Non-physiological parameters at lowest OBJ

From: Justin Wilkins <jwilkins@uctgsh1.uct.ac.za> Subject: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/5/2003 6:16 AM Hi all, Just as a general discussion point... Our group is faced with a situation which goes as follows: In a given one-compartment (ADVAN2) model, one set of initial estimates minimizes successfully with parameter estimates that are in broad agreement with prior published information. However, another set of initial estimates minimizes successfully with an objective function 200 units lower, but with physiologically impossible parameter estimates. Both sets completed the covariance step successfully as well. Any ideas on the best way to deal with this, and its potential causes? The first case appears to be reaching a local minimum, but its results are believable, whereas the second's are obviously not correct. The only solution appears to be constrain initial estimates to physiological limits. Both analyses currently underway at our site have independently run into this problem. Best regards, Justin Wilkins Division of Pharmacology Faculty of Health Sciences University of Cape Town

From: William Bachman <bachmanw@globomax.com> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/5/2003 8:32 AM NEVER base model discrimination on objective function alone. Some questions you should be asking yourself: What do the magnitudes of the variances look like? What do your diagnostic plots look like? What estimation method are you using? (Is the estimation method chosen appropriate for your data?) William J. Bachman, Ph.D. GloboMax LLC 7250 Parkway Drive, Suite 430 Hanover, MD 21076 410-782-2212 bachmanw@globomax.com

From: Diane R. Mould <drmould@attglobal.net> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/5/2003 9:30 AM Bill I think that this is excellent advice, and good common sense. One of the primary aspects of modeling is to explain variability and there are definitely situations where one model may better explain variability and yet have a higher OBJ than another. I think its also important to develop a useful model as well. A model that has very inappropriate or unreasonable parameter estimates may be descriptive but is usually not predictive. So another question we have to add to the list is what do you plan to do with this model? Diane

From: Atul Bhattaram <BhattaramA@cder.fda.gov> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/5/2003 9:45 AM Hello Justin You can do log-likelihood profiling and look at the surface for the local minima etc. It is logical to go with the model which gives physiologically relevant parameters. You may be able to justify the constraining of the parameters after looking at the log-likelihood profile. Venkatesh Atul Bhattaram CDER, FDA.

From: Justin Wilkins <jwilkins@uctgsh1.uct.ac.za> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/5/2003 10:14 AM Dear Bill and Diane, Thanks for the quick response! All the diagnostics look great and the fit is good with well-predicted individual curves at the higher objective function. Variances are also quite acceptable. The advice you've given supports my gut feeling - it's good to get some outside feedback though! What could account for this kind of thing? Justin

From: Ken Kowalski <Ken.Kowalski@pfizer.com> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/5/2003 10:36 AM Justin, What do you mean by physiologically impossible? If they are truly outside the feasibility domain of the parameter space (e.g., negative rate constants) then it is certainly prudent to constrain your search. However, if the estimates you obtained are theoretically feasible but physiologically unreasonable then we should be careful with placing constraints. Assuming the latter, I'd be inclined to investigate what is the root cause for the convergence to two different optimums. For example, you might inspect the histograms of your ETAs for any bi-modality. Perhaps the sensitivity to starting values is related to one particular parameter and if its distribution is bi-modal then depending on where the starting value is relative to its modes it may converge to different estimates. I wouldn't be inclined to accept either the constrained or unconstrained model fit without first pursuing the diagnostic plots and other suggestions that Bill has suggested. You may find a new avenue of model building (e.g., a mixture model) that may lead to a more stable and reasonable model fit with a lower OBJ then what you have with your current constrained and unconstrained model fits. Ken

From: Alan Xiao <alan_xiao@merck.com> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/5/2003 10:44 AM Justin, It might be helpful if you also apply the same diagnostics you performed on the set of results with the higher OBJ to that with the lower OBJ value. If all diagnoses are similar, testing the stability/uniqueness of your results and/or data distributions might be able to give you additional useful information. Sometime, one solution is not necessarily the real one if the solution is not unique, even though all kinds of diagnoses (still limited) are sufficiently good. Alan.

From: Rajesh Krishna <Rajesh.Krishna@aventis.com> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/5/2003 10:56 AM Justin: It would help us if you can be quantitative. Perhaps you can provide us with the appropriate endpts and their values. Rajesh

From: William Bachman <bachmanw@globomax.com> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/5/2003 11:14 AM It would also help if you gave us more info re: dense or sparse sampling used FO or FOCE study design

From: Stephen Duffull <duffull@pharmacy.uq.edu.au> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/5/2003 6:03 PM Hi Justin, I think that this is potentially a very interesting example. Obviously all of the advice to date has been prudent - but what I am interested in is along the same lines as Ken's comment. Just how unreasonable are the parameters? It would be nice to have an idea of whether we are talking about illegal parameters (e.g. a negative CL) - in which case I find it intriguing that you would be able to find a minimum that is so much better and that produced good diagnostic plots. Or, perhaps the variance components are greatly inflated >500% - which can cause the objective function to become quite small without affecting the apparent fit of the model. Or, alternatively you might be finding that some relationship that you thought was important a priori was not being supported by your data-model interaction, for example if you knew that the drug was 90% renally cleared but that from one set of initial estimates it minimised to a model where all the clearance was considered to be non-renal? Regards Steve ========================================= Stephen Duffull School of Pharmacy University of Queensland Brisbane 4072 Australia Tel +61 7 3365 8808 Fax +61 7 3365 1688 University Provider Number: 00025B Email: sduffull@pharmacy.uq.edu.au www: http://www.uq.edu.au/pharmacy/sduffull/duffull.htm PFIM: http://www.uq.edu.au/pharmacy/sduffull/pfim.htm MCMC PK example: http://www.uq.edu.au/pharmacy/sduffull/MCMC_eg.htm

From: Justin Wilkins <jwilkins@uctgsh1.uct.ac.za> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/6/2003 6:15 AM Hi to everyone, Thanks for all the comments so far, they've been very helpful. I've included the salient points of each scenario below: Case 1: Case 2: OBJ 1761.159 1983.937 KA: 0.053 (4%) 0.500 (28%) V: 3.10 (12%) 37.9 (5%) CL: 2.29 (6%) 2.13 (5%) ALAG: 1.49 (4%) 1.13 (11%) ADD error: 0.370 (29%) 0.336 (19%) EXP error: 0.150 (9%) 0.186 (14%) Figures in brackets represent residual standard error on each term. The data is rich (n=45, 2 occasions), and the analysis is using ADVAN2/TRANS2 with FOCE without interaction. The drug has a long half-life. The only difference between case 1 and case 2 are that case 2 has a lower constraint of 7 applied to the CL initial estimate. Justin

From: Ken Kowalski <Ken.Kowalski@pfizer.com> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/6/2003 8:01 AM Justin, With Case 1 you're getting flip-flop with ka < ke=CL/V. You might consider constraining your model so that the population estimate of ka > ke. You can do this with something like: TVCL=THETA(1) TVV=THETA(2) TVKE=TVCL/TVV TVKA=TVKE+THETA(3) CL=TVCL*EXP(ETA(1)) etc. where the thetas are all bounded >0. Others may know of a way to ensure against flip-flop of the individual-specific parameters as well (i.e., involving the etas)...can anyone comment? Hopefully, with these constraints you will find an optimum with the same OBJ as Case 1 but with more reasonable parameters. Ken

From: Justin Wilkins <jwilkins@uctgsh1.uct.ac.za> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/6/2003 8:18 AM Hi all, Thanks for the advice - I shall try sorting this out as you suggest. By the way, as you've probably noticed there was an error in my last posting - *V* was constrained to 7, not CL! Apologies for that! Constraining CL in that way would serve no useful purpose... Justin

From: William Bachman <bachmanw@globomax.com> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/6/2003 8:19 AM Justin, I don't recommend using "non-physiological" constraints for PK parameters (e.g. 7 as lower bound for CL). (Unless proven otherwise to be needed in the course of your analysis.) I start by imposing a lower bound of zero for PK parameters and no upper bound. If there are logical upper and lower bounds for a parameter, then I would use those bounds (e.g. 0 < F < 1.0 for bioavailability, etc.) So, that piece weighs in favor of Case 1. What interindividual error models are you using? May want to try additive error on KA and/or ALAG if you haven't already. On the other hand, if you intend to investigate covariates, you might want to pursue that avenue at this point. William J. Bachman, Ph.D. GloboMax LLC 7250 Parkway Drive, Suite 430 Hanover, MD 21076 410-782-2212 bachmanw@globomax.com

From: Alan Xiao <alan_xiao@merck.com> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/6/2003 8:34 AM I saw this is basically just a flip-flop phenomenon - not a problem at all. You just need make sure the drug PK is elimination control or absorption control. Alan.

From: Sam Liao <sliao@pharmaxresearch.com> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/6/2003 8:46 AM Hi Justin: I think this is due to flip-flop of KA and Kel. There are ways to prevent it. My preference is to use bound on Ka initial estimate. Sam

From: Ron A.A. Matht <r.mathot@erasmusmc.nl> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/6/2003 9:02 AM Hi Justin In case 1 you're dealing with flip-flop kinetics: Ka < Ke This situation should be avoided and is furthermore in contrast with the fact that you know that the drug has a long elimination half life. Flip-flop kinetics can be circumvented by defining Ka as follows: TVKA=CL/V + THETA(1) KA=TVKA*EXP(ETA(1)) On basis of the above your Ka will be constrained to be greater than Ke. Regards, Ron ================================================= Ron A.A. Matht, PharmD, PhD Department of Clinical Pharmacy and Clinical Pharmacology Erasmus MC University Medical Center Rotterdam PO Box 2040 3000CA Rotterdam The Netherlands Tel 31-10-4633202 Fax 31-10-4366605 E-mail: r.mathot@erasmusmc.nl

From: Vladimir Piotrovsky <VPIOTROV@PRDBE.jnj.com> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/6/2003 9:27 AM Hi all, I think the following should work at the individual level (just an expansion of Ken's suggestion): CL=THETA(1)*EXP(ETA(1)) V=THETA(2)*EXP(ETA(2)) KE=CL/V KA=KE+THETA(3)*EXP(ETA(3)) Alternatively error recovery using EXIT may help Best regards, Vladimir

From: Leonid Gibiansky <lgibiansky@emmes.com> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/6/2003 10:34 AM Vladimir, I do not know any better way, and use it as well, but KE=KA+THETA(3)*EXP(ETA(3)) looks unsatisfactory, because this representation imposes strong correlation between KE and KA. Is there any better way to insure individual KA / KE relationship? We may use full OMEGA (1-3) matrix to compensate for the imposed correlation. EXIT statement looks better, have you compared the results of two approaches (EXIT vs sum)? Thanks, Leonid

From: Chuanpu Hu <chuanpu.2.hu@gsk.com> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/6/2003 11:32 AM Leonid, I do notthat there is a universally better way. Although there may be desirable reasons to have a model having independent KA and KE, I doubt that is necessary or theoretically sound for the following reason. The correlation between KA and KE is not all bad, because when they are close, the constraint KA>KE implies a strong correlation. Ideally, this correlation should become small when the difference gets larger, which is indeed how the model ... KA=KE+THETA(3)*EXP(ETA(3)) behaves like (from a formula in my 1998 intermediate NONMEM workshop handout). That is, what Vladimir (and the NONMEM workshop) proposed does have good properties, and is easy to implement. Chuanpu

From: Ludger Banken <LUDGER.BANKEN@roche.com> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/6/2003 11:36 AM Hi Justin, if this is a flip-flop you should be able to obtain an OBJ of 1761.159 with KA: 0.739 V: 3.10 CL: 0.164 (ke 0.053) ALAG: 1.49 ADD error: 0.370 EXP error: 0.150 Or did you had an upper constraint of 0.5 on KA? Best regards, Ludger

From: Alan Xiao <alan_xiao@merck.com> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/6/2003 12:14 PM It might be interesting to keep an eye on the correlationship between ETA1/ETA2 and this ETA3. Alan.

From: Rik Shoemaker <RS@chdr.nl> Subject: RE: [NMusers] Non-physiological parameters at lowest OBJ Date: 8/7/2003 2:50 AM Dear all, This solution for dealing with flip-flops is bound to work well, but is no one bothered by the fact that neither Ka nor its variability is ever estimated? Absorption half-life seems to me a parameter you'd want to report, not some compound parameter... Rik _______________________________________________________ For continuation of this discussion and related issues, refer to 99aug072003.html