Huadong,
Thanks for your further comments on the allometry debate. As you know, I prefer
to put my faith in the theoretical allometric models to predict changes in CL
and V as a function of body weight. I am not convinced of any exceptions to
this allometric model. Those who claim deviations have usually applied
allometric scaling quite naively without considering all other covariates e.g.
species, protein binding, renal function, age, abnormal body composition and so
on. It is really very important to understand that allometry ONLY predicts the
changes of CL and V that are associated with changes in normal body weight.
There is a special and important case of trying to understand how clearance
changes as babies grow into children and eventually into adults. In this case
the effects of changes in weight and changes in maturation of organ function
with age can be separated by proposing separate models using weight and age as
covariates. It has been my own preference to apply the theoretical allometric
model predictions to account for weight and then try to explain the remaining
difference using a function of age. The age models are quite empirical because
unlike allometry there is no guiding theory to specify the functional form. I
like to use an age function that asymptotes at an adult value so that the
overall weight and age model is consistent across the human age and weight
range.
If it is your own preference to apply empirical weight and age models then that
is your choice but I like to put my faith in plausible and experimentally
tested theory rather than make up ad hoc empirical functions if it can be
avoided. By using a consistent model for weight effects it is possible to
search for patterns of age/maturation effects across different drugs with
different elimination pathways. Because the weight model is consistent there is
then some hope that some broader patterns of age related changes in clearance
can be identified.
Nick
> Hi Jakob,
> Thanks for the comments and reference. I agree with your analysis on the
> volume, and also on the general thoughts by
> Green and Duffull on the use of body size descriptor.
>
> About allometry: there is no doubt that there must be some "consquences"
> following the changes on body size. And this
> is maybe called "allometry law", although I don't know where and when the
> term "allometry law" was first defined and
> agreed. The "power law" (or (1/4)^n), however, should not be so readily
> accepted, especially when we are talking about
> INDIVIDUAL compounds. Actually V is not too bad for most cases; CL is the bad
> boy. The situation of using
> allometrically based approach for scaling CL in the real world is worse than
> what have been seen from publications (I
> hope this will be agreed, esp. from those working in the industry). Obviously
> we have had "selection" on reporting and
> analysis of the applications of allometry in PK, although this bias has been
> realized, esp recently.
>
> I realized it may be argued that the overall observations do indicate that
> the exponents for CL tend to have a central
> tendency at 0.75, which is the reason, I think, for using this value in many
> modeling works. But I think it should be
> awared that application of allometry in modeling the known data (for example,
> infant and adult' data are known) and
> making predictions from known to unknown are totally two different stories.
> Let's look at the latter first. Because there
> are so many confounding factors (esp for CL), there exist great uncertainty
> in extrapolating the allometric relationship
> obatined from animals to human values, and so many times we have to cross our
> fingers to make a prediction. Therefore,
> it is not a bad idea to fix an exponent at a "typical" value. However, for
> the former situation when we do have the known
> data from both human and animals, or adults and infants, I don't see the
> strong reasons (the potential confoundings with
> others may be one) for fixing the value in moldeing, which has two potential
> problems. Let me use the infant and adult as
> an example. First, it should be recognized that Nick's model itself has no
> problem,and age proved to be signifiant factor
> that can explain the remaining difference after BW. But let's assume a
> situations when the data of age is blind to you
> (whatever reasons.....) or age is NOT a good "helper", which might be true
> for other drugs, then there is a prolbem with
> fixing the exponent, because you have no "helper" to correct the potential
> inaccurate allometric relationship. The second
> pitfall about fixing the exponent is that we may lose an opportunity in
> accumulating our knowledge. There have been rare
> reliable analyses on the allometric relationship between infant and adults,
> for example. We can ask questions such as
> "Is 0.75 the best" etc, but we lack the answer because we don't have
> sufficient knowledge that have been accumulated.
> 0.75 works for many cases, but this is not saying it's working best. If we
> can accumulate such information by examing the
> individual cases and learning during this process, then some day we may be
> able to find an "optimized" value or rules (I
> cannot say "best" because this word seems to be a mission impossible). For
> example, for this class of compounds, the
> expnent is A; for that the compounds with this type of chemical structure,
> the exponent is B; for antibody, it is C; etc...
> This is what we finally want. But if no such effort is to be taken, I am
> afraid we will be still standing at the same place
> after many years.
> I can think of an extreme bad example of using allometry. The compound is
> UCN-01. By allometrically based approach,
> the prediction was off by more than 3000-fold in humans ( J Clin Pharmacol.
> 2006 Apr;46(4):398-400.). If the
> investigator did not have plamsa biniding data (actually the binding data
> were obtained later on when such huge
> difference in PK across species was observed), then modeling the allometric
> relationship with fixed exponent when both
> human and animal data were available, will be a problem.
>
> Again, I am not against the allometry law; I am just cautious in accepting
> the (1/4)^n law. For predicting purpose, fixing
> an exponent at a value that we have most confidence in is a good approach.
> But for modeling the known data, there may
> be some worth in putting some effort on finding the "optimized" exponent for
> individual cases, but I understand
> sometimes this will be limited to data size and potential confounding
> effects, but this would happen equally to other
> covariates as well (in this sense, we may not have "discrimination" on BW).
>
> Just some thoughts.
>
> Thanks
>
> Huadong
>
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:[EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/