RE: Block versus diagonal omega
Title: Block versus diagonal omega
Jeroen, You're experience is a little different from mine. I've often been impressed that permitting correlation of inter individual variation allow the OMEGAs to become larger. My explanation was that, if Mr A (a 100 kg person) appears to have + ETA on volume, requiring him to have a expected value to ETA (i.e. off diagonal value of 0) on clearance is a constraint. Allowing that ETA to be associated with a value other than 0, in my experience, frequently results in an even larger OMEGA. But, I really have no criteria for including off diagonal omegas, except my prior that pretty much everything in biology is correlated, and enforcing a lack of correlation is a contraint I'd like to avoid. I agree with you that plots of post-hoc ETAs (ETA(1) vs ETA(2)) can be misleading. I find that posthoc plots of anything are frequently misleading, but I do them anyway. So, I typically try to include as many off diagonals as I can numerically support. And I very much agree that it is important to include as much inter individual variability as possible (variances and covariances) if the purpose is simulation. So, in the end, we have the same advise, I think, put them in if you can. I do find that including them can greatly reduce residual (intra individual) variance, but that commonly the VPC bands are wider (making NPC, NPDE and PPC easier to pass, a side benefit). Mark Sale MD Next Level Solutions, LLC www.NextLevelSolns.com 919-846-9185 A carbon-neutral company See our real time solar energy production at: http://enlighten.enphaseenergy.com/public/systems/aSDz2458
Quoted reply history
-------- Original Message --------
Subject: RE: [NMusers] Block versus diagonal omega
From: "Elassaiss - Schaap, J. \(Jeroen\)" < [email protected] >
Date: Thu, August 26, 2010 3:58 pm
To: "yhb5442387" < [email protected] >, "nmusers"
< [email protected] >
Dear Hongbo, I would rather advocate to include off-diagonal elements if possible. The off-diagonals can trim down the magnitude of the inter-individual variability. And as we often notice that our VPC bands tend to be (initially) rather too wide than too narrow, that can be needed. It is certainly useful when one desires to simulate with the inter-individual variability components. One might want to be careful with basing decisions about off-diagonal elements on posthoc ETAs as shrinkage may induce or mask correlation between the emperical bayesian estimates. Indeed, I ment to indicate that off-diagonal elements are more difficult to estimate. Thank you! Best regards, Jeroen Modeling & Simulation Expert Pharmacokinetics, Pharmacodynamics & Pharmacometrics (P3) - DMPK MSD PO Box 20 - AP1112 5340 BH Oss The Netherlands [email protected] T: +31 (0)412 66 9320 F: +31 (0)412 66 2506 www.msd.com From: [email protected] [ mailto: [email protected] ] On Behalf Of yhb5442387 Sent: Thursday, 26 August, 2010 11:38 To: nmusers Subject: RE: [NMusers] Block versus diagonal omega Hi Al, Serge's suggestion is available in practise,however when we are considering to add one covariate such as body weight to the parameter-CL,e.g.,the number of off-diagonal elements retained in the base model may be different from the one in the covariate model .As I have noticed,one or above off-diagonal elements could cross the zero cutoff again and should be excluded from the OMEGA block structure.So it is hardly to keep the constructure of OMEGA block same during the model improvment . In my opinion,if all the diagonal elements fall in an acceptable interval,such as the CV of parameter is within 50%,there is no need to insert the off-diagonal element.The off-diagonal element which means covariance between the diagonal paramete,represents the correlation between them.So another way is to refer to the scatter plots between ETAs estimated by the model with diagonal elements .Which off-diagonal element is included depends on the correlation between two ETAs in the scaterr plots. Most frequently,the diagonal elements are enough.Do not be worried about that. By the way, when we discussed the off-diagonal issue,we should not forget the basic purpose of model building-to make the model predictive performance to be in accordance with the observed values as far as possible. Jeroen, Do you mean the off-diagonal elements instead of diagonal elements when you mentioned in the second paragraph,because I would like to believe the the off-digonal elements are more difficult to estimate hongbo ye from nanjing city. 2010-08-26 yhb5442387 发件人: "Serge Guzy" < [email protected] > 发送时间: 2010-08-26 04:46 主 题: RE: [NMusers] Block versus diagonal omega 收件人: "Berg, Alexander K., Pharm.D., Ph.D." < [email protected] >, < [email protected] > I am not sure there is one single statistical test you can use like we do with covariate selection (forward followed by backward deletion method). The easiest way to deal with this problem would be first to use a stable method like importance sampling assisted by MAP estimation (IMPMAP in NONMEM7) and getting the full variance covariance matrix and correlation matrix. NONMEM7 will give you also like SADAPT the standard errors associated with each correlation coefficient. A way to categorize these correlation coefficients would be to look at each correlation mean +- 2 standard errors and see if it crosses the zero cutoff. If so, you would assume this correlation not to be statistically significant. Once all the not statistically significant correlations are deleted, you have your new blocks to be considered (I guess you have sometimes to change the order of your parameters to define this new block in NONMEM7) and you refit your model with this new blocks. Of course, this is an approximation but at least it allows you ranking the most important correlations based on both their mean but also their corresponding standard errors. A pure diagonal variance covariance matrix will affect the outcome of your subsequent simulations and usually would inflate the response variability across the population as important correlations are may be missing. Serge Guzy; Ph.D President, CEO; POP_PHARM; INC; www.poppharm.com [email protected] 510 684 87 40 From: [email protected] [ mailto: [email protected] ] On Behalf Of Berg, Alexander K., Pharm.D., Ph.D. Sent: Wednesday, August 25, 2010 12:20 PM To: [email protected] Subject: [NMusers] Block versus diagonal omega Hello - I was curious if someone from the group could perhaps describe the basis for deciding whether to use a block (variance and covariance) versus diagonal (variance only) form of omega. Specifically, what tests if any can be performed to decide between the two forms and are there certain situations where one is preferred over the other as I often see only the diagonal form used. Any help would be much appreciated - Al Berg, PhD/PharmD Clinical Pharmacology Fellow Mayo Clinic - Rochester [email protected] The information contained in this email message may contain confidential or legally privileged information and is intended solely for the use of the named recipient(s). 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