From: "Gordi, Toufigh" Toufigh.Gordi@cvt.com
Subject: [NMusers] Inclusion of covariates and model improvement
Date: Wed, 19 Oct 2005 15:12:06 -0700

Dear all,

I have applied a 3-comp PK model with IIV on CL and VC on some data
(FOCE INTERACTION). Graphical inspections indicated a weak correlation
between VC and body weight. When BW was incorporated in the model,
affecting VC, the OFV dropped by over 20 points. VC is described as:

VC=THETA(x)*BW

THETA(x) is estimated to be 0.15. There are not much differences in
model parameters between the simple and the more complex model,
incorporating the BW. However, parameter CVs are mostly worse for the
latter, and the IIV corresponding to VC is only slightly decreased (from
0.35 to 0.26), while its CV has increased from 26% in the simple model
to 59% in the complex model.

I am reluctant to present the more complex model as the final one
despite the significant decrease in OFV. Any comments on which model is
preferred?

Toufigh Gordi 

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From: Leonid Gibiansky leonidg@metrumrg.com
Subject: Re: [NMusers] Inclusion of covariates and model improvement
Date: Wed, 19 Oct 2005 18:40:04 -0400

Toufigh

I think your BW model can/should be formulated differently.
Try
VC=THETA(1)*(BW/70)**THETA(2)

Leonid

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From: "Gordi, Toufigh" Toufigh.Gordi@cvt.com
Subject: Re: [NMusers] Inclusion of covariates and model improvement
Date: Wed, 19 Oct 2005 16:27:05 -0700

Hi Leonid,

I am not sure of the basis for the way your model is written but it
certainly did the job . :)

When I look at the VC vs. WT, there seems to be a simple linear
correlation between the two and that's why I used the simpler coding. Am
I correct in my guess that part of your proposed model is due to
allometric scaling and other is a general median weight being 70?

Toufigh  

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From: Leonid Gibiansky leonidg@metrumrg.com
Subject: Re: [NMusers] Inclusion of covariates and model improvement
Date: Thu, 20 Oct 2005 00:47:27 -0400

Hi Toufigh,

This is the black magic that I practice when I have time :)

Actually, this is the standard way to include weight into the model (with the
exception of strict allometric scaling approach that assumes that THETA(2) should
always be equal to 1). This model allows for not-so-steep increase of VC with weight.
70 is the mean-median value; normalization should not change the model but simplifies
the interpretation (THETA(1) is the VC of a typical 70-kg patient). I am not 100%
sure, but normalization may also influence the precision of estimation.

Leonid


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From: Nick Holford n.holford@auckland.ac.nz
Subject: Re: [NMusers] Inclusion of covariates and model improvement
Date: Thu, 20 Oct 2005 18:03:18 +1300

Toufigh,

The model proposed by Leonid is an empirical allometric model. However, there is a
substantial amount of theory and evidence to believe that the allometric exponent is
1 for volume and 0.75 for clearance. I would recommend using theory rather than
empiricism if you intend to use your model for prediction or simulation (extrapolation).

A more coherent approach would be to apply allometric scaling to all PK parameters
that are known to vary with size e.g. CL, Q, V1, V2. I can think of no sensible
reason to believe that these parameters should be modelled as if they did not vary
with size.

Centering of the parameter e.g. on a weight of 70 kg is always a good idea. Primarily
because it means that the population parameter estimate refers to a general individual
of standard and clearly specified size (or age or Clcr etc). There may also be some
statistical advantages in producing more robust parameter estimates (lower imprecision)
but this is not very sensitive in my experience to any plausible value e.g. there is no
appreciable difference in the predictions if one centers on 70kg or on 10 kg when doing
analyses of children with a median weight around 10 kg.

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/
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From: Stephen Duffull steveduffull@yahoo.com.au
Subject: Re: [NMusers] Inclusion of covariates and model improvement
Date: Thu, 20 Oct 2005 17:38:14 +1000 (EST)

Toufigh.
 
I think there are 2 issues here that can be considered:
 
1)  What did you write in your analysis plan?  If you wrote that the OBJF and
BSV (IIV in your notation) should decrease when a covariate is included and this
has happened then why not include the covariate?  Certainly as your model gets
more complex then SE's may well increase since there is a finite amount of
information in a design which has to be distributed amongst the parameters of
interest.  It would be interesting to see whether centring your parameter by
standardising your weight to 70kg (or whatever number) may result in lower
standard errors.
 
2)  Does inclusion of the covariate help explain some drug effect of interest;  i.e.  would
you alter the dosing regimen based on inclusion of a PK covariate?  When considering this
latter case it is important to remember that patient demographics in clinical studies are
invariably not as extreme as is seen in clinical practice.
 
Regards
 
Steve

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From: "Bernd Meibohm" meibohm@utmem.edu
Subject: Re: [NMusers] Inclusion of covariates and model improvement
Date: Thu, 20 Oct 2005 08:44:17 -0500 

Toufigh:

If you wish to get some more background information on Leonid's 'black magic'
and Nick's allometric size adjustments, some colleagues and myself discussed
the pros and cons of these approaches for size adjustments in POPPK analyses
in a recent paper in
AAPS J (http://www.aapsj.org/view.asp?art=aapsj070248;
Mathplayer (http://www.dessci.com/en/products/mathplayer/download.htm)
needs to be installed for browsers to read equations in AAPS J acticles correctly).

Best regards,

Bernd 

*************************************************
Bernd Meibohm, Ph.D., F.C.P.
Associate Professor of Pharmaceutical Sciences
College of Pharmacy
University of Tennessee
874 Union Avenue, Suite 5p
Memphis, TN 38163, U.S.A.
Phone (901) 448-1206
Fax (901) 448-6940
Email bmeibohm@utmem.edu
                meibohm@attglobal.net
*************************************************

Also:
http://cop.utmem.edu/pharmacy/pharmsci/faculty/pharm/bmeibohm/bmeibohm.html

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