Re: [NMusers] Reporting Modeling Results

I have received a lot of great feedback in response to my original email, =
both on and off the board. But I think my original point was missed by =
some (or I wasn't very clear in making it). There is no question that I =
would like to make the results of an analysis accessible to any caregiver =
administering drug to a patient. I also would never suggest that dosing =
guidance be based on calculating a patient's dose from an allometric =
expression, particularly when there is an age effect confounding the =
matter.

What I am attempting to resolve is the issue of developing a model using a =
particular methodology (normalized to median body weight), but reporting =
only results normalized to 1 kg. As stated in my original email, I am not =
opposed to transforming parameters to reflect the per kg value (i.e., CL =
in L/h/kg^0.75). I have also supplied parameter values for various ages =
and weights.

As far as reporting parameters in a linear fashion, the modelers here at =
our institution have had great success in convincing researchers that the =
traditional way of reporting CL in L/m2 or any other linear fashion is not =
appropriate. What I can't seem to overcome is the thinking that parameters =
should be reported only as normalized to one kg, even when scaled =
allomtrically and even when the modeling procedure hasn't reflected this. =
My frustration lies in the fact that this is the only way that this =
investigator would like to see the results. This isn't the end of the =
world for me, I have reported parameters in this fashion previously when I =
have been able to describe the data with an appropriately structured =
covariate model.

As far as using 70 kg as a standard weight, that has met even more =
opposition. The curious thing about that is that in reality, we compare PK =
in children to that of adults and attempt to explain differences routinely.=
 So I will stop beating this dead horse and move onto the other issue.

Leonid - here is the code from the PK block. The bootstrap was stratified =
to include a representative number of subjects above and below 20 months =
(approximately 5 CL maturation half-lives). When I originally saw the =
boostrap results from the model with parameters normalized to one kg, I =
chalked it up to numerical instability (due to estimating an age effect on =
CL in a one kg child which doesn't exist). Maybe I wasn't thinking =
correctly. Interestingly, structural model parameters are fine, it's the =
CL maturation parameters that yield wide CI's.

$PK
  
 TVCL = THETA(1)*(WT/10.4)**0.75
 BETA = THETA(5)
 TCL = THETA(6)
 FCL = 1-BETA*EXP(-(AGE-1)*0.693/TCL)
 TVCL2 = TVCL*FCL
 CL = TVCL2*EXP(ETA(1))

 TVV1 = THETA(2)*(WT/10.4)
 V1 = TVV1*EXP(ETA(2))

 TVV2 = THETA(3)*(WT/10.4)
 V2 = TVV2*EXP(ETA(3))
 
 TVQ = THETA(4)*(WT/10.4)**0.75
 Q = TVQ

Thanks for all of your input - JM



>>> Nick Holford <n.holford_at_auckland.ac.nz> 10/25/2007 2:40:49 PM >>>
Mark,

We have a different view of the big picture. Regulatory and marketing are =
minor shadows in the big picture of using medicines to improve health.

My job as a university based researcher is not to fill forms for companies =
to send to regulatory agencies to tick boxes and write regulatory =
labels.

I work with clinicians to develop practical insights into treating =
children. Brian Anderson is a paediatric specialist who applies and =
teaches the concepts of rational dosing to clinicians. We work together to =
help understand PKPD in children and find ways to bring it to clinical =
use.

The idea is to define the science first and then to apply it eg. with =
tables of doses at different ages and weights. These tables are simple to =
generate and distribute for clinicians to use. We certainly dont expect =
people to apply the complex models that have been used to describe and =
understand the biology at the bedside.

I would hope that John Mondick can be supported by contemporary scientific =
literature to educate his colleague about science. After that they can =
find a way to apply the science in a suitable format for busy clinicians.

Nick

>
>
>
> Nick,
> I think, in the big picture, it is important to remember =
why we do all this. It isn't for our own
> entertainment, or to congratulate each other on how =
insightful we are. It is to provide useful
> information to providers. We are not (we hope) the real =
audience for our work. It probably isn't
> realistic to expect non-oncologist pediatricians to scale =
doses allometrically. It seems to be
> unrealistic for other physicians (except neurologists) to =
scale doses at all. Dose/kg may be the best
> we can hope for. I'm quite sure it is unrealistic to =
expect drug companies to request labels for non!
> -chemotherapy drugs based on allometric scaling (really =
bad marketing move) Doing so - although
> perhaps scientifically correct, would likely lead to even =
more dosing errors that we currently see,
> with undemonstrated clinical benefit.
> So, how to report depends on who your audience is. If =
it is a bunch of nerds who know what
> eignevalues are, allometric scaling is great, if it is =
people who have 12 minutes to examine,
> diagnose and treat a patients, maybe we can keep it =
simple. Doing otherwise puts use are risk for
> irrelevance.
>
>
>
> Mark Sale MD
> Next Level Solutions, LLC
> www.NextLevelSolns.com
> 919-846-9185
>
> -------- Original Message --------
> Subject: Re: [NMusers] Reporting Modeling Results
> From: Nick Holford <n.holford_at_auckland.ac.nz>
> Date: Thu, October 25, 2007 12:20 am
> To: nmusers <nmusers_at_globomaxnm.com>
> Cc: Brian Anderson <briana_at_adhb.govt.nz>
>
> John,
>
> Leonid correctly points out that it makes no =
difference in terms of parameter
> estimation what weight is used for parameter =
'normalization' because this is just a
> linear scaling factor.
>
> My colleague, Brian Anderson, and I have preferred =
to consider this 'normalising'
> weight as a standard weight. We do not try to make =
anything 'normal' but simply
> choose a scale that will provide us with a =
parameter that represents a standard
> human. We use a weight of 70 kg as the standard =
(Holford 1996). This makes it
> easier to compare parameters estimated in different =
populations, e.g. adults and
> children, because the parameters are scaled to the =
same standard size. Recently
> we have pointed out that use of a size standard =
with a suitable model for
> maturation allows the simple prediction of adult =
clearances from data collected in
> children (Anderson et al 2007b). We note that this =
cannot be done in the reverse
> direction i.e. adult data cannot be used to predict =
the maturational changes in
> clearance which occur in very young humans.
>
> Leonid mentions that results are "routinely =
reported as V/kg or CL/m^2, etc" but
> this is simply tradition without any discernible =
scientific rationale - especially the
> use of the square metre as the standardising =
factor. Drugs are not eliminated to any
> important extent via the skin so there is no =
mechanistic reason for this. The surface
> area method is a hangover of discredited theories =
of allometric scaling. The per kg
> method of scaling clearance is also a problem =
because it leads to the misguided
> viewpoint that clearance is larger in children in =
adults (Anderson & Holford 1997).
>
> Perhaps you can help your investigator colleague to =
read some of the published
> literature in this area so that he/she can get a =
clearer understanding of the size
> scaling issue.
>
> The bottom line:
>
> 'We conclude with the proposal that, at least in =
terms of pharmacokinetics, the
> widely quoted aphorism "Children are not small =
adults" should be changed to
> "Children are small adults * babies are young =
children." ' Anderson & Holford
> 2007a
>
> Nick
>
> 1. Holford NHG. A size standard for pharmacokinetics=
. Clinical Pharmacokinetics
> 1996;30:329-332
> 2. Anderson BJ, McKee AD and Holford NHG. Size, =
myths and the clinical
> pharmacokinetics of analgesia in paediatric =
patients. Clin Pharmacokinet
> 1997;33:313-27
> 3. Anderson BJ, Holford NH. Mechanism-Based =
Concepts of Size and Maturity
> in Pharmacokinetics. Annu Rev Pharmacol Toxicol =
2007a Oct 3; [Epub ahead of
> print]
> 4. Anderson BJ, Allegaert K, Van den Anker JN, =
Cossey V and Holford NH.
> Vancomycin pharmacokinetics in preterm neonates and =
the prediction of adult
> clearance. Br J Clin Pharmacol 2007b;63:75-84
>
>
> Leonid Gibiansky wrote:
> >
> > Hi John,
> > I think you can safely separate statistics/mathema=
tics and clinical use.
> > I would fit the model in the shape and form =
suitable to get the best
> > results (normalized to a typical patient in your =
case) and then report
> > the results in the form most convenient for the =
clinical use. If this is
> > per-kg values, then report it as they request. If =
you look in the
> > literature, results are routinely reported as =
V/kg or CL/m^2, etc.
> >
> > On a side not, I am actually surprised that you =
got different results
> > with different scaling. For the allometric =
scaling with fixed power, two
> > parameterizations:
> >
> > CL=TCL*WT^0.75 and CL=TCL*(WT/10)^0.75
> >
> > differ by the fixed factor
> > (1/10)^0.75 = 0.18
> >
> > I am not sure how this can influence your model =
CI so strongly. I would
> > check how you stratify the bootstrap data sets. =
Could it be that
> > stratification on something else depend on =
parameterization?
> >
> > If you would estimate the power:
> >
> > CL=TCL*(WT/10)^THETA()
> >
> > then parametrization would be more likely to =
affect CI, but for the
> > fixed power I would look for other explanations =
of the differences. It
> > would be easier to discuss the model if you would =
attach the PK block of
> > the nonmem code.
> >
> > Leonid
> >
> > --------------------------------------
> > Leonid Gibiansky, Ph.D.
> > President, QuantPharm LLC
> > web: www.quantpharm.com
> > e-mail: LGibiansky at quantpharm.com
> > tel: (301) 767 5566
> >
> > John Mondick wrote:
> > > I would like to get some feedback from the =
group concerning the reporting of
> modeling results. I have a Pop PK model developed =
from data arising from 124
> pediatric patients, age 1 to 48 months. All of the =
structural parameters have been
> scaled allometrically, with the median body weight =
used as the reference value.
> After accounting for body size, a covariate model =
was incorporated to describe
> maturational changes in CL for young children. The =
maturation of clearance was
> modeled using an exponential model proposed in:
> > >
> > > Andersen et al. Population clinical pharmacology=
 of children: modelling
> covariate effects. Eur J Pediatr. 2006
> > >
> > > Two parameters are estimated as part of this =
model * the fractional change in
> CL for a typical one month old patient (beta - =
estimated to be 0.76 (0.589, 0.96)
> for this analysis) and a maturational half-life =
(TCL - 3.82 (1.57, 6.95) months).
> CI's are from the bootstrap.
> > >
> > > The problem that I am running into is how to =
report the modeling results. It
> seems very natural to me to report the model =
results normalized to median body
> weight (L/h/10.4 kg^0.75). One of the study =
investigators disagrees with me and
> would like to report the results on a per kg basis =
(L/h/kg^0.75). This seems to be
> counterintuitive to me, as I tend to think about =
what represents the "typical
> patient." It also makes no sense to me to represent =
the CL in a one kg child. The
> argument is that reporting in this manner makes =
more sense to clinicians and that
> there is no such thing as a typical child.
> > >
> > > So in an attempt to appease the investigator, I =
fit the same model with no
> weight normalization. The estimated parameters are =
equivalent to what would be
> scaled from the weight-normalized model, but there =
is no covariance matrix (not
> surprising). It becomes problematic when the =
bootstrap results are considered *
> beta = 0.78 (0.005, 0.995), TCL = 3.90 (0.001, =
6.018). Again, this is not
> surprising given that the covariate model is not =
centered.
> > >
> > > I have attempted to make several compromises, =
including reporting the
> parameter estimates in both median weight-normalized=
 terms and normalized per
> kg. I have also included scaled CL estimates for =
typical patients at several ages
> and body weights. This hasn't met the approval of =
the investigator, who is now
> insisting that I report the model building =
procedure from the median weight model,
> but report scaled parameters only on a per kg =
basis. This is wrong in my opinion
> and is actually more confusing to someone who is =
trying to understand the model.
> > >
> > > Can I get the group's opinion on this? Am I =
being stubborn looking at the
> world through a modeler's point of view?
> > >
> > > Thanks,
> > >
> > >
> > >
> > >
> > > John Mondick PhD
> > > Research Assistant Professor
> > > Division of Clinical Pharmacology and Therapeuti=
cs
> > > The Children's Hospital of Philadelphia
> > > Tel (267) 426-2292
> > > FAX (215) 590-7544
> > > Email: mondick_at_email.chop.edu
> > >
> > >
>
> --
> Nick Holford, Dept Pharmacology & Clinical =
Pharmacology
> University of Auckland, 85 Park Rd, Private Bag =
92019, Auckland, New Zealand
> n.holford_at_auckland.ac.nz tel:+64(9)373-7599x86730 =
fax:+64(9)373-7090
> www.health.auckland.ac.nz/pharmacology/staff/nholfor=
d
>
>
>
>



--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New =
Zealand
n.holford_at_auckland.ac.nz tel:+64(9)373-7599x86730 fax:+64(9)373-7090
www.health.auckland.ac.nz/pharmacology/staff/nholford
Received on Thu Oct 25 2007 - 16:26:45 EDT