Hi Jeroen,
I think we might be on the same page but I wanted to get clarification about your suggestion that we “not apply the concept of over-parameterization” with respect to evaluating the omega structure. I’m assuming by ‘over-parameterization’ you mean a model that has more elements in omega than might be necessary to be parsimonious. If so, I certainly agree but I wouldn’t call such a model that has more parameters than necessary to be parsimonious as necessarily over-parameterized. An over-parameterized model is one in which there can be an infinite set of solutions to the parameter values that yields the same fit. Such a setting can occur when the R-matrix in NONMEM is singular. Such over-parameterized models are often also referred to as being ill-conditioned or not stable. I think we should always avoid over-parameterization, ill-conditioning and unstable models regardless of the source (i.e., fixed effects, IIV random effects and omega-structure, or residual error structure). However, I do agree that parsimony in omega is probably not as important as say looking for a parsimonious set of covariate parameter fixed effects when performing covariate modeling to obtain a final model for prediction purposes. This is why in my earlier response below I suggested fitting the “largest omega structure that can be supported by the data”. What I meant by this statement is that we fit the largest number of elements of omega while avoiding over-parameterization or ill-conditioning. Such an omega structure might not be parsimonious (i.e., the smallest omega structure that adequately describes the features in the data). The point I was trying to make is that the smallest omega structure that adequately describes the features in the data may not be a diagonal omega structure (i.e., when correlations do exist) particularly if we are interested in describing the variation in the data and not just in predictions of central tendency. Best, Ken From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On Behalf Of Jeroen Elassaiss-Schaap Sent: Monday, September 29, 2014 7:00 PM To: ken.kowal...@a2pg.com; nmusers@globomaxnm.com; joseph.stand...@nhs.net; non...@optonline.net; d.j.elev...@umcg.nl Subject: Re: [NMusers] OMEGA matrix Dear Pavel, others, The underlying technical difference is that SAEM is in its core a sampling methodology. Off-diagonal elements (as explained by Bob Bauer) are available as sample correlations and do not have to be separately computed in contrast to linearization approaches such as FOCE. The more interesting question to me, as also eluted to by Ken, is what criteria to set up for inclusion of an off-diagonal element. I completely support his argument for simulation performance of the model, as e.g. judged using a VPC. Whether to score it as an additional degree of freedom may be up to debate. An off-diagonal element in essence limits the freedom of the model as the random space in which samples can be generated will be smaller. In that perspective one could argue to retain any off-diagonal element that is sufficiently deviating from zero regardless of ofv changes, and to not apply the concept of over-parametrization (or at least not in comparison to other types of parameters). In practice inclusion of an important off-diagonal is mostly accompanied by a sound improvement in ofv anyway. More can be found in earlier discussions we had on this list, see e.g. https://www.mail-archive.com/nmusers@globomaxnm.com/msg02736.html for quite an extensive one from 2010. Here also an r-script to visualize the parameter space impact can be found ;-). In cases where a larger full or banded omega block is found, I would advice to explore its properties further using matrix decomposition approaches (PCA etc) to evaluate propagated correlations across the matrix. But also on the basis of physiology/pharmacology as a data sample may not be informative enough to support robust interpretation of correlations. A discussion along those lines in reporting seems the more fruitful to me. Best regards, Jeroen http://pd-value.com -- More value out of your data! -----Original Message----- From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On Behalf Of Standing Joseph (GREAT ORMOND STREET HOSPITAL FOR CHILDREN NHS FOUNDATION TRUST) Sent: Friday, September 26, 2014 09:15 To: Kowalski, Ken; 'Eleveld, DJ'; 'Pavel Belo'; nmusers@globomaxnm.com Subject: RE: [NMusers] OMEGA matrix Dear Pavel, To answer your question I suggest you go on Bob Bauer's NONMEM 7 course. The understanding I gleaned from that course (which I think was enhanced by the excellent wine we had at lunch in Alicante) was that with appropriate MU parameterisation there is virtually no computational disadvantage to estimating the full block with the newer algorithms. So you might as well do it, at least in early runs where you want an idea of which parameter correlations might be useful/reasonably estimated. BW, Joe Joseph F Standing MRC Fellow, UCL Institute of Child Health Antimicrobial Pharmacist, Great Ormond Street Hospital Tel: +44(0)207 905 2370 Mobile: +44(0)7970 572435 _____ From: owner-nmus...@globomaxnm.com [owner-nmus...@globomaxnm.com] On Behalf Of Ken Kowalski [ken.kowal...@a2pg.com] Sent: 25 September 2014 22:43 To: 'Eleveld, DJ'; 'Pavel Belo'; nmusers@globomaxnm.com Subject: RE: [NMusers] OMEGA matrix Warning: This message contains unverified links which may not be safe. You should only click links if you are sure they are from a trusted source. Hi Douglas, My own thinking is that you should fit the largest omega structure that can be supported by the data rather than just always assuming a diagonal omega structure. This does not necessarily mean always fitting a full block omega structure, as it can often lead to an ill-conditioned model, however, there may be a reduced block omega structure that is more parsimonious than the diagonal omega structure. Getting the omega structure right is particularly important for simulation of individual responses. For example, if you always simulate from a diagonal omega structure for CL and V when there is evidence that the random effects are highly positively correlated then you may end up simulating individual PK profiles for combinations of individual CLs and Vs that are not represented in your data (i.e., high correlation would suggest that individuals with high CL will tend to also have high V and vice versa whereas a simulation assuming that they are independent will result in simulating for some individuals with high CL and low V and some individuals with low CL and high V that might not be represented in your data). This could lead to simulations that over-predict the variation in the concentration-time profiles even though the diagonal omega may be sufficient for purposes of predicting central tendency in the PK profile. You can confirm this by VPC looking at your ability to predict say the 10th and 90th percentiles in comparison to the observed 10th and 90th percentiles in your data. That is, if you simulate from the diagonal omega when there is correlation in the random effects you may find that your prediction of the 10th and 90th percentiles are more extreme than that in your observed data. I see this all the time in VPC plots where the majority of the observed data are well within the predictions of the 10th and 90th percentiles when we should expect about 10% of our data above the 90th percentile prediction and 10% below the 10th percentile prediction. Best regards, Ken Kenneth G. Kowalski President & CEO A2PG - Ann Arbor Pharmacometrics Group, Inc. 110 Miller Ave., Garden Suite Ann Arbor, MI 48104 Work: 734-274-8255 Cell: 248-207-5082 Fax: 734-913-0230 ken.kowal...@a2pg.com www.a2pg.com -----Original Message----- From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On Behalf Of Eleveld, DJ Sent: Thursday, September 25, 2014 4:36 PM To: Pavel Belo; nmusers@globomaxnm.com Subject: RE: [NMusers] OMEGA matrix Hi Pavel, My question is: Why is it desirable to fit a complete omega matrix if its physical interpretation is unclear? Etas are variation of unknown origin i.e. not explained by the structural model. A full omega matrix allows the unknown variation of one paramater to have a (linear?) relationship with some other thing that is also unknown. If unknown A is found to have a linear relationship with unknown B, then what knowlegde is gained? I do think it can be instructive to to look at correlations and use this information to make a better structural model. But I think diagonal OMEGA matrix is more desirable if it works ok. warm regards, Douglas Eleveld _____ From: owner-nmus...@globomaxnm.com [owner-nmus...@globomaxnm.com] on behalf of Pavel Belo [non...@optonline.net] Sent: Thursday, September 25, 2014 4:24 PM To: nmusers@globomaxnm.com Subject: [NMusers] OMEGA matrix Hello Nonmem Community, It seems like NONMEM developers may advise to start with full OMEGA matrix at the beginning of model development. Monolix developers may advise to start with a diagonal matrix. Is there something different in NONMEM SAEM algorithms that makes model stable when a lot of statistically insignificant correlations/covariances are estimated in the model? It seems like NONMEM SAEM can be very stable in very "hard cases" (a lot of outliers, partially misspecified model, overparameterized model, etc.). The omega matrix is a part of the puzzle. When it is impossible to test every correlation coefficient for significance due to some limitations, it becomes a regulatory issue. We may need to be able to make a statement that the model is safe and sound even when OMEGA matrix can be overparameterized (tries to estimate too many insignificant parameters within the OMEGA matrix). Kind regards, Pavel _____ De inhoud van dit bericht is vertrouwelijk en alleen bestemd voor de geadresseerde(n). Anderen dan de geadresseerde(n) mogen geen gebruik maken van dit bericht, het niet openbaar maken of op enige wijze verspreiden of vermenigvuldigen. Het UMCG kan niet aansprakelijk gesteld worden voor een incomplete aankomst of vertraging van dit verzonden bericht. The contents of this message are confidential and only intended for the eyes of the addressee(s). Others than the addressee(s) are not allowed to use this message, to make it public or to distribute or multiply this message in any way. 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