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Hi, all:
I am trying to use Berkeley Madonna to do some PBPK modeling and
simulation work. I have simulated some data sets using Berkeley
Madonna. But when I use the curve fit function to fit the exact data
sets back to the original model, I got some problems. I have
simulated 7 organs and each organ has 12 time points. If I only use
one or two organs' data, the estimated parameters were the same as
the original code. But if I simultaneously fit more than two organs'
data back, the estimated parameters are far away from the original
values. Since the data set are simulated from the model, the data
sets should be refitted back to get the same parameters. This seems
to be a bug in BM. Has anyone else had a similar experience?
I also would like to know where to look for the standard errors of
the estimated parameters for curve fit in Berkeley Madonna. I would
appreciate any kind of help!
Lucy
the Ohio State University
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Dear Lucy,
Whilst the Berkeley Madonna (BM) software is an excellent tool for
modelling, especially on the simulation side (=forward modelling),
there are no built in outputs providing the standard errors of the
parameter estimates, or other useful measures of goodness of fit (for
reverse engineering). You would either have to set up the functions
to calculate them yourself, or, what I do, is use an alternative
software such as SAAM II, NONMEM or WinNonlin where fitting
statistics are provided. I find SAAM II very useful for PBPK. Others
prefer ADAPT II, ACSL/Simusolv or Matlab. Not heard of anyone using
NONMEM (anyone from PharmPK?)
With Berkeley Madonna all you can do is have a careful look at the
observed versus predicted plots. One thing I do do when using the
curvefit function is turn on the sliders for each of the parameters
being optimised. Then, as the optimiser is running, they move left
and right as different values are searched. If you watch carefully
you will notice that some parameters hardly move whilst others are
moving violently from left to right - these are ones where there is
little information in the data to support their estimation, so will
need "support" from independent experiments. The same can be seen in
e.g. NONMEM if you plot the parameter estimates versus iteration. Not
as much fun to watch though.
What may be an issue with BM is the error model. There is no built in
weighting system, so the data and the output function should be
transformed appropriately, such as to the logarithm. This may help if
the data covers many orders of magnitude. I have never done it, but
there is also an option in BM to build your own objective function
then use "Optimize" rather than "Curvefit". Perhaps someone else in
PharmPK could help here?
Also, given that in PBPK, all organs are by definition supplied by
arterial blood, the function for the arterial supply can be
predefined by an arterial concentration-time curve. This may be a
polyexponential, or an interpolation between data points. However,
once you get close to the final partition coefficients (and
permeability-surface area coefficients for a permeability-limited two-
compartment per organ model) then you should be able to carry out a
global optimisation against all the data simultaneously, including
the arterial and/or venous blood. However, if the initial estimates
are not close, the optimiser will disappear off into hyperspace - the
parameter space has many dimensions.
Best regards, Phil.
Philip Lowe PhD
Senior Fellow, Modelling & Simulation
Novartis Pharmaceuticals AG
4002 Basel
Switzerland
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Dear Philip Lowe,
I can not agree with you any more about 'optimization' and
'curve fit'. But I think that that Lucy can not get her original
parameters is because BM stepped into local minimum. If there was no
random effect, the original parameters are global minimum to the
simulated data sets.
If a model is too complex, it is impossible to find a global
minimum (original parameters). The reason is that 'optimization' and
'curve fit' algorithms are like down hill process. It is very
difficult to find a proper position (initial values) to global minimum.
I bet that to set initial values could solve this problem. :p
close to the original parameters. The second choice is to make the
model more simple. I mean to set some of the parameters constant.
This could help to find the global minimum.
Best Regards,
Ma Guangli
[Starting from different initial values can help find the global
minimum. I have a 'mode' in boomer that starts the simplex method
from random, different points for the simplex coupled with a repeat
function. With simple models I get the same WSS for most of the runs
of say a total of 10. With more difficult models I'll commonly see
only 2-3 hit the 'global' minimum with others runs stopping with
higher WSS values. A grid search can help. I've also tried initially
holding some parameters constant to help in approaching the global
minimum with more complex models - db]
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The following message was posted to: PharmPK
Dear Philip,
About one aspect of your mail:
[..]
>software such as SAAM II, NONMEM or WinNonlin where fitting
>statistics are provided. I find SAAM II very useful for PBPK. Others
>prefer ADAPT II, ACSL/Simusolv or Matlab. Not heard of anyone using
>NONMEM (anyone from PharmPK?)
I read a discussion of PBPK modeling in the material of the advanced
course ran by L. Sheiner. Indeed I found some documentation of NONMEM's
use in PBPK:
http://www.page-meeting.org/page/page2006/P2006IV_20.pdf#search=%22PBPK%
20site%3Apage-meeting.org%22
You can find more examples with a google search:
http://www.google.nl/search?hl=nl&q=PBPK+site%3Apage-meeting.org+NONMEM&
meta=
Best regards,
Jeroen
J. Elassaiss-Schaap
Scientist PK/PD
Organon NV
PO Box 20, 5340 BH Oss, Netherlands
Phone: + 31 412 66 9320
Fax: + 31 412 66 2506
e-mail: jeroen.elassaiss.aaa.organon.com
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Dear Ma,
You are most likely correct, that the reason that BM failed to get
back to the original values (global minimum) is that it found a local
dip in the parameter space, or it is just heading off into the wrong
valley (my hyperspace analogy). The downhill analogy is great. Just
like skiing. Head the wrong way (wrong initials) and you do not get
back to the chalet.
Given that PBPK models have many many dimensions, the initial
estimates must be very close to get the final optimisation to all
data to work. This is why the process of creating the model normally
involves estimating the Kp and PS parameters for each organ
independently with a defined input, or forcing function, of the
arterial concentration-time profile. This should enable reasonable
initial estimates for the final assault on the global minimum. But
base camp must be well set up (sorry for the mixed metaphores of
climbing and skiing).
Best regards, Phil
[I've thought about a Bayesian approach to this problem. Some of the
parameters of a PBPK model are well documented but with some
variability, e.g. blood flow, organ weight, etc. If this information
could be included as population values and population variances, the
'program' might have a better chance of finding the global minimum by
adjusting the parameters you don't know as well more freely (by
giving them a large variance). I like the skiing analogy, in my
version I'm just walking, taking one step, blindfolded, to feel the
terrain and then jumping to the next iteration. Ok if there aren't
too many cliffs, but then that can be a problem with skiing too - db]
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