IIV on %CV-Scale - Standard Error (SE)

Hi all, I think that Paul stumbled on a rather important issue. The SE of the residual error may not be of primary interest, but the same as discussed under this thread also applies to the standard error of omega. (I changed the name of the subject since this thread now is about omega) I prefer to report IIV on the %CV scale, i.e. sqrt(OMEGAnn) for a parameter with log-normal distribution. It then makes no sense to report the standard error on any other scale. For log-normally distributed parameters the relative SE of IIV then becomes: sqrt(SE.OMEGAnn)/(2*sqrt(OMEGAnn))*100% Notice the factor 2 in the denominator. I got this from Mats Karlsson who picked it up from France Mentré, but I have never seen the actual mathematical derivation for this formula. I think this is what Varun is doing in his e-mail a few hours ago. However, I am not sure; being illiterate I could not understand the derivation. Either way, if we are satisfied with the approximation of IIV as the square root of omega, the factor 2 in the approximation of the SE on the %CV-scale is exact enough. If you would like to convince yourself of that the factor 2 is correct (up to 3 significant digits), you can load the below Splus function and then run with different CV:s, e.g: ratio(IIV=1) ratio(IIV=0.5) Regards Jakob "ratio" <- function (IIV.stdev=1) { ncol <- 1000 #1000 Studies, in which IIV is estimated ETAS <- rnorm(n=1000*ncol, 0, IIV.stdev) ETA <- matrix(data=ETAS, ncol=ncol) IIVs.stds<- colStdevs(ETA) #Estimate of IIV on sd-scale IIVs.vars<- colVars(ETA) #Estimate of IIV on var-scale SE.std <- stdev(IIVs.stds)/sqrt(ncol) SE.var <- stdev(IIVs.vars)/sqrt(ncol) CV.std <- SE.std/IIV.stdev CV.var <- SE.var/(IIV.stdev^2) print(paste("SE on Var scale:", SE.var)) print(paste("SE on Std scale:", SE.std)) print(paste("Ratio CV var, CV std:", CV.var/CV.std)) invisible() }