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RE: VPC appropriateness in complex PK

From: Wang, Diane <Diane.Wang>
Date: Fri, 18 Sep 2009 18:53:15 -0400


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.



Diane D. Wang, Ph.D.
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

-----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

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

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

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


Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
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
> assessing the perfomance of population pharmacokinetic models.
> I recently came across this abstract from the 2009 PAGE meeting:
> .
> This abstract states that situations when VPC is not feasible but a
> "Standardized Visual Predictive Check (SVPC) can be used are as
> - Patients received individualized dose or there are a small number of

> patients per dose group and PK or PD is nonlinear, thus observations
> not be normalized for dose
> - There are multiple categorical covariate effects on PK or PD
> - Covariate is a continuous variable which made stratification
> - Study design and execution varies among individuals, such as
> design, difference in dosing schedule, dose changes and dosing time
> varies during study, protocol violations
> - Different concomitant medicines and food intake among individuals
> 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 - 18:53:15 EDT

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