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Hi All,
I'm wondering if there is a way to fix the residual error in Phoenix NLME?
Background: I'm trying to analzye animal PK data collected using
destructive sampling method(1 sample per subject). And fixing the residual
error would enable me to explore the BSV of PK parameters.
Thanks!
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Yes you can!
In the structure tab next to the Residual (where you select additive, multiplicative, etc) you
should see a check box for freeze - this will freeze residual error.
If you are using a textual model you can also freeze the error by adding 'freeze' as such:
error(CEps(freeze) =)
Regards,
Devin Pastoor
Research Scientist
Center for Translational Medicine
University of Maryland, Baltimore
www.ctm.umaryland.edu
Pastoor, Devin
--
Hi,
In edit as textual mode, you can change the code to :
error(CEps (freeze) = 0.12)
Hope it helps.
Thanks
Shailly
www.ctm.umaryland.edu
Shailly Mehrotra
--
If you mean FIX in the NONMEM-like sense of setting it to a given user-specified value as opposed to
determining it through a likelihood optimization -
PHOENIX uses the terminology "freeze" for that and there is an option in the UI where you input the
initial eps value to do just that.
If you want to do it manually in the PML language, then for example to freeze(or fix) EPS1 to 1
looks like
error(EPS1(freeze) = 1)
Bob Leary
Bob Leary
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Hi David,
Thanks!
Continuing on the question of dealing with destructive sampling data(one
sample per animal) with PopPK method, I also found a very interesting paper
on using resampling methods to estimate PK parameters by generation of
"pseudoprofiles" of PK data (which is composed of e.g. 1000 full PK profile
over 7 time points):
Mager H, Göller G.Resampling methods in sparse sampling situations in
preclinical pharmacokinetic studies.J Pharm Sci. 1998 Mar;87(3):372-8.
The authors used this method to estimate AUC, CL, t1/2 etc.
non-compartmental PK parameters. I'm wondering if this method can be
extended to compartmental PK parameters (K12, K21, alpha, beta) estimation
or even for more complicated PK/PD model parameters given PD data resampled
at the same time.
Thanks!
Regards,
Jie
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Dear Jie,
Maybe I am misunderstanding your question, but development of Pop PK methodologies (ie NLME
modeling) was specifically designed for the issue of sparse sampling! As such, assuming you have an
appropriate experimental design (ie you can't determine if it is a one vs two compartment model if
you only have sampling at ~ Cmax and terminal phase) compartmental parameters can be obtained
regardless of whether samples were obtained through destructive sampling of many individuals or
sparse sampling of some or rich sampling of few...etc. For example getting 6 concentrations .at. 8 time
points should give similar results if you get 1 destructive sample x 48 individuals vs 2 samples x
24 individuals vs 4 samples x 12 individuals....
To put it more concisely - it "shouldn't" matter whether you've obtained your concentration-time
profile via destructive sampling or by sparse/rich sampling of individuals. It should handle all
scenarios. As to how precisely you can estimate the parameters is another matter :-)
While we're on it - if you are going for a compartmental approach I'd recommend using physiological
parameters (CL/V) rather than micro/macro constants due to ease of interpretation!
Best Regards,
Devin Pastoor
Research Scientist
Center for Translational Medicine
University of Maryland, Baltimore
www.ctm.umaryland.edu
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Hi,
I think this part of Devin's response needs some further clarification
about what is an appropriate experimental design:
"assuming you have an appropriate experimental design (ie you can't determine if it is a one vs two
compartment model if you only have sampling at ~ Cmax and terminal phase) compartmental parameters
can be obtained regardless of whether samples were obtained through destructive sampling of many
individuals or sparse sampling of some or rich sampling of few...etc."
NLME methods typically have two levels of random effects -- random variability of parameters across
subjects and random residual variability around observations. The original question for this thread
was about a special design -- one observation per subject -- which cannot distinguish the random
variability across subjects from the residual variability around observations. In this case, one
approach is to assume a model and parameter(s) for the residual error variability, fix (aka
'freeze') the residual error parameter(s) and then estimate the random variability across subjects
under some structural model (e.g. a compartmental PK model). Thus the destructive sampling design is
not really interchangeable with designs with more than observation per subject as Devin seems to
imply:
"For example getting 6 concentrations .-at-. 8 time points should give similar results if you get 1
destructive sample x 48 individuals vs 2 samples x 24 individuals vs 4 samples x 12 individuals...."
You will not get similar results in the destructive sample case without
an appropriate assumption about the residual error. That assumption
rests on what other information you have from other experiments.
I would also like to comment that NLME methods were not developed for
the sparse sampling case. They were applied to sparse sampling in
clinical settings and following that many people assumed that any kind
of sparse data design would be useful. There are however no free
lunches. Sparse data designs produce sparse results. If you want to
really learn something from using modelling you should use optimal
design methods so that you can appreciate when sparse designs are too
sparse to be useful. A rule of thumb that I try to follow is to have at
least as many observations per subject as you have parameters in the
model that you are interested in taken at times that are informative
about those parameters.
Nick Holford
--
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
email: n.holford.at.auckland.ac.nz
http://holford.fmhs.auckland.ac.nz/
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Hi Devin,
Thanks for your kind reply!
Sorry I may have confused you a little bit regarding to the question. From
previous discussion and references, I understand that popPK is a useful
method to deal with destructive sampling data(one per sample) by fixing the
RUV.
In addition, another interesting re-sampling method is also proposed to
estimate the PK parameters via bootstrapping for destructive sampling data.
H. Mager & G. Goeller, J. Pharm.Sci. 87, 372-378 (1998)
The method(Pseudoprofile-based bootstrap) is illustrated as:
1) resample with replacement at one concentration at each time point
2) construct a pseudoprofile of matrix [ncol=number of time points,
nrow=bootstrap times], e.g. matrix [ncol=7, nrow=1000]
3) calculate target parameter from each row of full time profile data, e.g.
1000*T1/2
4) draw 2000 (number of animals per time point*T1/2) from step 3 and obtain
location parameter(mean or median) to get 2000*T1/2(mean of 3 animals)
5) estimation of T1/2 and its distribution
In summary, pseudo-full profile PK data is generated via re-sampling,
"individual" parameters are then calculated for each round of sample and
parameter distributions are estimated via a 2nd round of bootstrapping.
My question is whether the parameters estimated above are only constrained
to NCA parameters such as AUC and CL? How about parameters from 2-CMT or
PK/PD data models with more complicated functions?
I imagine people prefer the PopPK method or simple naive-pooled data
method, but just wondering if re-sampling is a 3rd reasonable way for
analysis of sparse data.
Thanks!
Regards,
Jie
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Nick,
Thank you very much for the correction, I jumped a little ahead of myself. I think I should
rephrase...
Jie's initial question was regarding the ability to obtain compartmental parameters from data
gathered via destructive sampling. To that regard, I presume this should be possible using a naïve
pooled technique to get an estimate of 'population' level parameters regardless of destructive vs
sparse sampling.
As you pointed out, without some prior information about one level of the random effects hierarchy,
it would most likely not be feasible to estimate both population and individual level parameters as
provided NLME.
One question I do have, you say:
> A rule of thumb that I try to follow is to have at least as many observations per subject as you
> have parameters in the model that you are interested in taken at times that are informative about
> those parameters.
>
I won't argue with more observations per subject being preferential, but given the same number of
total observations, do you really feel your results will be so skewed as you decrease the # of obs
per individual while increasing the # of individuals.
For example, if you had an experimental design where due to the invasiveness of the procedure or
contamination you could only take 2-3 samples per individual - would the end results of your model
fit be so different than if you had half the number of individuals but 4-6 samples per individual.
I can see where this could potentially present identifiability issues with high variability - be it
residual or BSV, I am just wondering if there is a 'threshold' in which the sparser designs become
significantly more biased.
I guess nothing a few simulations couldn't help elucidate :-)
Devin Pastoor
Research Scientist
Center for Translational Medicine
University of Maryland, Baltimore
www.ctm.umaryland.edu
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Devin,
You wrote:
> To that regard, I presume this should be possible using a naïve pooled technique to get an
> estimate of 'population' level parameters regardless of destructive vs sparse sampling.
It is not really relevant that sampling is destructive. What is relevant
is the number of observations per subject. It is quite possible to have
only one sample per subject without destroying the subject. The naive
pooled method can be applied with any number of samples per subject but
by definition the method does not distinguish between subject
variability (BSV) in the parameters. If BSV is small relative to
residual unidentified variability (RUV) then good estimates of the
population parameters may be obtained with a single observation per
subject. This is quite often seen when studying effectively cloned
non-human species such as laboratory mice. This method is the natural
alternative to fixing the RUV to some value and using single
observations per subject to estimate BSV.
You also asked:
> I won't argue with more observations per subject being preferential, but given the same number of
> total observations, do you really feel your results will be so skewed as you decrease the # of obs
> per individual while increasing the # of individuals.
It depends what result you are interested in. A study with 10
observations and 3 structural parameters in 6 subjects is richly sampled
for estimation of the structural parameters but is sparse for estimation
of the parameter BSV (Sheiner used to say that at least 25 subjects are
required for a reasonable estimate of BSV). On the other hand 2
observations per subject with 3 structural parameters and 30 subjects is
sparse for the structural parameters but maybe reasonable for BSV. Of
course the adequacy of estimation of structural and BSV parameters are
linked. As noted previously the use of an optimal design program can be
helpful in evaluating designs with a trade off between number of samples
and timing of samples versus the number of subjects. If the model is
correct then there is no reason to suppose the parameters would be
biased ('skewed').
Furthermore you asked:
> I can see where this could potentially present identifiability issues with high variability - be
> it residual or BSV, I am just wondering if there is a 'threshold' in which the sparser designs
> become significantly more biased.
Identifiability issues will arise when you have only one : observation
per subject -- then it is impossible to identify RUV 2: one subject --
then it is impossible to identify BSV. Some really bad designs (e.g only
trough concentrations) will mean some structural parameters will not be
identifiable (e.g. oral absorption).
Otherwise it a really a question of estimability -- the precision and
adequacy of the estimate will depend upon the number of subjects and
number of observations and timing. There is no threshold. The more data
you have and the better the design then the better the parameter
estimates will be in the sense of being more precise. As noted above, if
the model is correct then there is no reason to suppose there would be bias.
I hope that helps you sort out some of the issues.
Best wishes,
Nick
--
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
email: n.holford.at.auckland.ac.nz
http://holford.fmhs.auckland.ac.nz/
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