RE: BOV

From:"Nick Holford" n.holford@auckland.ac.nz Subject: RE: [NMusers] BOV Date: Tue, September 21, 2004 3:09 pm Pravin, You say "I have made a basic mistake in my derivation". It is not clear to me which part of your previous response contains a mistake. It seems to me that there are 2 issues involved: 1. Estimation of CV by sqrt(omega) I had commented to Renee that this is only an approximate CV and gave a formula for an 'exact' CV that would be true if ETA was normally distributed (and thus P would be log normally distributed). Stuart Beal wrote about this issue some years ago http://gaps.cpb.ouhsc.edu/nm/91sep2697.html His view is that either method (CV=SQRT(OMEGA) or CV=SQRT(EXP(OMEGA)-1) should not be trusted when using NONMEM parameter estimates: "it does not follow that the "extra accuracy" given by the lognormal formula really represents extra accuracy; it can just as well be garbage" His recommendation was 'we should probably avoid reporting the CV as a "CV", but report it as an "apparent CV"'. You described a derivation of the CV from OMEGA given the random effects model P=Ppop*EXP(ETA). Included in your remarks was a comment that NONMEM approximates EXP(ETA) with 1+ETA. You went on to conclude that the CV can be calculated from SQRT(OMEGA). Are you saying that because of the first order approximation made by NONMEM when computing the likelihood that this means that CV is exactly SQRT(OMEGA) even with this random effects model P=Ppop*EXP(ETA)? 2. Calculation of PPV from estimates of BSV and BOV In your original posting you concluded the following which looks OK except for a typo (either remove the % or add *100 to rhe right hand side): > > %CVCL = Sqrt[Var(ETA(1)) + ..+ Var(ETA(n))] You then clarified this in your latest contribution. This looks OK to me. > Given Occasion 1: %CV of Pi = SQRT(BSV*BSV + BOV(1)*BOV(1))*100 > Given Occasion 2: %CV of Pi = SQRT(BSV*BSV + BOV(2)*BOV(2))*100 > .... > Given Occasion n: %CV of Pi = SQRT(BSV*BSV + BOV(n)*BOV(n))*100 So where is your 'basic mistake'? Nick -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556 http://www.health.auckland.ac.nz/pharmacology/staff/nholford/