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Re: VPC appropriateness in complex PK

From: Leonid Gibiansky <LGibiansky>
Date: Fri, 18 Sep 2009 15:44:13 -0400

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 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


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 JPKPD,
> 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:
> .
> 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 - 15:44:13 EDT

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