Re: Epsilon shrinkage and IWRES

On 22 sep 2011, at 17:14, "Rik Schoemaker" <[email protected]> wrote: > Dear Leonid, > > Thank you! > > I do believe this means that the simple representation in the manual is not > covering this ingenious construct, and although theoretically they might be > the same (who am I to judge? :-) ) it might explain why I get different > numbers when I calculate it myself... > > Kind regards, > > Rik > > -----Original Message----- > From: Leonid Gibiansky [mailto:[email protected]] > Sent: 22 September 2011 4:36 PM > To: Rik Schoemaker > Cc: 'nmusers'; Bauer, Robert > Subject: Re: [NMusers] Epsilon shrinkage and IWRES > > I spare Bob Bauer from the need to re-type the answer since we discussed it > at some point, and he provided the following info (see below). The following > error model was discussed: > > Y=IPRED(1+EPS1)+EPS2 > that is equivalent to > Y=IPRED + W*EPS(1) > where > > W=SQRT(sigma1^2+sigma2^2*IPRED^2) > > where sigma 1 and sigma 2 are some parameters and variance of EPS1 is 1 > > ;;;;;;;;;;;;;;;;;;;;;; > For each data point i, > > Wi=SQRT(sigma1^2+sigma2^2*IPREDi^2) > > Each Wi from each data point is used in assessing sigma1 and sigma2. As > long as IPREDi is non-zero for every data point, then every Wi is used in > assessing both sigma1 and sigma2 in the optimization process. > However, when IPREDi=0, then that particular Wi is > > Wi=SQRT(sigma1^2) > > Which contributes to evaluation of sigma1, but does not contribute to > sigma2. How does the EPSshrink algorithm figure this out? By in fact using > the H gradient that NONMEM provides, which NONMEM uses to estimate > sigma1 and sigma2. The actual residual variance is in matrix form evaluated > as > > H'SigmaH > > Here H is the partial derivative of yi with respect to sigmaj. The Wi is > itself not decomposed, but the decision to add the Wi to the accumulator for > sigmaj is determined by whether partial hi with respect to sigmaj is > non-zero. > > And wherever H' is not 0, the EPS shrink accumulator adds the contribution > of that Wi for a sigma, and where-ever H is zero, it does not attribute that > Wi for that sigma. This is how it is known which Wi pertain to PK data, and > which Wi pertain to PD data as well, by assessment of the H gradient that > NONMEM assesses. > > The epsilon shrinkage formula honors the H'SigmaH structure, as it should, > since NONMEM's FO and FOCE methods themselves utilize that structure to > estimate Sigma1 and Sigma2. > > To reiterate, normally with proportional and additive sigma, all Wi are > involved in both sigmas, and hence both sigmas have identical shrinkage, > since they are always having non-zero H together. But when some IPREDi are > zero, the additive error has contributions from all Wi, whereas the > proportion sigma collects Wi information only from non-zero IPREDi. > > > -------------------------------------- > Leonid Gibiansky, Ph.D. > President, QuantPharm LLC > web: www.quantpharm.com > e-mail: LGibiansky at quantpharm.com > tel: (301) 767 5566 > > > > On 9/22/2011 9:26 AM, Rik Schoemaker wrote: >> Dear all, >> >> Can someone enlighten me on a NONMEM implementation? >> Since NONMEM 7, epsilon shrinkage is reported in the output, and the >> manual states that it is calculated as: >> 100%*[1-SD(IWRES)] >> in accordance with "Karlsson MO and Savic RM. Diagnosing Model > Diagnostics. >> Clinical Pharmacology and Therapeutics, 2007; 82(1): 17-20" as one >> would expect. >> However, as far as I know, the user needs to manually code the IWRES >> bit using the "Uppsala implementation": >> >> IPRED = F >> IRES = DV - IPRED >> W = THETA(3) >> IWRES = IRES/W >> Y = IPRED+W*EPS(1) >> >> SIGMA 1 FIXED >> >> So how does NONMEM arrive at epsilon shrinkage? And is there by any >> chance an (undocumented?) IWRES item that can be exported in a table file > as well? >> >> Kind regards, >> >> Rik >> >> >> >> Rik Schoemaker, PhD >> Exprimo NV >> Tel: +31 (0)20 4416410 >> E-mail: [email protected] >> Web: www.exprimo.com >> >> This e-mail is confidential. It is also privileged or otherwise >> protected by work product immunity or other legal rules. The >> information is intended to be for use of the individual or entity >> named above. If you are not the intended recipient, please be aware >> that any disclosure, copying, distribution or use of the contents of >> this information is prohibited. You should therefore delete this >> message from your computer system. If you have received the message in >> error, please notify us by reply e-mail. The integrity and security of > this message cannot be guaranteed on the Internet. >> >> Thank you for your co-operation. >> >> >> >> ---------------------------- >> This e-mail message has been scanned for Viruses by Norman Virus >> Control and it's Content by MailMarshal >> >