R/ImputeSMDVariance.R

In SAMURAI: Sensitivity Analysis of a Meta-analysis with Unpublished but Registered Analytical Investigations

ImputeSMDVariance <-
function(table
                              # , matchedgroups=FALSE
                         ){
  # Imputes the variance of the standardized mean difference (SMD) of unpublished studies,
  # depending on the SMD and the sample sizes of those studies. 
  # 
  # Args: 
  #   table:  A data set with the following information: 
  #             sample sizes for both arms 
  #             SMD's (Hedges' g, which is a sample estimate of the SMD)
  #
  # Returns:  The same data set with imputed variance of Hedges' g of unpublished studies.
  #           It estimates variance of Hedge's g using a "very good" approximation by Borenstein. 
  #
  # Reference: 
  #   Michael Borenstein, "Effect Sizes for Continuous Data", page 226,
  #   Chapter 12 in Cooper, Hedges, and Valentine, Handbook of Research Synthesis and Meta-analysis
  
  ## testing
  #   table <- table4
  
  table$flagmissing <- as.numeric(is.na(table$vi))
  
  n1 <- table$ctrl.n
  n2 <- table$expt.n
  
  df <- n1+n2-2
  j <- 1 - 3/(4*df-1)  # correction factor between Cohen's d and Hedge's g
  
  ## convert to Cohen's d
  hedgesg <- table$yi
  cohensd <- hedgesg/j
  ## find variance of Cohen's d; convert to variance of Hedges' g
  cohensd.v <- (n1+n2)/(n1*n2) + cohensd^2/(2*(n1+n2))
  table$hedgesg.v <- j^2 * cohensd.v
  ##
  table[table$flagmissing==1,]$vi <- table[table$flagmissing==1,]$hedgesg.v  
  ## drop columns
  table$flagmissing <- NULL
  table$hedgesg.v <- NULL
  return(table)
}