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We are interested in doing a study of an approved drug in infant
subjects. The age range is 2 months to 2 years and this will be a
single dose study. The drug of interest is an antibiotic and has been
studied in adult patients as well as patients between 2-17 years. The
drug is renally excreted.
I would apprecite input in understanding the infant physiology a
little better; specifically in the age-range of 2 months-2 years. How
well developed are their kidneys and what are some of the things to
keep in mind while calculating doses in patients this young.
Obviously, these will not be healthy subjects. How does one go about
calculating the doses for these subjects?
Thanks
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The following message was posted to: PharmPK
Dear Martin
I think you need to have a look at the following papers.
Anderson BJ and Holford NHG (2008) Mechanism-Based Concepts of Size and
Maturity in Pharmacokinetics. Annual Review of Pharmacology and
Toxicology
48:303-332.
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.
Hope you find these useful.
Regards
Masoud
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Martin,
I suggest you look here for a description of how glomerular filtration
rate matures in youg children:
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. 2009;24(1):67-76.
These two recent reviews should give you some ideas about dosing in
children:
Anderson BJ, Holford NH. Mechanism-based concepts of size and maturity
in pharmacokinetics. Annu Rev Pharmacol Toxicol. 2008;48:303-32.
Tod M, Jullien V, Pons G. Facilitation of drug evaluation in children
by population methods and modelling. Clin Pharmacokinet. 2008;47(4):
231-43.
Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
n.holford.aaa.auckland.ac.nz
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
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The following message was posted to: PharmPK
Having read the other responses in this email thread, I think that there
other sources of information:
Mahmood I. Prediction of drug clearance in children: impact of
allometric exponents, body weight, and age. Ther Drug Monit. 2007
Jun;29(3):271-8.
Mahmood I. Prediction of drug clearance in children from adults: a
comparison of several allometric methods. Br J Clin Pharmacol. 2006
May;61(5):545-57.
I am at present involved with a study of a renally cleared drug in the
age group 0 - 2 years. Mahmood proposed that allometric scaling in the
age range 0 - 1 year gives an exponent of 1 which means that doses can
be administered on a mg/kg basis. In the study that I am supporting,
the dose administered to 1 year old children is X mg/kg and so this was
set as the starting dose for the study. My suggestion would be to divide
the study into cohorts covering smaller age ranges: 2 - 4 months, 5 - 9
months, 10 - 12 months, 1 to 2 years. Your starting dose in mg/kg would
be the approved dose given to 2 year old subjects. If you have a
therapeutic range of exposures covering efficacy and safety, you could
recruit into the cohorts sequentially, collect PK data and assess
whether the correct dose is being given so that you obtain the exposures
that you want. You would not need to recruit the whole cohort before
enrolling in the next lower cohort.
The fact that renal function develops over the first year of life should
not be a problem with careful monitoring of the subjects. Performing
this type of study in a developing child is not easy so I wish you good
luck.
Hope this makes sense
Brian
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Brian,
The difference between the empirical allometry of Mahmood et al. and
theoretical allometry (West et al 1999, Savage et all 2004) is that
the empiricists have to propose a different exponent on an ad hoc
basis (as you illustrate with an exponent of 1 for age 0-2 y) while
the theoretical approach predicts the dose based on size over the full
range of sizes (in humans and across species) and recognizes other
factors may also need to be included (e.g. body temperature, age).
The ad hoc empirical allometrist fails to distinguish between size and
maturation (as you illustrate by using age as a criterion for an
allometric exponent).
Allometry is primarily concerned with how structure and function
change with size -- not age. Factors other than size are also
important in biology e.g. maturation during foetal life and in early
childhood. A rational approach to pharmacokinetics can be based upon
distinguishing size and maturation. Muddling up size and maturation is
not a good basis for understanding and prediction.
Anybody can propose mg/kg doses for specific ad hoc groupings and they
will be in general quite reasonable and practical as all trial and
error approaches must eventually become. The power of science (e.g.
theory based allometry) is that it can predict things without ad hoc
empiricism. There is no need to reinvent the wheel for every drug that
comes along and imagine it is somehow special and needs a new
allometric coefficient.
1. West GB, Brown JH, Enquist BJ. The fourth dimension of life:
fractal geometry and allometric scaling of organisms. Science.
1999;284(5420):1677-9.
2. Savage VM, Gillooly JF, Woodruff WH, West GB, Allen AP, Enquist
BJ, et al. The predominance of quarter-power scaling in biology.
Functional Ecology. 2004;18(2):257-82.
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
n.holford.-a-.auckland.ac.nz
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
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The following message was posted to: PharmPK
Theoretical allometry is a mere theory and an incorrect theory. It is
surprising that Holford cites West and Savage et al's work, yet fails to
recognize and acknowledge the criticism of West and savage et al's work
by other experts in the field (1-5).
Here is what Glazier (3) described in his paper.
The '3/4-power scaling law' of metabolic rate is not universal, either
within or among animal species. Significant variation in the scaling of
metabolic rate with body mass has been observed not only for animals but
for uni-cells and plants. These variations can be related to taxonomic,
physiological, and/or environmental differences, which have not been
adequately explained by existing theoretical models. In order to
completely understand metabolic scaling, one will require the
identification of both proximate (functional) and ultimate
(evolutionary) causes. Ontogenetic changes in the metabolic intensity of
four component processes (i.e. growth, reproduction, locomotion, and
heat production) appear to be important in these different patterns of
metabolic scaling. The scaling of metabolism is not the simple result
of a physical law, but rather appears to be the more complex result of
diverse adaptations evolved in the context of both physico-chemical and
ecological constraints".
In an article White et al (4) maintain that:
"The lack of support for a single exponent model suggests that there is
no universal metabolic allometry and represents a significant challenge
to any model that predicts only a single value of b" (b is the
allometric exponent).
Packard and Birchard (5) describe that:
"We found that a straight line fitted to logged data for the basal
metabolic rate (BMR) of mammals ranging in size from a 2.4 g shrew to a
3672 kg elephant does not satisfy assumptions underlying the analysis
and that the allometric equation obtained by back-transformation
underestimates BMR for the largest species in the sample. Thus, the
concept of 3/4-power scaling of metabolic rate to body mass is not well
supported because the underlying statistical model does not apply to
mammalian species spanning the full range in body size. Our findings
have important implications with respect to methods and results of other
studies that used the traditional approach to allometric analysis".
Interestingly, Holford shuns from all the criticism of the so-called
theoretical allometry and portraits one-sided picture of a highly
controversial issue that has not been accepted by many experts in the
field.
Logically it is difficult to perceive that the exponent of allometry for
a given parameter will revolve around a fixed number. Therefore, one has
to clearly understand the nature of the exponents (which Holford
incorrectly mentions as the coefficient of allometry) of the allometry.
The exponents of the allometry have no physiological or biological
meaning. The exponents of allometry widely vary and will depend or
change with the number of species in the scaling (even for the same
drug). Holford fails to recognize this data-driven fact and continues
to insist on a fixed exponent which so far has been proven wrong. Due
to the variable nature of the exponent, a fixed exponent of 0.75 or any
other arbitrarily selected exponent fails to predict human drug
clearance in most of the instances as compared to an allometric model
developed for a given drug. In a recently published paper, through
comparative analysis, I have shown the inappropriateness of exponent
0.75 for the prediction of human drug clearance (6). Off course,
depending upon the species, there will be many drugs whose exponents
will be 0.75 or around but this does not justify the use of a fixed
exponent for all drugs. One should also recognize that basal metabolic
rate and clearance (as defined in pharmacokinetics) are two unrelated
terms and the application of exponent 0.75 obtained from basal metabolic
rate against body weight across dozens of different kinds of species to
predict human drug clearance from 3 to 4 well controlled lab species is
simply illogical and not surprisingly, results in highly erratic
prediction.
The notion provided by Holford that the theoretical approach "predicts
the dose based on size over the full range of sizes (in humans and
across species)" is entirely incorrect. Despite all his arguments (that
is simply citing West et al's work and failure to describe the works of
critics of West's work) in favor of a fixed exponent of 0.75, Holford
has never provided any comparative data to demonstrate that the
so-called theoretical allometry predicts the drug clearance or dose in
children better than the empirical allometric approach as he mentions
"in humans and across species". On the other hand, I have shown by
comparative data analysis that a fixed exponent of 0.75 predicts
clearance in children under 2 years of age with incomprehensible error
(can reach even more than 1000%). In older children, 0.75 does provide
more accurate prediction of clearance but the prediction remains
inferior to the empirical allometric model developed for each and every
drug (7, 8, 9). Furthermore, the application of arbitrary selected
exponents of 0.8 and 0.85 provided the same degree of prediction
accuracy or error as seen with exponent 0.75 (7). This belies the
notion that 0.75 is the best exponent for the drug clearance in
children. In other words, If Holford thinks that his aforementioned
view is correct then he should demonstrate this by comparative
(theoretical vs empirical allometry) data analysis rather than
constantly citing West and Savage's works which have been heavily
criticized.
Maturation is a physiological process and any model which does not
incorporate physiological parameters such as blood flow, enzymatic
activity, the processes of renal elimination and other physiological
parameters across age is not a maturation model. A plot of age against
clearance is not a maturation model because both weight and age are
physical not physiological parameters. Holford talks about
distinguishing size and maturation and recognizes that an allometric
plot of age and a PK parameter does not distinguish between size and
maturation. Yet, amazingly, Holford in association of others has
proposed a maturation model for morphine (10) which is based on a
sigmoidal plot of age against clearance. This proposed model of Holford
and associates by no means is a maturation model. This model's
limitation needs to be understood. Firstly, it will only predict
clearance in the children within the age group from which this so-called
maturation model has been developed. Secondly, this model's only
function appears to be correcting the substantial error introduced by
the illogical use of exponent 0.75. In other words, one has to
construct separate so-called maturation model for each age group (it
seems to me that Holford fails to recognize this and considers this
model as a universal model). One should also recognize the weakness and
uselessness of this model. The model is weak because it can not be used
outside the age range from which it has been developed and useless
because if one does not use the fixed exponent of 0.75 on clearance then
there is no need for this model. Therefore, Holford's argument (without
any data support) that using so-called theoretical allometry and a
maturation model is the best way to predict clearance across all age
groups is incorrect. In essence, the proposed so-called maturation model
with a fixed exponent of 0.75 is not universal and this belies Holford's
view of usefulness of theoretical allometry.
On the other hand, a simple allometric model, developed using body
weight and clearance from few children data (gestational age 24 to 40
weeks) provided an excellent prediction of morphine clearance in this
age group. The data was validated on 68 children (within the same GA)
and the root mean square error by allometric model, fixed exponent 0.75,
and the maturation model was 64%, 1205%, and 102% of the mean,
respectively. The error (1205%) produced by the fixed exponent of 0.75
indicate the real usefulness of theoretical allometry. I will discuss
in details the weakness and uselessness of the so-called maturation
model across age groups and the use of fixed exponent of 0.75 in the
children for the prediction of clearance in an upcoming publication.
I suggested the first-in-children (under 2 years) dose based on the
exponents observed during my data analysis (7-9). This was not pulled
from the air or was not an arbitrary suggestion. I observed that 0.75
was an inappropriate exponent for dose selection in very young children
and a better approach was just using mg/kg which was equal to exponent
1. At that time I did not have enough data to suggest any other
exponent than 1 (basically mg/kg) but now I have more data to suggest
different exponents in children in different age groups which will be
suggested in an upcoming manuscript.
The statement by Holford that "The power of science (e.g. theory based
allometry) is that it can predict things without ad hoc empiricism" is
incorrect. Holford has never provided any comparative data to support
his power of science approach. My comparative data analysis (both for
interspecies scaling and pediatric allometric model) has clearly shown
the absurdness of a single exponent theory or theoretical allometry
(which remains a theory with no practical application). As mentioned
earlier, Holford and colleagues proposed so-called maturation model will
require different models for different age groups. His model is not
universal hence all his claims regarding theoretical allometry are
incorrect.
If Holford thinks that the theoretical allometry is of practical value
and is a correct theory then he needs to show by comparative data
analysis (as I have done by comparative analysis) that theoretical
allometry is sound and more useful then empirical allometry. In other
words, he should demonstrate that the PK parameters can be predicted
with reasonable accuracy using a fixed exponent or theoretical allometry
as compared to allometric models developed with different allometric
exponent for individual drugs. Furthermore, he should also demonstrate
that there is a universal model for children of all age groups for the
prediction of PK parameters based on the theoretical allometry. Unless
he does this, his views are mere theories and of no practical value.
In short, the concept of theoretical allometry is baseless and of no
practical value because a single exponent can not provide sound and
acceptable results. Allometry can not be divided as theoretical and
empirical; allometry is empirical and will remain empirical and for
every drug whether it is interspecies scaling or prediction of a PK
parameter in children, it will require a separate exponential model
based on drug or age. There is no universal allometric model or
exponent for all the drugs as well as there is no universal model for
children of all age group for a reasonably accurate prediction of a PK
parameter. If Holford disagrees with this statement then he should
demonstrate it by comparative data analysis.
Iftekhar Mahmood, Ph. D.
1. Taylor CR, Maloiy GM, Weibel ER, Langman VA, Kamau JM, et al. Design
of the mammalian respiratory system III. Scaling maximum aerobic
capacity to body mass: wild and domestic mammals. Resp Physiol
1981;44:25-37.
2. Nawaratne S, Brien JE, Seeman E, Fabiny R, Zalcberg J, et al.
Relationships among liver and kidney volumes, lean body mass and drug
clearance. Br J Clin Pharmacol 1998;46:447-52.
3. Glazier DS. Beyond the '3/4-power law': variation in the intra- and
interspecific scaling of metabolic rate in animals. Biol Rev Camb
Philos Soc 2005;80:611-62.
4. White CR, Cassey P, Blackburn TM. Allometric exponents do not
support a universal metabolic allometry. Ecology 2007;88: 315-23.
5. Packard GC, Birchard GF. Traditional allometric analysis fails to
provide a valid predictive model for mammalian metabolic rates. J Exp
Biol. 2008;211(Pt 22):3581-7.
6. Mahmood I. Application of fixed exponent 0.75 to the prediction of
human drug clearance: An inaccurate and misleading concept. Drug Metab
& Drug Interaction 2009; 24,57-81.
7. Mahmood I. Prediction of drug clearance in children from adults: a
comparison of several allometric methods. Br J Clin Pharmacol
2006;61:545-57.
8. Mahmood I. Prediction of drug clearance in children: Impact of
allometric exponents, body weight and age. Therap Drug Monitor
2007;29:271-8.
9. Mahmood I. Pediatric pharmacology and pharmacokinetics, 2008, Pine
House Publishers
10. Anand KJ, Anderson BJ, Holford NH, Hall RW, Young T, Shephard B,
Desai NS, Barton BA; NEOPAIN Trial Investigators Group. Morphine
pharmacokinetics and pharmacodynamics in preterm and term neonates:
secondary results from the NEOPAIN trial. Br J Anaesth.
2008;101(5):680-9.
The views provided in this e-mail are of author (Iftekhar Mahmood) and
is not based on the official policy of the FDA or is supported by the
FDA.
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The following message was posted to: PharmPK
I read with great interest the posting on allometric scaling laws.
However, I have some concerns about assertions regarding the nature of
science in the context of theory, empiricism and prediction.
Science by consensus has never been an appropriate way to think about
new ideas - yet - your comments indicate that more experts refute this
etc. without further development on what this means to the
understanding of the system. Refutation requires that we re-examine
the theory but I don't see how the stated refutation helps us
understand the underlying system better. It seems to be empirical
evidence that we need to consider that other factors may be involved
than just the optimization of flow based nutrient delivery and waste
removal. It is important, therefore, to systematically examine what
those factors may be.
The 3/4 law comes from fundamental assumptions about optimization of
delivery of nutrients and removal of wastes under fractal
organizational assumptions. These assumptions really take into
account only something that will be maximally removed when delivered
by whatever flow mechanism is present in the branching tree model that
they used. Fractal organization describes many biological processes
that involve heterogeneity.
I also have a concern with the assertion "well we predicted it much
better with unique exponents etc." - to me this is not the point. The
point is that we probe the system with the fractal assumptions and if
there is deviation that this is accounted for by different factors
(many of which are listed in your message). This means that one needs
to probe this to understand what is going on better and really
generate understanding - not just prediction (to paraphrase David
Deutsch).
The assertion of the uselessness of theoretical approaches needs to be
carefully considered - knot theory was supposed to be "useless" and
"just for fun" and it turns out explain the DNA machinery of
transcription and translation unreasonably well. The mathematician
Hardy boasted about how his math was going to be of totally no
practical use - it has become a critical part of understanding
inheritance (hardy-weinberg equilibrium).
Just predicting is not really the whole story. Having a "probe" to
examine a system can yield much more in the understanding of the
system. With greater understanding of the system, one is better
equipped to predict outside the operating conditions where the
typically data are generated.
Robert R Bies Pharm.D.Ph.D.
Assistant Professor of Pharmaceutical Sciences and Psychiatry
Schools of Pharmacy and Medicine
University of Pittsburgh
805 Salk Hall
3501 Terrace Street
Pittsburgh, PA 15261
rrb47.at.pitt.edu
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I'd like to comment on some of the remarks made by Dr Mahmood on this
topic.
First of all, it seems clear to me that Dr Mahmood (with others that
he cites) have different belief systems from my own. Belief is not
usually something that can be changed by data but it can be modified
by discussion and appreciation of different viewpoints.
My belief system is based on a quantitative, biologically based
allometric theory (most clearly described by West et al. 1999, Savage
et al. 2004) to predict how body function and structure changes with
body size. This means I have a theoretical belief system.
Dr Mahmood does not accept this allometric theory and indeed dismisses
the idea that a theory can be useful by describing it as a 'mere
theory'. He puts his faith in observed data - I will refer to this as
the empirical belief system.
Let me try to explain the differences in belief systems by referring
to a very old clash between theory and empirical beliefs.
For the empiricist it is quite clearly obvious that the sun revolves
around the earth. All of us can easily see this happening every day.
This is called the geocentric viewpoint because the earth appears to
be the centre of the universe. It is entirely data based but sometimes
is 'explained' by invoking one or more Gods who operate the mechanism.
Copernicus developed a theory of planetary motion which explains a
large number of subtle observations relating to relative motions of
the planets, the stars and Helios (our solar system star). This is
called the heliocentric viewpoint because the sun now appears to be at
the centre. Much later the American astronomer Hubble showed by
mathematical theory and specialized observations at the Mt Wilson
observatory that the sun was just part of a galaxy within the universe
whose size and rate of expansion he was able to predict -- so the
centre of the universe moved again. This shows how theories can grow
and evolve.
You can choose your own belief system (geocentric, heliocentric,
universal) and live an ordinary life without having to worry too much
if you are right or wrong. However, I believe in the power of physical
theories to help explain what we observe and lead us to deeper
insights into how the physical world operates.
It is for this longer term reason that I advocate a theoretical
allometric model to predict the contribution of size to
pharmacokinetic parameter differences between and within species.
There are of course numerous other factors apart from size that will
lead to differences e.g. age, species, metabolic enzyme pheno/
genotype. Some of these, especially age, are very hard to pose in a
theoretical framework because age is really nothing more than time and
time itself is not an explanation of why or when maturation occurs. In
this case one may have to resort to an empirical description until a
good theory comes along (see below).
Empirical allometry typically ignores the essential principal of
theoretical allometry that it only explains how things change with
size. Dr Mahmood illustrates this confused viewpoint by implying that
the empirical model used to describe maturation from the very youngest
living humans upto young adults is somehow part of a 'universal
model'. Allometric theory does not predict how other factors such as
this may operate.
Given a theory of how size influences biology it is possible to
explore how other factors may operate -- conditional on the allometric
theory for size. The Copernican theory was extended by Galileo, Newton
and Hubble to bring in other factors apart from the relative location
of the planets and stars.
Theoretical allometry has been used as a starting point to allow
models ('theories') for other factors such as body composition
(closely related to what is meant by size) and age (maturation) to
predict changes in glomerular filtration rate over a wide range of
size, composition and age (see Rhodin et al. 2009). Note that this
publication does not ignore the empirical perspective. Indeed, as
expected, the goodness of fit with an empirical allometric model was
better compared with the theoretical allometric model but not
sufficiently different to make any visible difference in describing
the observations.
There is an interesting statement on the Wikipedia page describing
heliocentic vs geocentric views:
http://en.wikipedia.org/wiki/Copernican_heliocentrism
"Copernicus' system was not experimentally better than Ptolemy's
model. Copernicus was aware of this and could not present any
observational "proof" in his manuscript, relying instead on arguments
about what would be a more complete and elegant system."
Even the Copernican theory was recognized to be no better at the time
than the geocentric Ptolemaic predictions but the Copernican theory
was able to evolve and lead to major breakthroughs in understanding.
So Dr Mahmood can rest assured that his empirical approach may fit the
data better than a theoretical approach but explaining how these
differences arises comes from having a theory. It is this kind of
science I like to believe in.
Nick
West GB, Brown JH, Enquist BJ. The fourth dimension of life: fractal
geometry and allometric scaling of organisms. Science. 1999;284(5420):
1677-9.
Savage VM, Gillooly JF, Woodruff WH, West GB, Allen AP, Enquist BJ, et
al. The predominance of quarter-power scaling in biology. Functional
Ecology. 2004;18(2):257-82.
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. 2009;24(1):67-76.
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
n.holford.at.auckland.ac.nz
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
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