Box-Cox tranformation

Dear All, Could statisticians out there help me to understand the use of the Box-Cox transformation? I found the old discussion here: http://www.cognigencorp.com/nonmem/current/2010-June/1721.html Specifically: Box-Cox transformation TVCL=THETA(1) BXPAR=THETA(2) PHI = EXP(ETA(1)) ETATR = (PHI**BXPAR-1)/BXPAR CL=TVCL*EXP(ETATR) I think the idea is to use transformation in cases when true CL is not log-normal. However, here is what we do here 1: use normally distributed ETAs to create log-normal PHI 2: use Box-Cox to create ETATR (and the idea of Box-Cox is to make normal out of something that is not normal) 3: Use ETATR (that is normal? at least that is what Box-Cox is supposed to do) to create CL. If it is working (and I suppose it is working as otherwise it would not be used), it is working because exp() + Box-Cox create something not-normal out of normal ETA(1). But this is not an intended use of this transformation. Would it be better to use the following: 1: Use normally-distributed logCLbc=THETA(1)+ETA(1) 2: Use inverse Box-Cox to get something not normal: logCL=(1+lambda*logCLbc)**(1/lambda) (we need to make sure that logCLbc is positive, so we may shift it as needed) 3: return back to CL scale CL=EXP(logCL) This version also has an advantage of being easily MU-referenced (that is required for the application of the IMP/SAEM/etc. estimation methods) Have anybody tried this second version and compared it with the first one? Thanks! Leonid -------------------------------------- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel: (301) 767 5566