Felipe,
In addition to the concerns raised by Jakob and Sebastien about
bootstraps (which I agree with) I would also like to ask what you mean
when you say you have measurements from 2 out of the 3 compartments of
the model:
"I am modeling some PK data using a linear 3-compartment model, in which
drug concentrations were measured in two of these compartments
simultaneously after i.v. dose."
Empirical compartmental models are used to describe the concentrations
in typically just one compartment e.g. central compartment where you
sample the blood. The other compartments are just descriptive and
usually have no physical reality that would allow you to claim you can
measure in that compartment. So where exactly are you making the
measurements of concentration?
Best wishes,
Nick
On 24/04/2013 1:29 a.m., Sebastian Frechen wrote:
Dear Felipe,
I totally argree with Jakob. Maybe just some more comments on the
bootstrap to support this.
Each estimator comes up with its own sampling distribution reflecting
the uncertainty for the obtained estimate given your data and model.
You can do assumption on this distribution, for example the arithemtic
mean as an estimate for the "true average in a population" follows in
general a normal distribution if the sample size is suffiently large
enough. However, this does not apply for every estimator! One of the
basic ideas of the bootstrap is now that you do not know the
underlying sampling distribution of your parameter estimate. But using
the non-parametric bootstrap method (sample from you dataset with
replacement), you construct this distribution (and it is not
necessarily Gaussian) by estimating your parameter in each of the
generated sample. This in turn gives you a fairly good feeling of how
precise your estimate is given your model and the sample size.
With respect to your volume: Have you tried fitting the data to one-
or two-compartment models?
How does the volume behave then? Why are you using a three-compartment
model?
Best regards,
Sebastian
------------------------------------------------------------------------------------
Dr. Sebastian Frechen
Department of Pharmacology, Clinical Pharmacology
Cologne University Hospital
-----------------------
Gleueler Str. 24
50931 Cologne
Germany
------------------------------------------------------------------------
*Von:* [email protected] [[email protected]]" im
Auftrag von "Ribbing, Jakob [[email protected]]
*Gesendet:* Dienstag, 23. April 2013 22:30
*An:* Felipe Hurtado; [email protected]
*Betreff:* RE: [NMusers] Right skewness in bootstrap distribution
Dear Felipe,
The distribution obtained from the (nonparametric) bootstrap
represents uncertainty in the population parameters, and the histogram
for V1 should _not_ be interpreted as a distribution of individual
parameter values. There are issues with relying on the nonparametric
distribution based on only eight subjects. The tail to the right may
be just due to one or two subjects with a larger central volume.
Otherwise (disregarding too few subjects in this specific example);
there is nothing wrong with a right-tailing uncertainty distribution.
In fact, it may even be expected when uncertainty is high and
parameter is restricted to positive values. You would obtain a similar
uncertainty distribution from the nonmem covmatrix by estimating
(typical) central volume on log scale. This should not change OFV, but
will alter the covmatrix.
It is difficult to comment on whether the Vc estimate is unreasonable
or not. If early observations are well predicted by the model, then
what amount is located in central compartment, and what amount is
available in the two peripheral compartment at these early time
points? If you do not understand how the model may describe the
observed data you could output these amounts in a table and
investigate disposition at these early time points. NCA extrapolations
to time zero may not agree, but that to me is mostly a theoretical
issue – it would be pointless to measure concentrations at the same
time as a (bolus) dose.
Best regards
Jakob
*From:*[email protected]
[mailto:[email protected]] *On Behalf Of *Felipe Hurtado
*Sent:* 23 April 2013 19:57
*To:* [email protected]
*Subject:* [NMusers] Right skewness in bootstrap distribution
Dear NONMEM users,
I am modeling some PK data using a linear 3-compartment model, in
which drug concentrations were measured in two of these compartments
simultaneously after i.v. dose. The model fits the data reasonably
well, and all parameters seem reasonable except for V1 (volume of the
central compartment, which occurs to be the dosing compartment).
Estimate for V1 is very small, what does not make sense considering
the average dose given and the mean Cp0 calculated by NCA. This result
suggests drug distribution is restricted to plasma, however it was
observed extensive distribution to tissues. IIV for V1 is relatively
small (19.6%, n=8 subjects). The histogram for V1 (nonparametric
bootstrap with 100 replicates) shows a right skewed distribution with
the presence of a subpopulation and broad confidence interval (5th
percentile tends to zero).
I tried to solve this by fixing V1 to a reasonable value, running the
model to calculate all other parameters, and then changing the initial
estimates to these parameters in order to recalculate V1, but it turns
out to the same small estimate.
Any suggestions will be appreciated! Thanks in advance.
Felipe
--
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(7)85 36 84 99
email: [email protected]
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
