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Re: VPC appropriateness in complex PK

From: Leonid Gibiansky <LGibiansky>
Date: Fri, 18 Sep 2009 20:27:47 -0400

I probably worded it incorrectly. I was going to say that for
concentration or effect controlled trails you cannot use straightforward
VPC simulation based on the actual dosing history; you have to be more
careful. Let me show the example that illustrates how VPC/SVPC behaves
in the concentration or effect controlled trials.

Assume that we conduct the two-dose study. The first dose (same for all
subjects) is given to learn the kinetics. The second dose is adjusted
(based on the previous data) in order to get the same Cmax for all
subjects. For simplicity, assume that the world is nearly perfect: no or
small residual variability, no or small inter-occasion variability. Then
the dose adjustment can be perfect, and the second-dose Cmax for all
subjects would hit the target. No or small second-dose Cmax variability
would be observed.

Now, let's do VPC. If you simulate based on the actual dosing history
(even from the from the true model), your first-dose Cmax will be
distributed similar to the observed data. However, your second-dose Cmax
will vary significantly (even more than the first-dose Cmax) because you
use the actual dose, rather than adjust the dose based on the individual
parameters. Thus, standard VPC/SVPC/NPDE/PC-VPC/etc. will be misleading.
One needs to simulate using the same dose adjustment algorithm as in the
actual study. Only for these simulations predictive check plots can be


Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
e-mail: LGibiansky at
tel: (301) 767 5566

Wang, Diane wrote:
> Leonid,
> Thank you for the explanation. I was writing the response but found
> your email stated it even better than what I could do myself. :)
> Basically, VPC is less sensitive, when your data set is not homogeneous,
> for evaluating random effects, because the 95% percentile interval of
> predicted concentrations based on the full model reflects not only the
> random effects (inter- and intra-subject variability) but also fixed
> effects (difference in study design and covariate effects). SVPC solved
> this problem as you described.
> Regarding stratifying the plots by dose and influential covariates when
> using SVPC, our solution is to group subjects by the covariate of
> interest (e.g. dose, and influential covariates) using different colors
> and see if the colors are uniformly distributed in the SVPC plot. This
> can also be used to identify potential covariates. I have a couple
> examples in the presentation slides.
> I am not sure I agree with you that SVPC can not be used for
> concentration or efficacy controlled trials. In concentration or
> efficacy controlled trials, patient's dose is adjusted based on
> concentration or efficacy observed. As long as we have the dosing
> record, we should be able to get the percentile for each observation of
> each patient based on predicted PK/PD endpoints using this patient's
> dosing record, and then pool all observation percentiles together
> regardless of each patient's dose and dosing schedule.
> Thanks,
> Diane
> Diane D. Wang, Ph.D.
> Director
> Clinical Pharmcology
> Oncology Business Unit
> Pfizer La Jolla
> 10555 Science Center Dr. (CB10/2408)
> San Diego, CA 92121
> Office Phone: (858) 622-8021
> Cell Phone: (858) 761-3667
> email:
> -----Original Message-----
> From: owner-nmusers
> On Behalf Of Leonid Gibiansky
> Sent: Friday, September 18, 2009 12:44 PM
> To: Dider Heine
> Cc: nmusers
> Subject: Re: [NMusers] VPC appropriateness in complex PK
> Hi Dider,
> VPC is very good when your data set is homogeneous: same or similar
> dosing, same or similar sampling, same or similar influential covariates
> that results in similar PK or PD predictions. In cases of diverse data
> sets, traditional VPC is more difficult to implement, and it may not be
> useful.
> To see the problem, consider VPC (without stratification) for the data
> with two dose groups, 1 and 100 units (with the rest being similar).
> Obviously, all data that exceed 95% CI would come from the high dose,
> and all data below 5th percentile would come from the low dose, and
> overall, VPC plots and stats will not be useful. With two doses, it is
> easy to fix: just stratify by dose. If you have more diverse groups, you
> have to either do VPC by group, or find the way to plot all values in
> one scale. In cases of dose differences and linear kinetics, one can do
> VPC with all values normalized by dose. In nonlinear cases, it is more
> difficult.
> SVPC offers the way out of this problem. In this procedure, each
> observation is compared with the distribution of observations at the
> same time point, with the same dosing, and with the same covariate set
> as in the original data. Position of the observation in the distribution
> of simulated values is characterized by the percent of simulated values
> that is above (or below) the observed value. If the model is correct,
> then percentiles should be uniformly distributed in the range of 0 to
> 100. This should hold for any PRED value, and dose, any time post-dose
> etc.
> It is important not to combine all observed points together (to study
> overall distribution of the SVPC percentiles): in this case the test in
> not sensitive. SVPC is useful when these percentile values are plotted
> versus time, time post dose, or PRED (but not IPRED or DV !!) values.
> Then, they can be use to see the problems with the model, similar to how
> WRES vs TIME and WRES vs PRED plots are used. The disadvantage is that
> you loose visual part: your percentile versus time profiles should look
> like a square filled with the points rather than like concentration-time
> profiles. Even in this procedure, it make sense to stratify your plots
> by dose, influential covariates, etc. to see whether the plots are
> uniformly good. Dose, covariate, time or PRED dependencies of the SVPC
> plots may indicate some deficiency of the model.
> Note that none of these procedures can be used to evaluate the
> concentration or effect controlled trials, or trials with non-random
> drop out. In order to use VPC-based procedures for these cases, you need
> to simulate accordingly: with dosing that depend on simulated values
> (for concentration or effect controlled trials) or with the drop-out
> models.
> Thanks
> Leonid
> --------------------------------------
> Leonid Gibiansky, Ph.D.
> President, QuantPharm LLC
> web:
> e-mail: LGibiansky at
> tel: (301) 767 5566
> Dider Heine wrote:
>> Dear NMusers:
>> The Visual predictive check (VPC,
>> , and
>> Volume 35, Number 2 / April, 2008) has been touted as a useful tool
> for
>> assessing the perfomance of population pharmacokinetic models.
> However
>> I recently came across this abstract from the 2009 PAGE meeting:
> ictive%20Check%20in%20Model%20Evaluation%20-%20PAGE2009%20submit.pdf
>> .
>> This abstract states that situations when VPC is not feasible but a
>> "Standardized Visual Predictive Check (SVPC) can be used are as
> follows:
>> - Patients received individualized dose or there are a small number of
>> patients per dose group and PK or PD is nonlinear, thus observations
> can
>> not be normalized for dose
>> - There are multiple categorical covariate effects on PK or PD
> parameters
>> - Covariate is a continuous variable which made stratification
> impossible
>> - Study design and execution varies among individuals, such as
> adaptive
>> design, difference in dosing schedule, dose changes and dosing time
>> varies during study, protocol violations
>> - Different concomitant medicines and food intake among individuals
> when
>> there are drug-drug interactions and food effect on PK
>> However, the original VPC articles seem to suggest that these are the
>> exact situations when the VPC alone is an ideal tool for model
>> validation. Is there any justification for one approach over the
>> other? Has anyone ever seen an SVPC utilized elsewhere, I have found
>> nothing. Are these truly weaknesses of a VPC?
>> Cheers!
>> Dider
Received on Fri Sep 18 2009 - 20:27:47 EDT

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