Hello all: Sorry for my late response, but I had to browse through the source code and verify a few things.
1) Based on my tests, NONMEM correctly assess epsilon shrinkage, even in cases of multiple epsilons. I welcome looking at any problem a user may have where this appears not to be the case. 2) The description in the nm720.pdf manual is intended as an approximate description, although it is an exact representation for simple weighted residual problems. 3) Leonid's e-mail from me regarding how NONMEM actually evaluates IWRES for all cases, and how it parses each IWRES to a given epsilon for its shrinkage calculation, provides the most systematic solution of epsilon shrinkage, even for multiple epsilons, and even for mixed heteroscedastic and homoscedastic residual variances. This embellished description I shall add to the NONMEM_techinical_guide.pdf. 4) Unfortunately, there is no internal variable that holds the IWRES as calculated by NONMEM. A future release version of NONMEM will supply this extra variable. The manner in which NONMEM evaluates the IWRES is entirely consistent with the way users typically evaluate IWRES, whenever there are no L2 correlations in the model. 5) If there is L2 data, then the epsilon shrinkage is calculated by NONMEM a little more complicatedly. In this case, the residual information of two or more data points will be interconnected according to the matrix version of (y-df)'[(H'SIGMAH) inverse ](y-df) among the correlated data points in question. This will be more fully described when I add to the technical guide. Robert J. Bauer, Ph.D. Vice President, Pharmacometrics ICON Development Solutions Tel: (215) 616-6428 Mob: (925) 286-0769 Email: robert.ba...@iconplc.com Web: www.icondevsolutions.com -----Original Message----- From: Leonid Gibiansky [mailto:lgibian...@quantpharm.com] Sent: Thursday, September 22, 2011 1:20 PM To: Andrew Hooker Cc: Rik Schoemaker; nmusers; Bauer, Robert Subject: Re: [NMusers] Epsilon shrinkage and IWRES Hi Andy, Could you, please, provide an example of the model where Nonmem computations are wrong? In my limited experience of comparison, they always agree or very close to what I compute via IWRES. Thanks Leonid -------------------------------------- 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 1:11 PM, Andrew Hooker wrote: > Hi rik > > If you have multiple eps() in your model then the default nonmem calculation will be wrong (understandably). In those instances I define iwres myself and calculate using the psn option "-shrinkage". > > Best regards > Andy > > On 22 sep 2011, at 17:14, "Rik Schoemaker"<rik.schoema...@exprimo.com> 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:lgibian...@quantpharm.com] >> 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: rik.schoema...@exprimo.com >>> 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. 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