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Re: VPC appropriateness in complex PK

From: Nick Holford <n.holford>
Date: Tue, 22 Sep 2009 20:54:34 +1200


I am not understanding something in your example which you use to assert
that adaptive dosing should not be used in simulations for a VPC. if you
used adaptive dosing and the correct PK structural and random effects
model (as you seem to describe) then if there was no error in the
measured conc/timing then of course the simulated concs would exactly
match the observed concs in each subject. What is wrong with that? Your
example uses the correct simulation model for prediction of the original
data distribution and so the predictive check should of course confirm
the model. That is what a predictive check is about. It checks that the
model is adequate (i.e. good enough to to be the true model).

In reality adaptive designs based on measured concs will always have
errors in the measured conc or timing of concs in addition to the
between subject variability in PK parameters so using the nominal
adaptive design algorithm would always add some additional noise to the
predicted distribution.

Another real life feature is that clinical study staff dont follow the
protocol (or there may not even be a protocol!). If one can devise a
clinically reasonable adaptive design protocol then this is a useful
step in trying to perform a predictive check of a trial with an
unfollowed or unknown protocol. If the adaptive design protocol matches
the data using a VPC then one can have some confidence in using the PK
model and the adaptive design algorithm to simulate future trials which
are not expected to have a strictly followed adaptive protocol. The need
for this kind of auxiliary model to account for real life variations in
design has been recognized for dropouts due to informative missingness
mechanisms. It not only allows a predictive check to evaluate the
adequacy of the model but also gives a mechanism for future clinical
trial simulation.

With regard to your second point -- it has made me think more carefully
about the assumptions of the SPC method and I think I can now convince
myself that you are correct that the original dosing design needs to be
used for simulation. Here is my rationale which I hope you will be
willing to try to follow and see if the logic is reasonable. If this
logic is OK then I will retract my previous statement that SPCs would
fail if they did not simulate with an adaptive design.

My understanding of how SPCs work involves the basic idea of comparing a
measured conc to a distribution of simulated concs that arise from the
structural and random effects model under the original design that gave
rise to the measured conc. If the original design (i.e. "CRF" dosing
regimen) that gave rise to the measured concs is used then the
distribution of simulated concs will depend on the structural and random
effects model conditional on the original design. It is clear that the
mean simulated concentration for an individual will not match the
observed concentration in a particular individual because the random PK
parameters for that individual will be randomly different from the
actual PK parameters. This is why the CRF dose cannot be used for the
VPC (unless both the predictions and observations are 'normalized' so
that the actual dosing regimen does not matter as is done in the PC-VPC).

But it is plausible that the discrepancy of a single observed
concentration from the simulated distribution of concs at that time for
that individual will be random across individuals and thus the
prediction discrepancy would be uniform (if the PK structural and random
effects model is correct). However, the within subject correlation of
these discrepancies due to the PK parameter between subject differences
(which will affect all concentrations in that individual) will violate
the assumption of independent discrepancies and this is what the NPDE
method tries to achieve by removing the within subject correlation. Thus
I think we should not rely on PDE methods for SPC unless there is only
one observation per subject. The technology for doing uncorrelated PDEs
(e.g. NPDE) is now freely available
( so there is really no
justification to use correlated PDEs .


Wang, Yaning wrote:
> 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:
> "The contents of this message are mine personally and do not necessarily
> reflect any position of the Government or the Food and Drug
> Administration."
> -----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 ACOP.
> 2009.

Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
mobile: +64 21 46 23 53
Received on Tue Sep 22 2009 - 04:54:34 EDT

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