R/M_inf_sigc.R

In ra4bayesmeta: Reference Analysis for Bayesian Meta-Analysis

M_inf_sigc <- function(rlmc, df, alpha=0.5, truncation=5*10^6){
  # inputs:
  # rlmc: target RLMC value
  # df: data frame in bayesmeta format
  # alpha: quantile of the SGC distribution to use as reference threshold U_ref
  # truncation: upper bound for the parameter value to aviod numberical problems
  # output:
  # parameter m of the SGC distribution with C=sigma_ref^{-2}
  sigma.ref <- sigma_ref(df)
  log.quot <- -6*log(sigma.ref) + 2*log(1-rlmc) -2*log(rlmc) 
  # return(1- log(alpha)/log(1+exp(log.quot)))
  log.res <- log(-log(1-alpha)) - log(log(1+exp(log.quot)))
  res <- 1 + exp(log.res)
  return(min(res, truncation))
}