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RE: [Spam:******] Re: [NMusers] Understanding allometry

From: Graaf, P.H. van der <>
Date: Tue, 24 May 2016 07:27:35 +0000

Dear all,
At the PAGE meeting in a couple of weeks we will try to contribute to this =
debate from a rather different perspective:

B-08 Rob van Wijk: The zebrafish as model for translational systems pharmac=
ology: expanding the allometric scale in vertebrates with five orders of ma=
PAGE 25 (2016) Abstr 5909 []

Hope it will generate a good scientific discussion (and cheer folks up).



Piet H. van der Graaf, PharmD PhD
Professor of Systems Pharmacology
Leiden Academic Centre for Drug Research (LACDR)
Leiden University
2333 CC Leiden, The Netherlands

From: [] on behalf=
 of Dennis Fisher []
Sent: 23 May 2016 15:51
To: Holford Nick
Cc: nmusers
Subject: [Spam:******] Re: [NMusers] Understanding allometry


Your condescending tone is not appropriate — Steve did not insult you nor=
 should you insult him. An apology is due.

You, Steve, and I had the same mentor — Lewis Sheiner. His most importan=
t teaching was LET THE DATA SPEAK. When theory and evidence clash, Lewis w=
ould not blindly stick to theory. In this instance, Steve asked you to pro=
vide EVIDENCE to support your claim that allometric scaling would yield mar=
kedly better fits than weight-normalization. You offered the McCune articl=
e to support your argument (without mentioning your vested interest as an a=
uthor). In that article, you wrote:

all clearance (CL,Q) and volume (V1,V2) parameters were scaled for body siz=
e and composition using allometric theory and predicted fat free mass (FFM)=

It does not appear that you evaluated a weight-normalized model. If you do=
n’t look, you never see!

I also note that the table reports the following:
        CL Clearance L/h/62kg NFM CL 11.4 (1.1)
This brings up the issue of SAFETY. I was a clinician for several decades =
and Steve continues to be an active clinician. I don’t know if you see p=
atients. However, many participants in this mailing list have never select=
ed a dose of a drug, then administered it to a patient. I venture to say t=
hat most clinicians when faced with a dosing regimen that requires raising =
weight to the 3/4 power would run in the opposite direction (or, make a dos=
ing error). The entry in the table is even more problematic. A clinician =
first needs to calculate NFM, then they need to realize that the dose is no=
t proportional to 11.4 by a factor of weight/62.

If the goal of PK is publishing journal articles about pure science, your a=
pproach might be OK. But, as far as I know, the goal is to improve patient=
 safety. If there were a strong (or even moderate) preference for allometr=
ically-scaled models, I would support their use. But, Steve asked you to p=
rovide EVIDENCE for this and you failed to do you. You also cited Eleveld=
’s article. Although his manuscript did include one weight-normalized mo=
del, the allometric model required multiple additional terms to fit the dat=
a. In particular, that article (as yours) required a “maturation” term=
 to describe younger patients. In other words, neither of these articles d=
emonstrates that allometric models are sufficient to describe the range of =
sizes in humans. Had Eleveld added those extra terms to the weight-normali=
zed model, it might have performed as well as the model he published.

Over the past two decades, I have analyzed data from > 200 studies includin=
g many in infants and children. In many of these, I have compared weight-n=
ormalized and allometric (and, in adults, unscaled) approaches. In virtual=
ly all cases, the difference in fit between the weight-normalized and allom=
etric approaches was trivial and often favored the weight-normalized approa=
ch. Can you cite cases in which the allometric approach fares much better?

I also have had the opportunity to be an editor for a journal and to review=
 articles for many journals (and I have reviewed submissions by many people=
 who participate in this mailing list). In many instances, authors refuse =
to evaluate a weight-normalized model, citing you. In many of these instan=
ces, I have insisted that the authors conduct that analysis and (as far as =
I can recall) there has never been strong evidence to support the allometri=
c model.

I repeat — if you don’t look, you don’t see.

I suspect that Steve will have more to add.


Dennis Fisher MD
P < (The "P Less Than" Company)
Phone / Fax: 1-866-PLessThan (1-866-753-7784)

> On May 23, 2016, at 12:17 AM, Nick Holford <> wro=
> Steve,
> Thanks for your comments and questions on theory based allometry. I have =
cross-posted it to nmusers because this topic has been of interest there ov=
er many years.
> I am aware that you wrote an editorial on this topic with Denis Fisher wh=
ich you titled “Allometry, Shallometry!”. Having read your editorial an=
d your comments I don’t think the implication that allometry is shallow i=
s appropriate. On the contrary, I get the impression (see below) that you a=
nd Denis do not really understand the biological principles underlying allo=
metry and seem to be unaware of the substantial literature supporting theor=
y based allometry and its application in humans.
> Would your journal be willing to receive a rejoinder to your editorial wi=
th a deeper explanation of the science and the literature?
> Best wishes,
> Nick
> Nick Holford, MBChB, FRACP
> Professor of Clinical Pharmacology, University of Auckland
> Adjunct Professor of Bioengineering and Therapeutic Sciences, UCSF
> On 21-May-16 00:42, Steven L Shafer <> wrote:
>> Nick:
>> You say below:
>> "Theory based allometry predicts an exponent of 3/4 for many functional=
 processes e.g. basal metabolism, cardiac output, lung volume flow (West et=
 al 1997). It is not restricted to metabolism."
>> The article you cite by West is an excellent treatise on the subject of=
 scaling across species. There are numerous other papers that provide theor=
etical foundations for allometric scaling across species (e.g., Darveau, Na=
ture, 2002; West, J Exp Biol. 2005). The allometric theory accounts for dif=
ferences in rate-related functions across species that span many orders of =
magnitude in body mass. I am not aware of any theory that supports scaling=
 by weight to the 3/4 power WITHIN A SPECIES.
> NH: Unfortunately, you repeat a common misunderstanding of allometric the=
ory that it is somehow only applicable across species. Allometric theory as=
 originally proposed by West is based only on body mass (West, Brown et al.=
 1997). Allometric theory does not require consideration of species or any =
other covariate. This is the first commandment of allometry (Holford 2008).=
 If you read the work by West et al. you will find that there is nothing in=
 the theory that prevents its use for within species scaling using mass. Th=
erefore the theory of West supports the use of the 3/4 exponent within spec=
> SS:
>> Similarly, I am unaware of unambiguous data strongly supporting allometr=
ic scaling across the typical range of human weights.
> NH: I recommend that you read the paper by McCune et al. that formally te=
sts the allometric theory prediction of an exponent of 3/4 for clearance ba=
sed on a large study of busulfan across the human size range (McCune, Bemer=
 et al. 2014). The theory was tested explicitly and no evidence found to re=
ject the value of 3/4. Work with a drug where your expertise is renowned (h=
ttps:// has clearly demonstrated the =
benefit of allometric theory across humans from infants to adults. Eleveld =
showed the fit was improved using theory based allometric scaling (Eleveld,=
 Proost et al. 2014)Schuttler also demonstrated an improved fit with an est=
imated exponent for clearance 0.75 which is consistent with the theoretical=
 value of 3/4 (Schuttler and Ihmsen 2000).
> In the spirit of modern scientific philosophy are you aware of unambiguou=
s data (and analysis) that falsifies the theory of allometry (https://en.wi=
> SS:
>> As applied to human pharmacokinetics, I do not believe any theory suppo=
rts allometric scaling.
> NH: As noted above there is nothing in the theory of allometry proposed b=
y West that would mean it is not applicable to humans. If you do not want t=
o believe this theory then that is your personal choice, as it would be for=
 any religious belief, and I will not attempt to change your religion.
> SS:
>> You can see this if you consider the ends of the spectrum. Small size is=
 associated with children. They are not a separate species, but are humans =
undergoing metabolic maturation.
> NH: I have personally been a strong advocate on considering all humans, r=
egardless of age, as being a single species and have sought integrated expl=
anations of human clinical pharmacology. If you were aware of the paediatri=
c pharmacokinetic literature then you would know of many publications suppo=
rting the use of a combination of theory based allometry for size plus empi=
rical maturation models for age (see this review (Holford, Heo et al. 2013)=
> SS:
>> I am not aware of any allometric theory that accounts for metabolic matu=
ration with age.
> NH: From the first commandment it necessarily follows that changes associ=
ated with age are not predictable from the allometric theory of West et al.=
 There is no age related theory to predict quantitative changes. However, p=
lausible biological understanding of maturation means that clearance will b=
e zero (or at least very small) at conception and will approach a maximum w=
hen it will be indistinguishable from the mature adult value. So at least a=
t the extremes there is a biological and quantitative prediction of maturat=
ion. Joining these extremes requires an empirical approach. A monotonic sig=
moid emax function has been suggested (Tod, Jullien et al. 2008)and widely =
applied (Holford, Heo et al. 2013). A more complex function may be needed b=
ut this will need to be driven first by data not by theory.
> SS:
>> Similarly, very large size is associated with morbid obesity. I am not a=
ware of any allometric theory that suggests that clearance in morbid obesit=
y is best estimated using allometric principles. Between these extremes, sc=
aling by weight is not very different than scaling by weight to the three q=
uarters power.
> NH: Body composition contributes to body mass. Theory based allometry doe=
s not specify how differences in body composition affect allometric size. I=
t is plausible however to propose that the size that is the driving force b=
ehind allometric theory may not be determined simply by total body weight. =
Application of theory based allometry in conjunction with fat free mass can=
 be used to determine a normal fat mass (NFM) (Anderson and Holford 2009). =
The NFM concept has been used to account for body composition differences d=
etermining allometric size. NFM is not predicted from allometric theory but=
 is a biologically plausible extension of the theory of allometric size bas=
ed on mass. NFM has been used to show that total body mass rather than fat =
free mass provides a better description of propofol pharmacokinetics in the=
 obese (Cortinez, Anderson et al. 2010). It has also be used to show that f=
at free mass is a better predictor of dexmedetomidine but obesity is associ=
ated with reduced clearance independently of allometric size based on fat f=
ree mass (Cortinez, Anderson et al. 2015). This demonstrates how the comple=
xities of biology can be better understood based on a plausible theory of a=
llometry. The theory may not be perfect but it is compatible with a very la=
rge number of observation studies in many domains. Investigation of other p=
henomena such as maturation and obesity is aided by building on allometric =
> SS:
>> Of course, I will defer to data. Can you point me to human PK examples =
where allometric scaling of weight to the three quarters power reliably pro=
vides substantially better fits to the data than scaling by weight alone?
> NH: In addition to the large study of busulfan PK mentioned previously (M=
cCune, Bemer et al. 2014)I suggest you look at the prediction of morphine c=
learance across the human size and age range using theory based allometry w=
ith maturation. Prediction of clearance in a large external data set was cl=
early better than other approaches including empirical allometry (Holford, =
Ma et al. 2012). Other published examples can be found in this review (Holf=
ord, Heo et al. 2013).
> SS:
>> I can point to many examples where it makes no difference. I can also po=
int to many examples where investigators simply use allometric scaling with=
out first seeing if allometric scaling was supported by the data.
> NH: This is often the case when sample sizes are small, weight distributi=
on is narrow and power is small (Anderson and Holford 2008). A pragmatic ap=
proach given the challenges of falsifying allometric theory with small data=
 sets is to assume it is useful. It is certainly better than using empirica=
l allometry or ignoring size altogether.
> SS:
>> However, I know of only one or two examples where models were estimated =
with and without allometric scaling, and the allometric scaling worked bett=
er than the simpler non-scaled model. If allometric scaling for human pharm=
acokinetics was “true” on first principles, as your comments imply, the=
n the literature should abound with unequivocal examples.
> NH: If you know of examples of suitably powered studies which can also sh=
ow they have accounted for other mass correlated factors that would confoun=
d the estimation of a true allometric exponent then I would be glad to know=
 the details.
> If you read the literature carefully and exclude those that are underpowe=
red to truly detect the difference between an exponent of 3/4 and say an ex=
ponent of 1 or an exponent of 2/3 and have accounted for all other factors,=
 such as maturation, that are necessarily correlated with mass then you wil=
l not find many examples. I am not aware of any that are inconsistent with =
allometric theory.
> SS:
>> Thanks,
>> Steve
>> --
>> Steven L. Shafer, MD
>> Professor of Anesthesiology, Perioperative and Pain Medicine, Stanford U=
>> Adjunct Associate Professor of Bioengineering and Therapeutic Sciences, =
>> ########################################################################
>> PharmPK Home Page
>> Information about PK/PD Jobs can be found at
>> More information about my eBooks, including Basic Pharmacokinetics and P=
harmacy Math, and now iOS and tvOS apps can be found athttps://www.pharmpk.=
>> Thank you, David Bourne, PharmPK Moderator
>> To unsubscribe from the PHARMPK list, click the following link:
> Anderson, B. J. and N. H. Holford (2008). "Mechanism-based concepts of si=
ze and maturity in pharmacokinetics." _Annu Rev Pharmacol Toxicol_ *48*: 30=
> Anderson, B. J. and N. H. G. Holford (2009). "Mechanistic basis of using =
body size and maturation to predict clearance in humans." _Drug Metab Pharm=
acokinet_ *24*(1): 25-36.
> Cortinez, L. I., B. J. Anderson, N. H. Holford, V. Puga, N. de la Fuente,=
 H. Auad, S. Solari, F. A. Allende and M. Ibacache (2015). "Dexmedetomidine=
 pharmacokinetics in the obese." _Eur J Clin Pharmacol_ *doi:10.1007/s00228=
> Cortinez, L. I., B. J. Anderson, A. Penna, L. Olivares, H. R. Munoz, N. H=
. Holford, M. M. Struys and P. Sepulveda (2010). "Influence of obesity on p=
ropofol pharmacokinetics: derivation of a pharmacokinetic model." _Br J Ana=
esth_ *105*(4): 448-456.
> Eleveld, D. J., J. H. Proost, L. I. Cortinez, A. R. Absalom and M. M. Str=
uys (2014). "A general purpose pharmacokinetic model for propofol." _Anesth=
esia and analgesia_ *118*(6): 1221-1237.
> Holford, N. (2008). "Re: [NMusers] Scaling for pediatric study planning."=
> Holford, N., Y. A. Heo and B. Anderson (2013). "A pharmacokinetic standar=
d for babies and adults." _J Pharm Sci_ *102*(9): 2941-2952.
> Holford, N. H., S. C. Ma and B. J. Anderson (2012). "Prediction of morphi=
ne dose in humans." _Paediatr Anaesth_ *22*(3): 209-222.
> McCune, J. S., M. J. Bemer, J. S. Barrett, K. Scott Baker, A. S. Gamis an=
d N. H. G. Holford (2014). "Busulfan in Infant to Adult Hematopoietic Cell =
Transplant Recipients: A Population Pharmacokinetic Model for Initial and B=
ayesian Dose Personalization." _Clinical Cancer Research_ *20*(3): 754-763.
> Schuttler, J. and H. Ihmsen (2000). "Population pharmacokinetics of propo=
fol: a multicenter study." _Anesthesiology_ *92*(3): 727-738.
> Tod, M., V. Jullien and G. Pons (2008). "Facilitation of drug evaluation =
in children by population methods and modelling." _Clin Pharmacokinet_ *47*=
(4): 231-243.
> West, G. B., J. H. Brown and B. J. Enquist (1997). "A general model for t=
he origin of allometric scaling laws in biology." _Science_ *276*: 122-126.
> --
> Nick Holford, Professor Clinical Pharmacology
> Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A
> University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
> office:+64(9)923-6730 mobile:NZ+64(21)46 23 53 FR+33(6)62 32 46 72
> "Declarative languages are a form of dementia -- they have no memory of e=
> Holford SD, Allegaert K, Anderson BJ, Kukanich B, Sousa AB, Steinman A, P=
ypendop, B., Mehvar, R., Giorgi, M., Holford,N.H.G. Parent-metabolite pharm=
acokinetic models - tests of assumptions and predictions. Journal of Pharma=
cology & Clinical Toxicology. 2014;2(2):1023-34.
> Holford N. Clinical pharmacology = disease progression + drug action. B=
r J Clin Pharmacol. 2015;79(1):18-27.
Received on Tue May 24 2016 - 03:27:35 EDT

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