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Hi, everyone,
Just wonder if anyone can share some tricks to fix some parameters and
estimate others in WinNonLin.
Another question I have is how WinNonLin calculates the CV% SE of the
parameters for individuals.
Thanks!
Jun
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The following message was posted to: PharmPK
Dear Jun,
If I remember correctly, estimating some parameters
but not others works e.g. by putting the estimate and
lower and upper bound of a parameter to the value
that you want to fix it. Alternatively, you might use very
narrow bounds for some parameters.
Alternatively, you can define the parameter as a known
constant. This is the statistically probably most appropriate
way, however, I think this might only work for user defined
models in WinNonlin.
As far as I remember, WinNonlin uses a Taylor series
expansion to calculate approximate standard errors.
While this is done in many programs, Dr. Dan Weiner once
pointed out that this is an approximation and that these
standard errors should be interpreted with some caution.
For some models, the standard errors heavily depend on
the initial estimates, especially if you are using the standard-
two-stage method (as e.g. in WinNonlin). So one thing you
might want to do is to re-estimate your model parameters
with your final estimates from run 1 as your initials for run 2.
Sometimes using the final estimates and changing them
randomly by e.g. +/-15% works even better. This sometimes
helps to get the standard errors from NONMEM. However, I
did not study this exhaustively.
Hope this helps.
Best regards
Juergen
--
Juergen Bulitta, PhD, Post-doctoral Fellow
Pharmacometrics, University at Buffalo, NY, USA
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Dear Juergen,
Thank you very much for the trick. It really helps.
My second question arises from one confusion. To my understanding
standard error (SE) is a measurement of how well a sample represents
the population. SE=SD/SQRT(subject#). When it comes to individual
modeling by WinNonLin, if there is only one individual how the SE of
the parameters is calculated and what the SE really means. Does it
mean how well the individual represents the whole population or how
well the parameters are estimated? Here is what I get lost. And how
taylor series calculates the SE?
Appreicate any comments.
Thanks.
Jun
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The following message was posted to: PharmPK
Jun
> My second question arises from one confusion. To my
> understanding standard error (SE) is a measurement of how
> well a sample represents the population.
> SE=SD/SQRT(subject#). When it comes to individual modeling by
> WinNonLin, if there is only one individual how the SE of the
> parameters is calculated and what the SE really means. Does
> it mean how well the individual represents the whole
> population or how well the parameters are estimated?
The SE of a parameter describes the uncertainty in its estimate. It
relates
to the parameter in question.
For regression parameters, computation of the standard error is based
on the
estimated Fisher information matrix (where the SE of a parameter
estimate is
approximated by the square root of the diagonal elements of the
inverse of
the Fisher information matrix). There are many references that
describe how
to compute the Fisher information (Wikipedia has a reasonably good
description - albeit a little technical).
>From a practical perspective.
1) Any good nonlinear regression programme should give you the standard
errors of your parameter estimates automatically.
2) The better your experimental design the smaller the standard errors
(poor
experiments -> large standard errors).
3) You can use simulation or theory of design to assess the
informativeness
of your experiment (before you do the experiment).
4) SE are often used to estimate confidence intervals from which
hypothesis
testing can be performed, hence small SE yields a more powerful
experiment.
Hope this helps
Steve
--
Professor Stephen Duffull
Chair of Clinical Pharmacy
School of Pharmacy
University of Otago
PO Box 913 Dunedin
New Zealand
E: stephen.duffull.-a-.otago.ac.nz
Design software: www.winpopt.com
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The following message was posted to: PharmPK
Dear Jun,
If you were doing univariate statistics, SE of the mean is SD/sqrt(n).
Y~N(mu,sigma^2)
mu~N(mu,sigma^2/N), Var of mu=sigma^2/N
In case of linear regression
Y~N(mu=X*Beta,sigma^2)
where mu is a mean function described by predictors in design matrix X
and coefficients Beta.
then
Beta~N((X'X)-1X'Y,(X'X)-1*sigma^2); SE Beta are the square root of the
diagonal components of Matrix (X'X)-1*sigma^2 (Varinace Covariance
matrix of parameter estimates)
sigma^2 is sum( Yobs-Ypred)^2/(N-P) where P is the number of
coefficients in the model.
The variance covariance matrix of estimates for a nonlinear model is
given by (F'F)-1 sigma^2 obtained by linearized model through taylor
series expansion.
Where F is the matrix of partial derivatives. See Bates and
Watts(1988) for detailed description. CV% in Winonlin is SE(parameter
estimate)/Patrameter Estimate for the individual person. For derived
parameters like half-life SE are obtained by delta method, see
following thread in nmusers for information on delta method.
http://www.cognigencorp.com/nonmem/current/2008-February/0813.html
Hope it helps
Varun Goel
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The following message was posted to: PharmPK
CV is a relatively narrowly defined descriptive statistic. That
definition is equivalent to SD/MEAN and multiplied by 100.
--
Ed O'Connor, Ph.D.
Laboratory Director
Matrix BioAnalytical Laboratories
25 Science Park at Yale
New Haven, CT 06511
Web: www.matrixbioanalytical.com
Email: eoconnor.at.matrixbioanalytical.com
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