Dear Jon, As you point out the concept of residual error magnitude being dependent on anything else than the prediction itself is a straightforward. Yet it is, I think underused and that is why you may not see it much in the literature. In addition to what you mention, a large component is that model misspecification is not a homogeneous process. It is likely that most of our models are more specified for absorption than disposition. Absorption contains many processes that are discrete and difficult to easily capture in simple models. For most compunds, the absolute gradient is much higher during the absorption phase than the distribution phase and that is probably a contributing factor to what experience. You would probably get as good an improvement if you had a separate error magnitude during the absorption phase.
The model you mentioned with were outlined in the 1998 article below. I also add some other articles for the case you're further interested in residual error modeling. Best regards, Mats 1. A strategy for residual error modeling incorporating scedasticity of variance and distribution shape.<http://www.ncbi.nlm.nih.gov/pubmed/26679003> Dosne AG, Bergstrand M, Karlsson MO. J Pharmacokinet Pharmacodyn. 2016 Apr;43(2):137-51. doi: 10.1007/s10928-015-9460-y. Epub 2015 Dec 17. PMID: 26679003 [PubMed - in process] Free PMC Article Similar articles<http://www.ncbi.nlm.nih.gov/pubmed?linkname=pubmed_pubmed&from_uid=26679003> 2. The impact of misspecification of residual error or correlation structure on the type I error rate for covariate inclusion.<http://www.ncbi.nlm.nih.gov/pubmed/19219538> Silber HE, Kjellsson MC, Karlsson MO. J Pharmacokinet Pharmacodyn. 2009 Feb;36(1):81-99. doi: 10.1007/s10928-009-9112-1. Epub 2009 Feb 14. PMID: 19219538 [PubMed - indexed for MEDLINE] Similar articles<http://www.ncbi.nlm.nih.gov/pubmed?linkname=pubmed_pubmed&from_uid=19219538> 3. Three new residual error models for population PK/PD analyses.<http://www.ncbi.nlm.nih.gov/pubmed/8733951> Karlsson MO, Beal SL, Sheiner LB. J Pharmacokinet Biopharm. 1995 Dec;23(6):651-72. PMID: 8733951 [PubMed - indexed for MEDLINE] Similar articles<http://www.ncbi.nlm.nih.gov/pubmed?linkname=pubmed_pubmed&from_uid=8733951> 4. Assumption testing in population pharmacokinetic models: illustrated with an analysis of moxonidine data from congestive heart failure patients.<http://www.ncbi.nlm.nih.gov/pubmed/9795882> Karlsson MO, Jonsson EN, Wiltse CG, Wade JR. J Pharmacokinet Biopharm. 1998 Apr;26(2):207-46. PMID: 9795882 Mats Karlsson, PhD Professor of Pharmacometrics Dept of Pharmaceutical Biosciences Faculty of Pharmacy Uppsala University Box 591 75124 Uppsala Phone: +46 18 4714105 Fax + 46 18 4714003 www.farmbio.uu.se/research/researchgroups/pharmacometrics/<http://www.farmbio.uu.se/research/researchgroups/pharmacometrics/> From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On Behalf Of Jonathan Moss Sent: Friday, May 13, 2016 11:37 AM To: nmusers@globomaxnm.com Subject: [NMusers] Splitting the residual error Dear all, I would like to share with you and get people's opinions on a recent issue I had. I have a data set of 46 patients, orally dosed, with very dense sampling during absorption (0.25h, 0.5h, 0.75h, 1h, 1.5h, 2h, 3h, 4h, 6h, 8h, 12h, 24h, 36h), Cmax at around 4 hours. During modelling, I found that the residual error was not evenly distributed. Plotting CWRES against time after dose, the result looked like an "hourglass" shape. I.e. A wide spread during absorption, narrower near Cmax time, then wider at later time points. My thinking was as follows: Residual error contains both the assay / model spec. error, and the error in recorded observation time. When the gradient of the PK curve is large, any error in recorded observation time equals a large error in the recorded concentration, whereas if the gradient is small then the recorded concentration error will be small. I "split" the residual error into its assay/model spec and time-error parts in the $ERROR block: $ERROR GRAD = KA*A(2) - K20*A(3) IF (GRAD.LT.0) GRAD = -1*GRAD C_1 = A(3)/V ; Concentration in the central compartment IPRED = C_1 SD = SQRT(EPROP*C_1**2) ; Standard deviation of predicted concentration Y=IPRED+SD*(1+val*GRAD)*EPS(1) Note: Sigma is fixed to one and EPROP is estimated as a theta. Here, GRAD is the right hand side of the differential equation for A(3), in order to recover the gradient. Val is estimated by NONMEM. This approach vastly improved the model fit (OFV drop of around 350!). All GOF plots, VPCs, NPCs, NPDEs, individual fits looked good. This got me thinking, and I tried this approach on some of my other popPK models. I found for the simpler models, the result was nearly always a significant improvement in the model fit. For the more complicated models, NONMEM had trouble finishing the runs. I struggled to find any approach like this in the literature, which leads me to believe that there is something wrong, as it is a relatively simple concept. Please, what are peoples thoughts on this? Thanks, Jon Jon Moss, PhD Modeller BAST Inc Limited Loughborough Innovation Centre Charnwood Wing Holywell Park Ashby Road Loughborough, LE11 3AQ, UK Tel: +44 (0)1509 222908
