RE: BOV

From: "Nick Holford" n.holford@auckland.ac.nz Subject: RE: [NMusers] BOV Date: Mon, September 20, 2004 7:11 pm Renee, Renee Ying Hong wrote: > > Dear all, > > Say, the basic structural PK model is > > Pi = TVP * EXP(ETAi) ; P is PK parameters > CV% of P can be calculated as SQRT (ETAi). > The coefficient of variation of P is only approximately SQRT(OMEGA) when you define Pi = TVP * EXP(ETAi). The exact value is SQRT[exp(OMEGA) - 1]. It is helpful to recognize that exp(x) is approximately 1+x (when x is small) which is why CV is approximately SQRT(OMEGA). You also need to multiply by 100 to get CV%. Please also note that ETA is a random variable while OMEGA is the variance of ETA. > We know that: PPV = BSV + WSV ; PPV is the population parameter variability > WSV can be approximated by BOV, therefore, > > Pi = TVP * EXP(BSV+BOV) = TVP * EXP(ETAi + ETA1 * OCC1 + ETA2 * OCC2 > +......+ ETAn * OCCn) > > My question is how to calculate CV% of BSA and BOV after incoporating BOV > into the PK parameter variability? I am guessing you want to calculate PPV when you ask for 'CV% of BSA and BOV' and I assume you mean BSV (not BSA). This can be done like this: PPV = SQRT(BSV*BSV + BOV*BOV) The exact CV% of PPV is SQRT(exp(PPV*PPV)-1)*100 where BSV=SQRT(OMEGAi) and BOV=SQRT(OMEGA1) (using your ETA numbering in the expression for Pi). Most commonly BOV is estimated using the OMEGA BLOCK(1) SAME construction so that OMEGA1, OMEGA2, OMEGAn will all have the same estimate. 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/