Re: Understanding allometry
Nick
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 (FFM).(19–21)
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 published.
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
Dennis Fisher MD
P < (The "P Less Than" Company)
Phone / Fax: 1-866-PLessThan (1-866-753-7784)
www.PLessThan.com
Quoted reply history
> On May 23, 2016, at 12:17 AM, Nick Holford <n.holford_at_auckland.ac.nz>
wrote:
>
> 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_at_stanford.edu> 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 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 SPECIES.
>
> 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 ( https://www.youtube.com/watch?v=gD7BZIl2uzc) 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 ( https://en.wikipedia.org/wiki/Karl_Popper)?
>
>
> 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
>>
>>
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>
> 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_ *doi:10.1007/s00228-015-1948-2*.
>
> 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." http://www.cognigencorp.com/nonmem/current/2008-September/0182.html.
>
> 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*: 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
> email:n.holford_at_auckland.ac.nz
> http://holford.fmhs.auckland.ac.nz/
>
> "Declarative languages are a form of dementia -- they have no memory
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>
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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. 2014;2(2):1023-34.
> Holford N. Clinical pharmacology = disease progression + drug
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>