R/propdiff_ac.R

In miceafter: Data and Statistical Analyses after Multiple Imputation

#' Calculates the difference between proportions and standard error
#'  according to method Agresti-Caffo
#'
#' \code{propdiff_ac} Calculates the difference between proportions
#'  and standard error according to method Agresti-Caffo.
#'
#' @param y 0-1 binary response variable.
#' @param x 0-1 binary independent variable.
#' @param formula A formula object to specify the model as normally used by glm.
#' @param data An objects of class \code{milist}, created by
#'  \code{df2milist}, \code{list2milist} or \code{mids2milist}.
#'
#' @details As output the differences between proportions according to
#'  Agresti-Caffo and Wald are provided. The Agresti-Caffo difference is
#'  used in the function \code{pool_propdiff_ac} to derive the Agresti-Caffo
#'  confidence intervals. For the pooled difference between proportions
#'  the difference between proportions according to Wald are used.
#'
#' @return The difference between proportions according Agresti-Caffo,
#'  to calculate the confidence intervals, the standard error
#'  according to Agresti-Caffo, the complete data degrees of freedom
#'  (dfcom) as n-1 and the difference between proportions according to Wald.
#'
#' @references Agresti, A. and Caffo, B. Simple and Effective Confidence
#'  Intervals for Proportions and Differences of Proportions Result from
#'  Adding Two Successes and Two Failures. The American Statistician.
#'  2000;54:280-288.
#' @references Fagerland MW, Lydersen S, Laake P. Recommended confidence
#'  intervals for two independent binomial proportions. Stat Methods Med Res.
#'  2015 Apr;24(2):224-54.
#'
#' @author Martijn Heymans, 2021
#'
#' @seealso \code{\link{with.milist}}, \code{\link{pool_propdiff_ac}}
#'
#' @examples
#'
#' imp_dat <- df2milist(lbpmilr, impvar="Impnr")
#' ra <- with(imp_dat, expr=propdiff_ac(Chronic ~ Radiation))
#'
#' # same as
#' ra <- with(imp_dat, expr=propdiff_ac(y=Chronic, x=Radiation))
#'
#' @export
propdiff_ac <- function(y,
                        x,
                        formula,
                        data){

  call <- match.call()

  names_var <-
    all.vars(call, functions = FALSE)
  if(length(names_var) > 2)
    stop("Include only one independent variable in x or formula")

  if(!inherits(y,"formula")){
    eval_prop <-
      eval(call[[1L]], parent.frame())
    X <-
      data.frame(y, x)
  } else {
    call <-
      eval(call[[2L]], parent.frame())
    X <-
      model.frame(call)
    colnames(X) <-
      c('y', 'x')
  }
  if(!all(X$x==1 | X$x==0))
    stop("x variable should be a 0 - 1 variable")
  if(!all(X$y==1 | X$y==0))
    stop("y variable should be a 0 - 1 variable")

  sub1 <-
    subset(X, x==1)
  sub0 <-
    subset(X, x==0)

  n1 <-
    nrow(sub1)
  n0 <-
    nrow(sub0)

  x1 <-
    nrow(subset(sub1, y==1))
  x0 <-
    nrow(subset(sub0, y==1))

  dfcom <-
    (n0+n1)-1

  # Wald
  p0hat <-
    x0/n0
  p1hat <-
    x1/n1
  phat_diff <-
    p1hat - p0hat

  # Agresti-Caffo
  p0hat_ac <-
    (x0 + 1)/(n0 + 2)
  p1hat_ac <-
    (x1 + 1)/(n1 + 2)

  phat_diff_ac <-
    p1hat_ac - p0hat_ac
  se_phat_diff_ac <-
    sqrt((p0hat_ac * (1 - p0hat_ac)/(n0 + 2)) + (p1hat_ac * (1 - p1hat_ac)/(n1 + 2)))
  output <-
    matrix(c(phat_diff_ac, se_phat_diff_ac, dfcom, phat_diff), 1, 4)
  colnames(output) <-
    c("Prop diff AC", "SE", "dfcom", "Prop diff Wald")
  return(output)
}