R/Newcombe_hybrid_score_CI_2x2.R

In ocbe-uio/contingencytables: Statistical Analysis of Contingency Tables

#' @title The Newcombe hybrid score confidence interval for the difference between probabilities
#' @description The Newcombe hybrid score confidence interval for the difference between probabilities
#' @description Described in Chapter 4 "The 2x2 Table"
#' @param n the observed counts (a 2x2 matrix)
#' @param alpha the nominal level, e.g. 0.05 for 95% CIs
#' @examples
#' # An RCT of high vs standard dose of epinephrine (Perondi et al., 2004)
#' Newcombe_hybrid_score_CI_2x2(perondi_2004)
#'
#' # The association between CHRNA4 genotype and XFS (Ritland et al., 2007)
#' Newcombe_hybrid_score_CI_2x2(ritland_2007)
#'
#' @export
#' @return An object of the [contingencytables_result] class,
#' basically a subclass of [base::list()]. Use the [utils::str()] function
#' to see the specific elements returned.
Newcombe_hybrid_score_CI_2x2 <- function(n, alpha = 0.05) {
  validateArguments(mget(ls()))

  n1p <- n[1, 1] + n[1, 2]
  n2p <- n[2, 1] + n[2, 2]

  # Estimates of the two probabilities of success
  pi1hat <- n[1, 1] / n1p
  pi2hat <- n[2, 1] / n2p

  # Estimate of the difference between probabilities (deltahat)
  estimate <- pi1hat - pi2hat

  # Use Wilson score CIs for the two probabilities of success
  res1 <- Wilson_score_CI_1x2(n[1, 1], n1p, alpha)
  res2 <- Wilson_score_CI_1x2(n[2, 1], n2p, alpha)
  L <- estimate - sqrt((pi1hat - res1[["lower"]])^2 + (res2[["upper"]] - pi2hat)^2)
  U <- estimate + sqrt((pi2hat - res2[["lower"]])^2 + (res1[["upper"]] - pi1hat)^2)

  # Fix overshoot by truncation
  L <- max(-1, L)
  U <- min(U, 1)

  return(
    contingencytables_result(
      list("lower" = L, "upper" = U, "estimate" = estimate),
      sprintf(
        "The Newcombe hybrid score CI: estimate = %6.4f (%g%% CI %6.4f to %6.4f)",
        estimate, 100 * (1 - alpha), L, U
      )
    )
  )
}