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Re: Understanding allometry

From: Dennis Fisher <fisher>
Date: Mon, 23 May 2016 06:51:05 -0700


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 =
important teaching was LET THE DATA SPEAK. When theory and evidence =
clash, Lewis would not blindly stick to theory. In this instance, Steve =
asked you to provide EVIDENCE to support your claim that allometric =
scaling would yield markedly better fits than weight-normalization. You =
offered the McCune article to support your argument (without mentioning =
your vested interest as an author). In that article, you wrote:

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

It does not appear that you evaluated a weight-normalized model. If you =
don’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 patients. However, many participants in this mailing =
list have never selected a dose of a drug, then administered it to a =
patient. I venture to say that 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 dosing 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 not proportional to 11.4 by a =
factor of weight/62.

If the goal of PK is publishing journal articles about pure science, =
your approach 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 allometrically-scaled models, I would support their use. =
But, Steve asked you to provide EVIDENCE for this and you failed to do =
you. You also cited Eleveld’s article. Although his manuscript =
did include one weight-normalized model, the allometric model required =
multiple additional terms to fit the data. In particular, that article =
(as yours) required a “maturation” term to describe =
younger patients. In other words, neither of these articles =
demonstrates that allometric models are sufficient to describe the range =
of sizes in humans. Had Eleveld added those extra terms to the =
weight-normalized model, it might have performed as well as the model he =

Over the past two decades, I have analyzed data from > 200 studies =
including many in infants and children. In many of these, I have =
compared weight-normalized and allometric (and, in adults, unscaled) =
approaches. In virtually all cases, the difference in fit between the =
weight-normalized and allometric approaches was trivial and often =
favored the weight-normalized approach. 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 instances, 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 allometric 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 <n.holford
> 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 over many years.
> I am aware that you wrote an editorial on this topic with Denis Fisher =
which you titled “Allometry, Shallometry!”. Having read =
your editorial and your comments I don’t think the implication =
that allometry is shallow is appropriate. On the contrary, I get the =
impression (see below) that you and Denis do not really understand the =
biological principles underlying allometry and seem to be unaware of the =
substantial literature supporting theory based allometry and its =
application in humans.
> Would your journal be willing to receive a rejoinder to your editorial =
with 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 <sshafer
>> 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 =
theoretical foundations for allometric scaling across species (e.g., =
Darveau, Nature, 2002; West, J Exp Biol. 2005). The allometric theory =
accounts for differences 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 =
> NH: Unfortunately, you repeat a common misunderstanding of allometric =
theory 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. Therefore the theory of West supports =
the use of the 3/4 exponent within species.
> SS:
>> Similarly, I am unaware of unambiguous data strongly supporting =
allometric scaling across the typical range of human weights.
> NH: I recommend that you read the paper by McCune et al. that formally =
tests the allometric theory prediction of an exponent of 3/4 for =
clearance based 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 reject the value of 3/4. Work with a drug where your =
expertise is renowned ( =
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 estimated 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 =
unambiguous data (and analysis) that falsifies the theory of allometry =
> SS:
>> As applied to human pharmacokinetics, I do not believe any theory =
supports allometric scaling.
> NH: As noted above there is nothing in the theory of allometry =
proposed by West that would mean it is not applicable to humans. If you =
do not want to 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, regardless of age, as being a single species and have sought =
integrated explanations of human clinical pharmacology. If you were =
aware of the paediatric pharmacokinetic literature then you would know =
of many publications supporting the use of a combination of theory based =
allometry for size plus empirical 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 =
maturation with age.
> NH: From the first commandment it necessarily follows that changes =
associated with age are not predictable from the allometric theory of =
West et al. There is no age related theory to predict quantitative =
changes. However, plausible biological understanding of maturation means =
that clearance will be zero (or at least very small) at conception and =
will approach a maximum when it will be indistinguishable from the =
mature adult value. So at least at the extremes there is a biological =
and quantitative prediction of maturation. Joining these extremes =
requires an empirical approach. A monotonic sigmoid 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 but 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 aware of any allometric theory that suggests that clearance in =
morbid obesity is best estimated using allometric principles. Between =
these extremes, scaling by weight is not very different than scaling by =
weight to the three quarters power.
> NH: Body composition contributes to body mass. Theory based allometry =
does not specify how differences in body composition affect allometric =
size. It is plausible however to propose that the size that is the =
driving force behind 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 determining allometric size. NFM is not =
predicted from allometric theory but is a biologically plausible =
extension of the theory of allometric size based 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 fat free mass is =
a better predictor of dexmedetomidine but obesity is associated with =
reduced clearance independently of allometric size based on fat free =
mass (Cortinez, Anderson et al. 2015). This demonstrates how the =
complexities of biology can be better understood based on a plausible =
theory of allometry. The theory may not be perfect but it is compatible =
with a very large number of observation studies in many domains. =
Investigation of other phenomena such as maturation and obesity is aided =
by building on allometric theory.
> 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 provides substantially better fits to the data than scaling by =
weight alone?
> NH: In addition to the large study of busulfan PK mentioned previously =
(McCune, Bemer et al. 2014)I suggest you look at the prediction of =
morphine clearance across the human size and age range using theory =
based allometry with maturation. Prediction of clearance in a large =
external data set was clearly better than other approaches including =
empirical allometry (Holford, Ma et al. 2012). Other published examples =
can be found in this review (Holford, Heo et al. 2013).
> SS:
>> I can point to many examples where it makes no difference. I can also =
point to many examples where investigators simply use allometric scaling =
without first seeing if allometric scaling was supported by the data.
> NH: This is often the case when sample sizes are small, weight =
distribution is narrow and power is small (Anderson and Holford 2008). A =
pragmatic approach given the challenges of falsifying allometric theory =
with small data sets is to assume it is useful. It is certainly better =
than using empirical 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 better than the simpler non-scaled model. If allometric =
scaling for human pharmacokinetics was “true” on first =
principles, as your comments imply, then the literature should abound =
with unequivocal examples.
> NH: If you know of examples of suitably powered studies which can also =
show they have accounted for other mass correlated factors that would =
confound 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 =
underpowered to truly detect the difference between an exponent of 3/4 =
and say an exponent 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 will 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 University
>> Adjunct Associate Professor of Bioengineering and Therapeutic =
Sciences, UCSF
>> =
>> PharmPK Home Page
>> Information about PK/PD Jobs can be found =
>> More information about my eBooks, including Basic Pharmacokinetics =
and Pharmacy Math, and now iOS and tvOS apps can be found =
>> 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 =
size and maturity in pharmacokinetics." _Annu Rev Pharmacol Toxicol_ =
*48*: 303-332.
> Anderson, B. J. and N. H. G. Holford (2009). "Mechanistic basis of =
using body size and maturation to predict clearance in humans." _Drug =
Metab Pharmacokinet_ *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_ =
> 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 propofol pharmacokinetics: derivation of a pharmacokinetic =
model." _Br J Anaesth_ *105*(4): 448-456.
> Eleveld, D. J., J. H. Proost, L. I. Cortinez, A. R. Absalom and M. M. =
Struys (2014). "A general purpose pharmacokinetic model for propofol." =
_Anesthesia 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 =
standard for babies and adults." _J Pharm Sci_ *102*(9): 2941-2952.
> Holford, N. H., S. C. Ma and B. J. Anderson (2012). "Prediction of =
morphine dose in humans." _Paediatr Anaesth_ *22*(3): 209-222.
> McCune, J. S., M. J. Bemer, J. S. Barrett, K. Scott Baker, A. S. Gamis =
and N. H. G. Holford (2014). "Busulfan in Infant to Adult Hematopoietic =
Cell Transplant Recipients: A Population Pharmacokinetic Model for =
Initial and Bayesian Dose Personalization." _Clinical Cancer Research_ =
*20*(3): 754-763.
> Schuttler, J. and H. Ihmsen (2000). "Population pharmacokinetics of =
propofol: 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 the origin of allometric scaling laws in biology." _Science_ *276*: =
> --
> Nick Holford, Professor Clinical Pharmacology
> Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A
> University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New =
> office:+64(9)923-6730 mobile:NZ+64(21)46 23 53 FR+33(6)62 32 46 72
> email:n.holford
> "Declarative languages are a form of dementia -- they have no memory =
of events"
> Holford SD, Allegaert K, Anderson BJ, Kukanich B, Sousa AB, Steinman =
A, Pypendop, B., Mehvar, R., Giorgi, M., Holford,N.H.G. =
Parent-metabolite pharmacokinetic models - tests of assumptions and =
predictions. Journal of Pharmacology & Clinical Toxicology. =
> Holford N. Clinical pharmacology = disease progression + drug =
action. Br J Clin Pharmacol. 2015;79(1):18-27.
Received on Mon May 23 2016 - 09:51:05 EDT

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