lowerci = lowerci,
                    upperci = upperci))
}