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Re: Scaling for pediatric study planning

From: Nick Holford <n.holford>
Date: Sun, 21 Sep 2008 11:48:23 +1200


I think we are more in less in agreement on this. I applaud the efforts
built into programs such as SIMCYP which attempts to predict clearance
based on complex physicochemical and physiological models. However my
perspective is that the gold standard 'observations' of clearance come
from observing intact organisms. Predictive models can be evaluated by
procedures such as the visual predictive check which directly compare
distribution percentiles from predictions and observations (Karlsson &
Holford 2008).

The evaluation of the SIMCYP predictions reported in the CPK paper
(Johnson et al 2006) is hard to do. It is left to the reader to compare
apples and oranges (lines and ellipses) to try to imagine how good a
prediction has been made. If we could agree to use the same methods for
evaluation of predictions then we could directly compare the merits of
the different prediction methods. I would be very happy to collaborate
with you on such a project. My colleagues and I have some quite large
collections of individual clearances in paediatric and young adult
populations that could be used as the reference.

Thanks for the reminder about Amin Rostami's comparison of bottom up and
top down approaches. But once again its hard to evaluate because he has
a graph comparing the predictions of an empirical liver volume model
based on BSA with a more theoretically sound allometric model based on
WT but there are no observations to be seen (Slide 21). The same is true
in his other slide 22.

Some bits of SIMCYP are strongly mechanistic while others -- such as the
relationship between age and liver volume are only an empirical
description needed to turn a test tube enzyme activity into a clearance
prediction. There is only an approximate relationship between liver
structure (i.e. liver volume) and liver function based on a one
compartment homogeneous distribution assumption (the same assumption
used by PK compartmental models).

I think your claim that more than 5000 data points were used to build
the age and liver volume model is a bit misleading because the methods
section reads 'A total of 5,036 liver size measurements in subjects from
birth to 18 yr old, from 9 different reference
sources9-11,15,16,18,19,21,22 were included in our analysis. In the
majority of cases the individual data and associated covariates were not
reported, only mean values and variability) stratified for age groups.'.
This seems to be a naive pooled type of analysis and not a mixed effects
analysis based on over 5000 individuals as readers of nmusers might be

The weight and post-menstrual age model for GFR that we have reported is
based on 923 individual subjects and 1153 observations. The model is a
mixed effect analysis that was able to identify the fixed effects of age
and weight as well as random effects of between subject variability and
residual error. I will be very happy to send you a copy of the article
as soon as it appears which should be any time now.

Best wishes,


Karlsson MO, Holford NHG. A Tutorial on Visual Predictive Checks. PAGE
17 (2008) Abstr 1434 [wwwpage-meetingorg/?abstract=1434]. 2008.

Masoud Jamei wrote:
> Dear Nick
> Many thanks for your comments. The two years of age is an estimated
> post-natal age when most of the CYP enzymes, serum albumin level and also,
> to some extent, the body composition reach those of adults and the
> incorporation of maturation changes improved the predictions (the same
> previous paper).
> Of course everybody agrees that children are not like test tubes nor should
> they be modelled as one-, two- compartmental models. On the other hand, test
> tube data can provide very valuable knowledge about compounds that should be
> mechanistically incorporated into our models (e.g. whether a compound get
> metabolised by CYP2D6, its extent and the likelihood of polymorphism can be
> determined using in vitro data).
> As you once said at one of the PAGE meetings, it is not possible to imagine
> a case where weight doesn’t play a role, however this is sometimes taken out
> of the context and interpreted as “weight is the only player”. Then we tend
> to model everything using only weight even enzyme/receptor affinity or
> absorption rate.
> We are in full agreement that the age and size should be integrated to be
> able to make sensible predictions and for that reason these two are the
> fundamental elements in our “bottom-up” approach but not the only ones. It
> is generally accepted that the metabolic clearance is proportional to the
> size of the liver and based on more than 5000 data point a good equation for
> predicting the size of the liver is developed (Johnson TN, Tucker GT, Tanner
> MS, et al. Changes in liver volume from birth to adulthood: a meta-analysis.
> Liver Transpl 2005 Dec; 11(12):1481-93 – freely available at:
> However, the size of the liver is again
> not the only determinant of the metabolic clearance and we need to take into
> account other relevant covariates such as the enzyme abundances in the
> liver, blood flow, plasma protein biding and the haematocrite level which
> can be altered by polymorphism, ethnicity, disease states, etc. For
> instance, ignoring renal function maturation can simply bring about
> incorrect conclusions:
> (
> I see lots of common grounds between the “bottom-up” and “top-down”
> approaches and do not consider these two as competing but complementary
> approaches (last few slides of
> show and example of the consistency between the two approaches).
> Our argument is, let's mechanistically incorporate our collective knowledge
> from all reliable sources as much as and whenever possible into
> physiologically based models and use empirical models only when there is not
> any other alternatives.
> Yours Sincerely
> Masoud
> PS: I'd greatly appreciate receiving a print out of the Rhodin et al paper
> whenever it is out please.
> Masoud Jamei, PhD, SMIEEE
> Senior Scientific Advisor, Head of M&S
> Honorary Lecturer, School of Medicine, University of Sheffield
> Simcyp Limited
> Blades Enterprise Centre, John Street, Sheffield, S2 4SU, UK
> Tel +44 (0) 114 292 2327
> Fax +44 (0) 114 292 2333
> real solutions from virtual populations
> -----Original Message-----
> From: owner-nmusers
> Behalf Of Nick Holford
> Sent: 19 September 2008 23:11
> To: nmusers
> Subject: Re: [NMusers] Scaling for pediatric study planning
> Masoud,
> I dont know of any good reason to introduce an arbitrary cut-off above
> age 2 years for the usefulness of allometric scaling. Allometric theory
> is applicable from single cells to very large multicellular organisms.
> It should be expected to explain the size related changes in PK
> throughout life beginning from conception.
> As you point out there are major maturational changes, in addition to
> size, which need to be considered and indeed these effects can be
> comparable to those of size in young children (less than 1 year of age).
> The empirical models used to describe maturation in Johnson et al. 2006
> are somewhat limited because they use post-natal age rather than
> biological age to describe changes of in vitro enzyme activity. They
> also rely on the assumption that children are like test tubes. While it
> is can be debated if children are just small adults it seems less likely
> they are big test tubes.
> Alternative top-down approaches (i.e. based on intact humans not test
> tubes), while still being empirical for the description of maturation,
> do at least allow plausible extrapolation from conception to the fully
> mature adult because they use post-menstrual age in combination with
> allometric scaling for size at all ages (see references).
> An important practical application of an integrated age and size
> approach is the ability to make sensible predictions of drug clearance
> in young children when, as is usually the case, there is no reliable
> data available. When making extrapolations it is best to rely on
> mechanism based theory whenever possible but when forced to be empirical
> (all maturation models) then at least the model should extrapolate in a
> sensible way.
> Best wishes,
> Nick
> 1. Tod M, Lokiec F, Bidault R, De Bony F, Petitjean O, Aujard Y.
> Pharmacokinetics of oral acyclovir in neonates and in infants: a
> population analysis. Antimicrob Agents Chemother. 2001;45(1):150-7.
> 2. Allegaert K, de Hoon J, Verbesselt R, Naulaers G, Murat I.
> Maturational pharmacokinetics of single intravenous bolus of propofol.
> Paediatr Anaesth. 2007;17(11):1028-34.
> 3. Anderson BJ, Allegaert K, Van den Anker JN, Cossey V, Holford NH.
> Vancomycin pharmacokinetics in preterm neonates and the prediction of
> adult clearance. Br J Clin Pharmacol. 2007;63(1):75-84.
> 4. Anand KJS, Anderson BJ, Holford NHG, Hall RW, Young T, Barton BA.
> Morphine Pharmacokinetics and Pharmacodynamics in Preterm Neonates:
> Secondary Results from the NEOPAIN Multicenter Trial Br J Anaesth.
> 2008;Epub.
> 5. Potts AL, Warman GR, Anderson BJ. Dexmedetomidine disposition in
> children: a population analysis. Paediatr Anaesth. 2008;18(8):722-30.
> 6. Rhodin MM, Anderson BJ, Peters AM, Coulthard MG, Wilkins B, Cole M,
> et al. Human renal function maturation – a quantitative description
> using weight and postmenstrual age. Pediatr Nephrol. 2008. In Press.
> Masoud Jamei wrote:
>> I can't agree more with Jeff's comments that we should "pursue more
>> physiologic expressions" and this is a "place where "bottom-up"
> approaches"
>> are advantageous.
>> The allometric scaling may be useful for children older than 2 years but
> for
>> younger subjects surely the developmental factors should be considered as
>> explained in: Johnson TN, Rostami-Hodjegan A and Tucker GT (2006)
> Prediction
>> of the clearance of eleven drugs and associated variability in neonates,
>> infants and children. Clin Pharmacokinet 45:931-956.
>> Regards
>> Masoud
>>> -----Original Message-----
>>> From: owner-nmusers
>>> nmusers
>>> Sent: 19 September 2008 16:54
>>> To: Joachim.Grevel
>>> Cc: nmusers
>>> Subject: Re: [NMusers] Scaling for pediatric study planning
>>> Leonid / Joachim,
>>> I think we're pushing the envelope on empiricism here. Two facts of
>>> reality prevail here:
>>> 1) we seldom collect enough data during the absorption phase to assess
>>> any meaningful age/developmental dependencies across the age continuum.
>>> The fisrt-order assumption is always bad even in adults but we live
>>> with it because we seldom have absorption as a primary phase of
>>> interest.
>>> 2) a physiologic approach, in addition to a more fundamental
>>> approximation of reality also has more options with respect to
>>> functional expressions that can accomodate developmental factors such
>>> as changes in pH dependency, the surface area of the GI tract, or the
>>> site and expression of presystemic P450 enzymes all of which factor
>>> into the size surrogacy issue.
>>> Hence, I'm not sure that I would consider the allometric
>>> characterization of absorption in the same manner as one would treat CL
>>> or V considerations as it is indeed a hybrid process. I will defer to
>>> Nick's wisdom on this but if I am pressed for a guess, I would not
>>> scale but pursue more physiologic expressions. In actuality, this is a
>>> place where "bottom-up" approaches would seem to have a decided
>>> advantage.
>>> Jeff
>>> Jeffrey S. Barrett, Ph.D., FCP
>>> Research Associate Professor, Pediatrics Director, Pediatric
>>> Pharmacology Research Unit, Laboratory for Applied PK/PD Clinical
>>> Pharmacology & Therapeutics Abramson Research Center, Rm 916H The
>>> Children's Hospital of Philadelphia
>>> 3615 Civic Center Blvd.
>>> Philadelphia, PA 19104
>>> KMAS (Kinetic Modeling & Simulation)
>>> Institute for Translational Medicine
>>> University of Pennsylvania
>>> email: barrettj
>>> Ph: (267) 426-5479
>>>>>> Leonid Gibiansky <LGibiansky
>>> Just to add:
>>> c) how do we allometrically scale a VM rate constant of the Michaelis-
>>> Menten elimination model:
>>> C1=A(1)/V1
>>> DADT(1)= ... -A(1)*VM/(KM+C1)
>>> d) do we need to allometrically scale a KM constant of the Michaelis-
>>> Menten elimination model ?
>>> any experience with these quantities (for example, if they were
>>> estimated, what were the estimates, with the precision)?
>>> My suggestion would be NOT to scale a), b) and d), and scale VM as the
>>> rate constant (~ WT**(-0.25)) but I do not have "rock-solid" data to
>>> support those suggestions.
>>> Leonid
>>> --------------------------------------
>>> Leonid Gibiansky, Ph.D.
>>> President, QuantPharm LLC
>>> web:
>>> e-mail: LGibiansky at
>>> tel: (301) 767 5566
>>> Joachim.Grevel
>>>> Dear NM_Users,
>>>> we have all been good students and listened to Nick when he told us
>>>> again and again the rock-solid truths of allometry:
>>>> Volume: *(WT/70)
>>>> CL: *(WT/70)**0.75
>>>> any rate constant related to distribution or elimination:
>>> *(WT/70)**(-0.25)
>>>> Here my questions:
>>>> a) how do we allometrically scale a first-order rate constant of
>>>> absorption after oral dosing?
>>>> b) how do we allometrically scale a first-order rate constant of
>>>> absorption from a subcutaneous injection site?
>>>> Thank you for your thoughts,
>>>> Joachim
>>>> __________________________________________
>>>> Joachim GREVEL, Ph.D.
>>>> MERCK SERONO International S.A.
>>>> Exploratory Medicine
>>>> 1202 Geneva
>>>> Tel: +41.22.414.4751
>>>> Fax: +41.22.414.3059
>>>> Email: joachim.grevel
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Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
Received on Sat Sep 20 2008 - 19:48:23 EDT

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