R/tau2h-hm.r

In nshi-stat/pimeta: Prediction Intervals for Random-Effects Meta-Analysis

# Hartung--Makambi estimator for \eqn{\tau^2}
# 
# Returns the Hartung--Makambi estimator
# for \eqn{\tau^2} (Hartung & Makambi, 1983).
# 
# @name tau2h_hm
# @rdname tau2h_hm
# @param y the effect size estimates vector
# @param se the within studies standard errors vector
# @return
# \itemize{
# \item \code{tau2h}: the estimate for \eqn{\tau^2}.
# }
# @references
# Hartung, J., and Makambi, K. H. (2003).
# Reducing the number of unjustified significant results
# in meta-analysis.
# \emph{Commun Stat Simul Comput.}
# \strong{32}(4): 1179-1190.
# @examples
# data(sbp, package = "pimeta")
# pimeta::tau2h_hm(sbp$y, sbp$sigmak)
# @export
tau2h_hm <- function(y, se) {

  k <- length(y)
  vi <- se^-2
  qhm <- sum(vi*(y - sum(y*vi)/sum(vi))^2)
  tau2h <- max(0.0, qhm^2/((sum(vi) - sum(vi^2)/sum(vi))*(2.0*(k - 1.0) + qhm)))
  
  return(list(tau2h = tau2h))
  
}