Jakob, Leonid,
I think it should be pointed out more clearly that PKPD analyses can be
performed most simply using the PPP&D method. This method has better
properties compared with IPP and is easier to set up and run (see Zhang
et al Part I). Sequential methods are preferred over simultaneous
methods whenever there is a possibility of mis-specification of the
model linking concentration to effect. This is nearly always a real risk
so the sequential method is rarely a sensible choice (see Zhang et al
part II).
The IPP+SE method has properties similar to PPP&D but it technically
more challenging to use and cannot be used without a variance-covariance
matrix of the estimates. This can usually only be obtained with
oversimplified models (asymptotic $COV) or by time consuming bootstraps.
The bottom line is to use PPP&D.
Leonid makes a good point about using VPC for model evaluation. The VPC
is capable of detecting structural model misspecification for PKPD
analyses but it is not foolproof. A misspecified random effects model
can compensate for a misspecified structural model. See references
below for an example.
Best wishes,
Nick
Karlsson MO, Holford NHG 2008. A Tutorial on Visual Predictive Checks.
PAGE 17 (2008) Abstr 1434 [wwwpage-meetingorg/?abstract=1434] (last
accessed 11 February 2012).
http://holford.fmhs.auckland.ac.nz/docs/vpc-tutorial-and-datatop.pdf
On 19/02/2013 7:55 a.m., Leonid Gibiansky wrote:
Hi Matts,
One method to investigate the problem would be to conduct VPC. If VPC
with model-estimated variances provides good (not inflated) range of
PK profiles then one can argue that the PK model provides good
description of the data and can be used for simulations (including
PK-PD).
Another test could be to do VPCs for the PK-PD model: one with fixed
PK parameters (as was used in the sequential PK-PD modeling procedure)
and the other one with model-simulated ETAs for both PK and PD parts.
Again, if both provide good coverage of observed PK-PD data then
combination of PK and PD models can be trusted, and any of the
approaches can be applied. If one of the VPCs is inadequate, than it
should be noticeable in the too narrow or too wide prediction intervals.
Leonid
On 19/02/2013 5:20 a.m., Ribbing, Jakob wrote:
Resending, since my posting from this morning (below) has not yet
appeared on nmusers.
Apologies for any duplicate postings!
*From:*Ribbing, Jakob
*Sent:* 18 February 2013 09:59
*To:* "Kågedal, Matts"; [email protected]
*Cc:* Ribbing, Jakob
*Subject:* RE: Simulation settgin in the precence of Shrinkage in PK
when doing PK-PD analysis
Hi Matts,
I think you are correct; the problem you describe has not had much
(public) discussion.
It is also correct like you say that this is mostly a problem in case
of all of the below
·sequential PK-PD analysis is applied (IPP approach, Zang et al)
·non-ignorable degree of shrinkage in PK parameters _of relevance_
oOf relevance: the PK parameters effectively driving PD for the
mechanism, e.g. CL/F if AUC is driving. In addition, if PD response
develops over several weeks/months then shrinkage in IOV may be
ignored even for relevant PK parameters
·I would also like to add that for this to be an issue individual PK
parameters must explain a fair degree of the variability in PD, which
is not always the case
oIf driving PD with typical PK parameters (along with dose and other
PD covariates) does not increase PD omegas, compared to IPP, then
either PK shrinkage is already massive, or else it is not an issue for
the IPP-PD model
If only the IPP approach is possible/practical a simplistic approach
to simulate PD data is as follows:
·sample (with replacement) the individual PK parameters along with any
potential covariates (maintaining correlation between IIP and
covariates, i.e. whole subject vectors for these entities, but
generally not for dose since generally should only have only random
association with IPP or PK/PD-covariates)
·then use the re-sampled datasets for simulating PD according to the
PD model (driven by IPP, covariates, dose, etc). The degree of
shrinkage is then the same for PD estimation and simulation.
This approach may for example allow to simulate realistic PD response
at multiple dosing, based on only single dose PD. When the MD data
becomes available then one may find that variabilities shift between
PK and PD due to different PK shrinkage, but I would argue the
simulated PD responses still were realistic. This approach is useful
for predictions into the same population (especially if sufficient
number of subjects available for re-sampling), but may not allow
extrapolation into other populations where PK is projected to be
different.
When possible the obvious solution is to apply one of the alternative
approaches to simultaneous PK-PD fit; after you have arrived at a
final-IPP model.
If a simultaneous fit is obtainable/practical this is the best option,
but notice that e.g. if you have rich PK data in healthy and no PK
data in patients (plus PD data in both populations): You can estimate
separate omegas for PD parameters in healthy vs. patients, but it may
be difficult to tell whether patients higher PD variability is due to
PK shrinkage, or due to the actual PD variability being higher in this
population (or both). PD variability may be confounded by a number of
other factors that are actually variability in PK (fu, active
metabolites and bio phase distribution, just to mention a few where
information may be absent on the individual level). Depending on the
purpose of the modelling this often not an issue, however.
As you suggest there may be rare situations with IPP where a more
complicated approach is needed, with a) simulation and re-estimation
of PK model, to obtain Empirical-Bayes Estimates based on simulated
data, and then feed these into the subsequent PD model. I would see
this as a last resort. There are pitfalls in that if PD parameters
have been estimated under one degree of PK shrinkage, then applying
these estimates to a simulated example with different PK shrinkage
requires adjustment of PD variability. I am not sure anyone has had to
go down that route before and if not I hope you do not have to either.
Maybe others can advice on this?
Best regards
Jakob
Two methodological references:
Simultaneous vs. sequential analysis for population PK/PD data II:
robustness of methods.
Zhang L, Beal SL, Sheiner LB.
J Pharmacokinet Pharmacodyn. 2003 Dec;30(6):405-16.
Simultaneous vs. sequential analysis for population PK/PD data I:
best-case performance.
Zhang L, Beal SL, Sheiner LB.
J Pharmacokinet Pharmacodyn. 2003 Dec;30(6):387-404.
--
Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53
email: [email protected]
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
