RE: VPC appropriateness in complex PK
In my opinion, the concentration data after dose adaptation should not
be simulated based on the adaptive algorithm implemented in the original
design. Using the simple but extreme case proposed by Leonid, i.e. all
patients were targeting a common concentration level with no or small
residual variability and no or small inter-occasion variability. For
example, under iv infusion, the target is Css of 100ng/ml. All patients
start with the same infusion rate and the infusion rate will be adjusted
after steady state is achieved. For patient A, if the Css under the
initial infusion rate is 50ng/ml, then double the infusion rate. For
patient B, if the Css under the initial infusion rate is 200ng/ml,
reduce the infusion rate by half. After dose adaption, every one should
hit 100ng/ml. Then no matter what the model is, all the simulated
concentrations after dose adaptation will hit the same target (matching
exactly the observed data) if the original adaptive algorithm is used in
simulation. In this case, there is no way the structure model can be
wrong because it is very simple (R/CLi). But imagine we fit an
exponential between-subject variability model to a log-normally
distributed CLi. Then using the exponential distribution to simulate CLi
and then adjust individual infusion rate accordingly. All patients will
still hit 100ng/ml after dose adjustment. Of course, one can argue the
pre-adaptation concentration should pick up the mis-specification. The
point is that post-adaption data cannot be simulated based on the
adaptive algorithm.
On the other hand, simulation can be done based on original adapted
doses ("obtained from the CRF") assuming the whole set of simulated
individuals will also take the exact dose sequence that was taken by one
specific individual in the trial. The only difference among these
individuals will be due to the random between-subject variation on PK
parameters. SVPC or PDE should still show uniform distribution even for
those post-adaption data (even if all observed data are 100ng/ml).
Yaning Wang, Ph.D.
Team Leader, Pharmacometrics
Office of Clinical Pharmacology
Office of Translational Science
Center for Drug Evaluation and Research
U.S. Food and Drug Administration
Phone: 301-796-1624
Email: yaning.wang
"The contents of this message are mine personally and do not necessarily
reflect any position of the Government or the Food and Drug
Administration."
Quoted reply history
-----Original Message-----
From: owner-nmusers
On Behalf Of Nick Holford
Sent: Monday, September 21, 2009 1:54 AM
To: nmusers
Subject: Re: [NMusers] VPC appropriateness in complex PK
Hi,
Like Leonid, I am having trouble understanding how trials originally
conducted with adaptive designs can be used for predictive checks if the
simulation dose regimen is not based on the randomly assigned individual
PK parameters. If the original adapted doses ("obtained from the CRF")
are used then the simulated concentrations will not approach the
adaptive design target as they would have done in the original data.
Thus the distribution of simulated concentrations will be wider than the
distribution of observed concentrations (see Bergstrand et al 2009
Example 3 left hand plot).
Traditional visual predictive checks using the original doses will
clearly show that the distributions of observations and simulated
concentrations are different and would wrongly reject an adequate PK
model.
I would expect methods based on statistical predictive checks (PDE
(including SVPC), NPDE) would detect that the distribution of prediction
discrepancies is not as expected (uniform for PDE; normal for NPDE) and
also wrongly reject an adequate PK model.
PRED-corrected VPCs will not detect a difference between the
PRED-corrected simulated concentrations and the PRED-corrected
observations. This is because the PRED correction process is equivalent
to normalizing all subjects to the same dose at each time point. For a
linear PK model the variability in concs will have all the dose
information removed and thus the adaptive changes in dose become
irrelevant. Note that the PRED-corrected 'observations' will be quite
different from the original observations and the trend of the
PRED-corrected 'observations' variability will be quite unlike that seen
in the data (see Bergstrand et al 2009 Example 3 right hand plot). This
could be confusing but it should not lead to wrongly rejecting an
adequate model.
If the simulations are done using an adaptive dosing algorithm that is
similar to that used in the original study then the statistical
predictive checks and visual predictive checks (without or with
PRED-correction) should not reject an adequate PK model.
A non-PRED-corrected visual predictive check (NPC-VPC) should also
correctly represent the actual observations and the simulated
distributions if it used an adaptive dosing model. I think this is a key
difference between the empirical PRED-corrected and mechanism based
adaptive dose model approaches to a VPC. The mechanism based approach
gives more visual reassurance that the combined models i.e. the PK model
and the adaptive dosing model, can describe the data. This will give
visual support for using the model combination for future trial
simulations. The empirical PRED-corrected VPC does not give this kind of
support for future use of the PK model under an adaptive design
scenario.
Nick
Bergstrand M, Hooker AC, Wallin JE, Karlsson MO. Prediction corrected
visual predictive checks http://www.go-acop.org/acop2009/posters ACOP.
2009.