Leonid,
I agree with you that VPC can not be used for concentration, effect
controlled trials or trials with adaptive design. However SVPC does
work in all these situations. The dosing record for each patient
obtained from CRF is the adjusted dose based on the individual
parameters. Therefore, 95 and 5 percentiles of the simulated
concentrations based on this individual's information should only
reflect random effect as all fixed effects are the same.
Compared to PC-VPC, SVPC doesn't have the disadvantage Martin indicated
in his Acop abstract "Prediction Corrected Visual Predictive Checks"
that "PC-VPC only accounts for differences in typical subject
predictions; there may also be differences in expected variability
around this prediction". Rather than correcting for typical subject's
predictions, SVPC uses each individual's exact design template without
approximation and is not affected by the variability/uncertainty of the
predictions.
Diane
-----Original Message-----
From: Leonid Gibiansky [mailto:[email protected]] Sent:
Friday, September 18, 2009 5:28 PM
To: Wang, Diane
Cc: Dider Heine; [email protected]
Subject: Re: [NMusers] VPC appropriateness in complex PK
Diane,
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 used.
Thanks
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
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: [email protected]
-----Original Message-----
From: [email protected]
[mailto:[email protected]]
On Behalf Of Leonid Gibiansky
Sent: Friday, September 18, 2009 12:44 PM
To: Dider Heine
Cc: [email protected]
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: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
Dider Heine wrote:
Dear NMusers:
The Visual predictive check (VPC,
http://www.page-meeting.org/page/page2005/PAGE2005P105.pdf , 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:
http://www.page-meeting.org/pdf_assets/4050-Standardized%20Visual%20Pred
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
