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. Mathôt <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. Mathôt, 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