From: nplock@zedat.fu-berlin.de Subject: [NMusers] restraining eta code Date: Tue, 28 Mar 2006 11:46:57 +0200 (CEST) Dear all, I have a question regarding a model which restrains all individual parameter estimates to take values between 0 and 1. I´m using the following code: PHI=LOG(THETA(7)/(1-THETA(7))) P=EXP(PHI+ETA(4))/(1+EXP(PHI+ETA(4))) My question is: How do I calculate the coefficient of variation for THETA(7), if for example NONMEM gives a value of 0.7 for THETA(7) and and a value of 6.4 for the respective diagonal element of the omega matrix? It was called to my attention that in this case you cannot just take the square root of diagonal element? I would really appreciate your help! Nele _______________________________________________________ From: Leonid Gibiansky leonidg@metrumrg.com Subject: Re: [NMusers] restraining eta code Date: Tue, 28 Mar 2006 08:23:21 -0500 Nele, The best way to see what is going on is simulations (e.g., using R or S+). If you run this code: THETA7 = 0.7 ETA4 = rnorm(100000,mean=0,sd=sqrt(6.4)) PHI=log(THETA7/(1-THETA7)) P=exp(PHI+ETA4)/(1+exp(PHI+ETA4)) hist(P) p95CI = quantile(P,probs=c(0.025,0.975)) you will see that the distribution for P is not normal (at all!), and 95% confidence intervals are essentially from 0 to 1: 2.5% 97.5% 0.01641659 0.99714220 Leonid _______________________________________________________ From: nplock@zedat.fu-berlin.de Subject: Re: [NMusers] restraining eta code Date: Tue, 28 Mar 2006 15:24:00 +0200 (CEST) Dear Leonid, thanks a lot! What about the coefficient of variation? If I calculate it back from the obtained confidence intervals (THETA7-(97.5%quantile)/2) I would end up with values between 21 and 28%. So could one say that the coefficient of variation is approx. 25%, for example? Nele _______________________________________________________ From: "Mats Karlsson" mats.karlsson@farmbio.uu.se Subject: RE: [NMusers] restraining eta code Date: Tue, 28 Mar 2006 15:25:05 +0200 Hi Nele, The CV is approximately OMEGA(ETA(4))*THETA(7)*(1-THETA(7)). Where OMEGA is SD (not variance). Best regards, Mats -- Mats Karlsson, PhD Professor of Pharmacometrics Div. of Pharmacokinetics and Drug Therapy Dept. of Pharmaceutical Biosciences Faculty of Pharmacy Uppsala University Box 591 SE-751 24 Uppsala Sweden phone +46 18 471 4105 fax +46 18 471 4003 mats.karlsson@farmbio.uu.se _______________________________________________________ From: Leonid Gibiansky leonidg@metrumrg.com Subject: Re: [NMusers] restraining eta code Date: Tue, 28 Mar 2006 08:37:35 -0500 Nele, I do not think it is appropriate to describe the P distribution in terms of sd, cv etc. :just look on the histogram, that is U-shaped with the peaks at near 0 and 1. Individual P can be anywhere between 0 and 1 (and they are more likely be near 0 or 1 than in the intermediate points). If you need to report variability, use confidence intervals and mentions that probability cannot be described in terms of the normal-distribution terminology Leonid _______________________________________________________ From: "Mats Karlsson" mats.karlsson@farmbio.uu.se Subject: RE: [NMusers] restraining eta code Date: Tue, 28 Mar 2006 16:09:10 +0200 Nele, I didn't look at the size of your SD. When it is that large I totally agree with Leonid, that CV is not a useful descriptor of variability. Note also that whenever the typical value is close to 0 or 1, the distribution will be very skewed. Finally, a correction, it is the SD(P) that is approximately OMEGA(ETA(4))*THETA(7)*(1-THETA(7)). Best regards, Mats -- Mats Karlsson, PhD Professor of Pharmacometrics Div. of Pharmacokinetics and Drug Therapy Dept. of Pharmaceutical Biosciences Faculty of Pharmacy Uppsala University Box 591 SE-751 24 Uppsala Sweden phone +46 18 471 4105 fax +46 18 471 4003 mats.karlsson@farmbio.uu.se _______________________________________________________