Re: 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 <[EMAIL PROTECTED]> 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
>
Quoted reply history
> -------- Original Message --------
> Subject: Re: [NMusers] Reporting Modeling Results
> From: Nick Holford <[EMAIL PROTECTED]>
> Date: Thu, October 25, 2007 12:20 am
> To: nmusers <[email protected]>
> Cc: Brian Anderson <[EMAIL PROTECTED]>
>
> 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/mathematics
> 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 Therapeutics
> > > The Children's Hospital of Philadelphia
> > > Tel (267) 426-2292
> > > FAX (215) 590-7544
> > > Email: [EMAIL PROTECTED]
> > >
> > >
>
> --
> Nick Holford, Dept Pharmacology & Clinical Pharmacology
> University of Auckland, 85 Park Rd, Private Bag 92019,
> Auckland, New Zealand
> [EMAIL PROTECTED] tel:+64(9)373-7599x86730
> fax:+64(9)373-7090
> www.health.auckland.ac.nz/pharmacology/staff/nholford
>
>
>
>
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
[EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:+64(9)373-7090
www.health.auckland.ac.nz/pharmacology/staff/nholford