RE: BOV

From: "Pravin" jadhavpr@mail1.vcu.edu Subject: RE: [NMusers] BOV Date: Mon, September 20, 2004 8:29 pm Hi Renne, %CVCL = Sqrt[Var(ETA(1)) + ..+ Var(ETA(n))]*100 is the short answer to your question. [Add the variance of ETAs and take the square root] The long answer is provided below.I hope it makes sense. I am giving a shot at explaining this. We know that Expectation of a constant is that constant itself and the variance is zero. Meaning, E(a) = a and Var(a) = 0, where a is a constant. Now, a+bx or our case, CL=TVCL+TVCL*ETA(1) please note that NONMEM approximates CL=TVCL* EXP(ETA(1)) to that form. So we have, E(a+bx) = a+ b * mux and Var(a+bx) = 0+Var(bx) = b**2 * Var(x) Thus, E(CL)= TVCL and Var(CL)= TVCL**2 * Var(ETA(1)) Taking square root on both sides and rearranging, StdevCL / TVCL = Stdev(ETA(1)) %CVCL = Stdev(ETA(1))*100, where Stdev means standard deviation. Now the case you mentioned-- for simplicity I have only two random effects on clearance. CL = TVCL + TVCL * ETA(1) + TVCL * ETA (2) From the above logic, Var (CL) = TVCL**2 * Var(ETA(1)) + TVCL**2 * Var(ETA(2)) Rearranging, StdevCL/TVCL = sqrt[Var(ETA(1)) + Var(ETA(2))] %CVCL = Sqrt[Var(ETA(1)) + Var(ETA(2))]*100 Thus for n random effects on a parameter that can be explained with exponential or proportional error model, %CVCL = Sqrt[Var(ETA(1)) + ..+ Var(ETA(n))] So note that Stdev(ETA(p)) *100 = %CVP is valid only if exponential or proportional model is used in NONMEM. P is a single fixed effects parameter having random effects. When additive model is used %CV can be calculated as usual: %CVP= Stdev(ETA (p))*100/TVP Thanks to Dr. Atul Bhattaram for explaining this concept to me on the very first day I was exposed to error models in NONMEM. Thanks Pravin Pravin Jadhav Graduate student Department of pharmaceutics MCV/VCU