From: "Toufigh Gordi" tgordi@Depomedinc.com
Subject: [NMusers] GAM analysis and further action
Date: Wed, 29 Mar 2006 10:07:12 -0800

Dear all,

I have modeled the pharmacokinetics of a compound in very young children using the FOCE INTERACTION
option in NONMEM. Following that I looked at graphs of model parameters (CL and VC) vs. various
covariates (6 of them). None of the graphs show any obvious correlations or trends. However, running
a GAM analysis in Xpose I have the following results on CL (no effect on VC):
 

Start:  CL ~ 1; AIC= 29.056

Step :  CL ~ HB ; AIC= 27.886

Step :  CL ~ HT + HB ; AIC= 26.1178

Step :  CL ~ HT + BW + HB ; AIC= 24.9265

Step :  CL ~ ns(HT, df = 2) + BW + HB ; AIC= 24.3268

The analysis implies effect of HT, BW, and HB on CL, although the graphs indicate no correlations.
Any comments on how to proceed next? In general, are there any recommendations on the significance
of covariate with regard to the drop in AIC? Is a drop from 29 to 24 sufficient enough to justify
including 3 covariates in the model? (although not all of them might be needed depending on the NONMEM results)

Best regards,

Toufigh  

Toufigh Gordi, PhD
Associate Director of Pharmacokinetics
1360 O'Brien Drive
Menlo Park, CA 94025-1436
USA
Phone: 650-462-2752 ext. 273
Fax: 650-462-9993

_______________________________________________________

From: "Mats Karlsson" mats.karlsson@farmbio.uu.se
Subject: RE: [NMusers] GAM analysis and further action
Date: Wed, 29 Mar 2006 20:35:42 +0200

Hi Toufigh,

You have both BW and HT as candidate covariates. These are often highly correlated. Unless you
have a very large data set, it is unlikely that you can separate the influence from the two.
Allowing highly correlated covariates often results in models that have highly influential
individuals. You can look at Cook score diagnostics in Xpose and also delete individuals (also
doable in Xpose) to investigate sensitivity.
However, I would not use GAM results as the final and they are really quite uninteresting to
relate to p-values. It is a guide for what to try (and sometimes with what functional form) in NONMEM.

Best regards,

Mats

--

Mats Karlsson, PhD
Professor of Pharmacometrics
Div. of Pharmacokinetics and Drug Therapy
Dept. of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
SE-751 24 Uppsala
Sweden
phone +46 18 471 4105
fax   +46 18 471 4003
mats.karlsson@farmbio.uu.se
_______________________________________________________

From: Paul Hutson prhutson@pharmacy.wisc.edu
Subject: Re: [NMusers] GAM analysis and further action
Date: Wed, 29 Mar 2006 12:52:38 -0600

Toufigh:

Out of curiosity, what were the changes in the objective function when these (apparently
continuous) covariates were added to the NONMEM model?

Paul
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From: "Jakob Ribbing" Jakob.Ribbing@farmbio.uu.se
Subject: RE: [NMusers] GAM analysis and further action
Date: Wed, 29 Mar 2006 21:03:07 +0200

Dear Toufigh,

AIC=chi2  2 * #covariate-parameters

If you would use the AIC criterion for model selection within NONMEM then deltaAIC = deltaOFV  2 * delta#parameters.
However, you would not get the same results, partly because the empirical-bayes estimates (individual
eta or delta-parameters=CLi-TVCL) used in the GAM are shrunk towards the population mean (the NONMEM
model that you fit assumes that CL is independent of any covariates)[1]. As Mats pointed out, fitting
the model in NONMEM would therefore be a good idea, after selecting a set of covariates to test, which
are not highly correlated and which are biologically plausible (unless large dataset). As for letting the
data decide the functional form to test, this would also require many individuals (unless you follow the
individuals from very young until kindergarten :>)
You may also try looking at delta-parameters rather than etas to see the actual (but shrunk) relations between parameter and covariate.

Best regards,


Jakob

1. Wahlby, U., E.N. Jonsson, and M.O. Karlsson, Comparison of stepwise covariate model building strategies in
population pharmacokinetic-pharmacodynamic analysis. AAPS PharmSci, 2002. 4(4): p. 27.
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From: "Manish Gupta" guptam@email.chop.edu
Subject: Re: [NMusers] GAM analysis and further action
Date: Wed, 29 Mar 2006 14:06:39 -0500 

Toufigh,

I think you need to use an allometric model to describe between subject
differences in CL and V. CL and V in the pediatric population most
likely varies due to differences in body weight. If it is hepatically
cleared drug, an allometric exponent of 0.75 is used for CL and an
allometric exponent of 1 to be used for Volume of distribution. 
TVCL~CL*(BW/BWmedian)**0.75
TV~V*(BW/BWmedian)**1
For renally, cleared drugs, an exponent of 0.67 is used for CL. Once
you have included Clearance and Volume as a function of body weight in
your base model, you can look at the influence of other covariates like
Hb in your analysis.
As Mats pointed out, since HT and BW are highly correlated covariates,
you can only include one of them in your GAM analysis (most likely BW).
GAM analysis (in X-pose) does not account for correlated covariates
since univariate analyses are performed.
Some useful references discussing it
1. Anderson BJ, McKee D, Holford NHG. Size, myths and the clinical
pharmacokinetics of analgesia in paediatric patients. Clinical
Pharmacokinetics 1997;33:313-327 
2. Anderson BJ, Woolard G, Holford NHG. A model for size and age
changes in the pharmacokinetics of paracetamol in neonates, infants and
children. Br J Clin Pharmacol. 2000; 50:125-134 
3. Holford NHG. A size standard for pharmacokinetics. Clinical
Pharmacokinetics 1996;30:329-332 

I hope this was helpful
Manish

Manish Gupta, PhD
Post Doctoral fellow
Clinical Pharmacology & Therapeutics
The Children's Hospital of Philadelphia

Manish Gupta, PhD
Post Doctoral fellow
Clinical Pharmacology & Therapeutics
The Children's Hospital of Philadelphia
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From: Mark Sale - Next Level Solutions mark@nextlevelsolns.com
Subject: RE: [NMusers] GAM analysis and further action
Date: Wed, 29 Mar 2006 12:16:37 -0700

Mats, Toufigh,
 
I have, in general been unimpressed with both the sensitivity and specificiy of plots of
post-hoc etas vs potential covariates.  So, I would add your first "test" (plots) to Mats'
list of things that are at best, a guide on what to try.  I will, once again, suggest that
the complexities of the interdependencies of covariate relationships (and interdependencies
of structural effects)  are a violation of the assumptions on which the post-hoc-vs-covariate
plot modeling approach -and the step wise modeling approach, is based.  As such, we need to
reasses the basic tenets of how we select models.  I'm not sure about what assumptions
underlie that GAM approach.  Still looking for collaborators for a formal assessment of
traditional|GAM|WAM|GA model selection strategy - anyone interested?


Mark Sale MD
Next Level Solutions, LLC
www.NextLevelSolns.com 
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From: Dennis Fisher fisher@plessthan.com
Subject: [NMusers] GAM analysis and further action
Date: Wed, 29 Mar 2006 11:47:40 -0800

Manish suggested a allometric model.  Although this approach MIGHT be appropriate from a
PHYSIOLOGIC perspective, I truly doubt that it is helpful from a CLINICAL perspective.  If we report
that CL varies as a function of weight^0.75, what clinician will be able to use this information to
guide dosing?  So, I prefer to define models in terms that can be useful in the clinical setting.


Dennis Fisher MD
P < (The "P Less Than" Company)
Phone: 1-866-PLessThan (1-866-753-7784)
Fax: 1-415-564-2220
www.PLessThan.com
_______________________________________________________

From: "Charnick, Steven B" steven_charnick@merck.com
Subject: RE: [NMusers] GAM analysis and further action
Date: Wed, 29 Mar 2006 14:56:15 -0500Mark,
 
I would be very interested in the collaboration.  I've been working on variations of this approach
for some years now and while there appears to some meeting of the minds as to what is 'preferred',
I've seen no formal assessment.  I agree that it's needed.
 
Steven Charnick, PhD
Senior Investigator
Merck Research Laboratories
WP75B-1305
PO Box 4
West Point PA 19486
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From: "Gastonguay, Marc" marcg@metrumrg.com
Subject: Re: [NMusers] GAM analysis and further action
Date: Wed, 29 Mar 2006 16:01:36 -0500

Dennis - We'd probably all agree that modeling results are not effective unless presented in a
useful clinical perspective. This doesn't mean that we have to use a less than adequate model,
though. In fact, it has been shown that this can lead to biased interpretation of other model
components (Wade et al J Pharmacokinet Biopharm 1994; 22(2):165-77). As Manish suggested, this
is definitely a concern in pediatrics when body-size and age-dependent changes in physiology
are correlated.

We can actually meet both goals; build models that are structurally consistent with known physiology
and observed data and then use these models as simulation tools to explore the impact of simpler
clinical guidance.

Best regards,
Marc

Marc R. Gastonguay, Ph.D.
www.metrumrg.com 
_______________________________________________________

From: Nick Holford n.holford@auckland.ac.nz
Subject: Re: [NMusers] GAM analysis and further action
Date: Thu, 30 Mar 2006 09:15:46 +1200

Denis,

We all understand that clinicians are too busy to pay attention to the details of science and need simple
tables and rules of thumb so they can get on with more important things like diagnosing von Heffalumps Syndrome.

I think modellers have an obligation to get the science correct first. Then this can be simplified for
the clinicians. In the paediatric area the clinicians have learned empirically to use bigger mg/kg doses
in small children compared with adults. But there is no physiological basis for this rule of thumb. Clinician
'scientists' have attempted to interpret the larger mg/kg doses in a variety of speculative ways but they
provide no evidence for children being really any different from adults.  An allometric perspective indicates
that there is really no difference between children and adults when body size is appropriately adjusted (assuming
all other covariates are equivalent in children and adults).

Similar considerations apply to other covariates e.g. with a continuous covariate such as renal function the model
should try to predict renal function in a continuous way. Later when a regulatory label is written or other attempts
are made to communicate the science to the clinicians it can be simplified into ranges of creatinine clearance and
associated dosing rates.

Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
_______________________________________________________

From: "Jakob Ribbing" Jakob.Ribbing@farmbio.uu.se
Subject: RE: [NMusers] GAM analysis and further action
Date: Thu, 30 Mar 2006 11:39:56 +0200

Dear all,

Lewis Sheiner used to advocate investigating delta-parameters (e.g. CL-TVCL) on covariates when using the GAM or investigating
graphs of covariate effects. This is especially important if you plan to import the functional form found in the GAM into the
NONMEM model. Otherwise, if a linear relation is found between etaCL(=log(CL/TVCL)) and a covariate in the GAM this represents
an exponential function of the covariate in the NONMEM model. It is easy to output the delta-parameters in the table file and
use these instead of the etas, to avoid this problem.

Regarding this comment: "GAM analysis (in X-pose) does not account for correlated covariates since univariate analyses are performed."

For a graphical analysis of covariate relations this is correct, but I think that the GAM in Xpose do account for correlation
between covariates since it performs a stepwise-multiple regression[1] similar to what is performed in NONMEM using e.g. SCM[2].
The Xpose-GAM however does not manage correlation of estimate between structural parameters. For example, if we have correlation
on the population level between CL and V, the corresponding etas from the basic model may become (sometimes falsely) correlated
causing inclusion of a covariate on both parameters even if only one is supported when investigating within NONMEM. Is this
something you (with more experience on the GAM) often see when transferring models from xpose to NONMEM? It is not relevant in
Toufigh's example since covariates are found only for CL.

Also, I got the sign wrong my previous e-mail:

AIC is still: AIC=chi2  2 * #covariate-parameters

However, using this criterion in NONMEM it should be:

deltaAIC = deltaOFV + 2 * delta#parameters

This means that using the AIC criterion, a drop in OFV of 2 is required for each additional parameter which translates into a
p-value of 0.157 when comparing two nested models with one extra parameter.

Jakob

1.    Wahlby, U., E.N. Jonsson, and M.O. Karlsson, Comparison of stepwise covariate model building strategies in population
pharmacokinetic-pharmacodynamic analysis. AAPS PharmSci, 2002. 4(4): p. 27.

2.    Jonsson, E.N. and M.O. Karlsson, Automated covariate model building within NONMEM. Pharm Res, 1998. 15(9): p. 1463-8.
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