R/tau2h-sj.r

In pimeta: Prediction Intervals for Random-Effects Meta-Analysis

# Sidik--Jonkman estimator for \eqn{\tau^2}
# 
# Returns the Sidik--Jonkman estimator
# for \eqn{\tau^2} (Sidik & Jonkman, 2005).
# 
# @name tau2h_sj
# @rdname tau2h_sj
# @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
# Sidik, K., and Jonkman, J. N. (2005).
# Simple heterogeneity variance estimation for meta-analysis.
# \emph{J R Stat Soc Ser C Appl Stat.}
# \strong{54}(2): 367-384. 
# @examples
# data(sbp, package = "pimeta")
# pimeta::tau2h_sj(sbp$y, sbp$sigmak)
# @export
tau2h_sj <- function(y, se) {

  k <- length(y)
  tau2h0 <- sum((y - sum(y)/k)^2)/k
  w <- (1.0 + se^2/tau2h0)^-1
  tau2h <- max(0.0, sum(w*(y - sum(y*w)/sum(w)))/(k - 1.0))
  
  return(list(tau2h = tau2h))
  
}