From: Partha Nandy
Subject: [NMusers] Distribution of Simulated Cmax
Date: Sat, 19 Nov 2005 11:45:15 -0500

Hi All,

I am kindly seeking your opinion regarding an observation that I have made on a number of occasions. 
Here's the scenario:   First I first fit a PK model (1-, 2- or 3-compartment & covariates)
to the data and after validating the model, use the model to predict the concentration-time profiles.
I then take the simulated concentration-time data to compute AUCt, AUCINF, and Cmax, via.
non-compartmental approach.  Even though the distribution  of the PK parameter estimates generated
from boot-strap data are similar to the parameter distributions from the original data set, and PPC
(posterior predictive check) do not show obvious flaws in the model; most often the distribution of
Cmax estimated from the Simulated data sets are quite different from that of the observed/experimental
data set (I have used Chi-square and Kolmogorov-smirnov 2-sample test to compare distribution).  In
fact it appears that the the observed distribution and simulated distribution came from very different populations.
In this situation, if one wants to compare treatments using 90% confidence-intervals (80-125%), how
valid is the comparison when it appears that the simulated data is from a different population and
the observed data from a different population,  moreover the CIs from the observed Cmax was not
within 80-125%.  Have any one faced this dilemma and if so, can any one share their experiences?

Any suggestions from the group is appreciated.

Kind Regards,


Subject: Re: [NMusers] Distribution of Simulated Cmax
Date: Sat, 19 Nov 2005 18:58:46 +0100

Dear Partha,

I would start with a bootstrap re-sampling of the observed Cmax's of your original study.
If you generate a few thousand bootstrap pseudo-samples of the same sample size as used in your
study, you should get a good idea which degree of similarity in the distribution of Cmax you 
would expect from a population PK model.

As long as you have a reasonable number of subjects in your original study, the most adequate
population PK model should provide you similar simulated Cmax distributions as the bootstrap
pseudo-samples from the original study.

Did you check that the extent of absorption was similar, in case you pooled data from more
than one study?

Which between and within subject variability from ANOVA statistics did you get from the Cmax
of your original study? If you have only a few subjects and a large within subject variability
(between occasion variability), then such a formulation might fail to be bioequivalent to
itself in a bioequivalence trial.

Another idea would be to use a different error model around the expected Cmax region.
(Have not tried this myself, but might be worth to try.)

Best regards


Juergen Bulitta, M.Sc.
Scientific Employee, IBMP
Paul-Ehrlich-Str. 19, 90562 Nuernberg-Heroldsberg


From: Pravin Jadhav
Subject: Re: [NMusers] Distribution of Simulated Cmax
Date: Sat, 19 Nov 2005 12:55:27 -0500

Hi Partha,
 This is a classical simulation problem that we have on a few of occasions.
You say, PPC did not show obvious flaws in the model. It would really depend
on the metric that was used. Please take a look at our publication on the
very same topic.
 Jadhav, P. R.; Gobburu, J.V.S.; A New Equivalence Based Metric for
Predictive Check to Qualify Mixed-Effects Models, AAPS Journal, Vol. 7 No. 3
 My initial guess is, the predictive check was done to assess average
behavior of the data (Pp in our publication). Take a look at the equivalence
based metric that was proposed. This metric would have been able to assess
inconsistency between your data and the model (at Cmax). We think, this is
one of the prime applications of predictive check, especially when used with
the equivalence based metric. It will allow you to locate domains of
interest where 'the model fails to reproduce the observed data'- underlying
aim of the predictive check.
 You will need to take a look at the parameters that were used for
simulation again. Look for any unusual values of CL, V, Ka etc./unusual
combinations of those and then truncate the distributions accordingly
(within the limits of the observed data).
 Hope it helps.
 Pravin Jadhav


From: Paul Hutson
Subject: Re: [NMusers] Distribution of Simulated Cmax
Date: Sat, 19 Nov 2005 15:10:28 -0600

Is it tri-exponential decay, or is the third comp the gut depot?
Also, how are you calculating the Cmax using a non-compartmental approach?


From: Partha Nandy
Subject: Re: [NMusers] Distribution of Simulated Cmax
Date: Sun, 20 Nov 2005 23:17:58 -0500

Hi Paul,

It is a tri-exponential decay... As for estimating Cmax,  I am feed ing the simulated data
into WinNonlin / SAS or S-Plus.

Kind Regards,