R/Inv_sinh_CI_ratio_2x2.R

In contingencytables: Statistical Analysis of Contingency Tables

#' @title The inverse hyperbolic sine confidence interval for the ratio of probabilities
#' @description The inverse hyperbolic sine confidence interval for the ratio of 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
#' Inv_sinh_CI_ratio_2x2(perondi_2004)
#' Inv_sinh_CI_ratio_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.
Inv_sinh_CI_ratio_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 ratio of probabilities (phihat)
  estimate <- pi1hat / pi2hat

  # The upper alpha / 2 percentile of the standard normal distribution
  z <- qnorm(1 - alpha / 2, 0, 1)

  # Calculate the confidence limits
  tmp <- asinh(0.5 * z * sqrt(1 / n[1, 1] + 1 / n[2, 1] - 1 / n1p - 1 / n2p))
  L <- exp(log(estimate) - 2 * tmp)
  U <- exp(log(estimate) + 2 * tmp)

  # Fix zero cell cases
  if (n[1, 1] == 0) {
    U <- ((z^2) / n1p) / (n[2, 1] / n2p)
  }
  if (n[2, 1] == 0) {
    L <- (n[1, 1] / n1p) / ((z^2) / n2p)
  }

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