R/Katz_log_CI_2x2.R

In contingencytables: Statistical Analysis of Contingency Tables

#' @title The Katz log confidence interval for the ratio of probabilities
#' @description The Katz log 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
#' Katz_log_CI_2x2(perondi_2004)
#' Katz_log_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.
Katz_log_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 ratio of probabilities (phihat)
  estimate <- pi1hat / pi2hat

  # Standard error of log(estimate)
  SE <- sqrt(1 / n[1, 1] + 1 / n[2, 1] - 1 / n1p - 1 / n2p)

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

  # Calculate the confidence limits
  L <- exp(log(estimate) - z * SE)
  U <- exp(log(estimate) + z * SE)

  # Uncomputable limits -> uninformative interval
  if (n[1, 1] == 0 || n[2, 1] == 0) {
    L <- 0
    U <- Inf
  }

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