RE: FW: VPC appropriateness in complex PK
Hello all,
I am sorry to revive this thread after a few days, but I have to say, I am
really confused - both by the discussion and issues. I must admit that I do
not really have much experience with concentration controlled or random
dose-adapted trials (not fixed titration), so please let me know if I am not
thinking about this clearly or correctly.
The first thing that confuses me is this. If have a true model for the
response and dose adaption and simulate one trial. Then if I simulate 100
trials from the same model, shouldn't these look stochastically similar?
Shouldn't I be able to find a plot that shows that the first simulation is
compatible (comparable) with the 100? (Perhaps this is what Nick was saying
early on in this thread and sorry if I am miss-paraphrasing you here Nick -
please correct me if so).
If I fit the true model to data with a reasonable sample size, shouldn't the
estimates be close to the true values of the parameters and put me in a
situation like described in the paragraph immediately above (compatible data
and simulations)?
If I have a true model and observed dosing history, shouldn't the empirical
distribution of the dosing history be compatible with simulated dosing
histories such that they look stochastically similar? If so, then should it
matter if we use the observed dosing history or the random rule in the
simulations as long as the correlations between etas and doses are
preserved?
It seems to me that the simulation model is readily constructed and easy to
think about. If the above 3 paragraphs are reasonable, then what I am
struggling with is that perhaps this suggests the analysis model may not
correct. That is, the "compatibility" of the responses and doses may not be
adequately addressed when constructing the likelihood. Is the correlation
between doses and etas being appropriately expressed in the likelihood?
This thread reminded me of the article: Beal SL. Conditioning on certain
random events associated with statistical variability in PK/PD. J
Pharmacokinet Pharmacodyn. 2005 Apr;32(2):213-43. Therein he discussed dose
titration; and if memory serves, the likelihood for conditioning on the
observed doses is pretty complicated in order to keep the responses and etas
and doses compatible (perhaps). Perhaps his article will shed some light on
the situation?....
Kind regards,
Matt
Quoted reply history
-----Original Message-----
From: [email protected] [mailto:[email protected]] On
Behalf Of Nick Holford
Sent: Tuesday, September 22, 2009 6:13 AM
To: nmusers
Subject: Re: FW: [NMusers] VPC appropriateness in complex PK
Martin,
I understand it is a problem to simulate adaptive dosing when the rules
used by the clinicians are unknown (or not followed). However, I see no
reason not to use a plausible set of rules to try to simulate the know
adaptive dosing. Ignoring this will lead to differences between observed
and predicted distributions as shown by a VPC even if the structural and
random effects model derived from the original data is fine.
Adding a dosing regimen model to the simulation structure is not really
any different from changing other components of the original model. It
may involve a few "informed guess" parameters but if you can get a good
agreement between observations and simulated predictions then this can
be rewarding in two ways:
The first is that it may produce a VPC that helps to confirm the
structural and random effects model assumptions and parameter estimates.
An example of this is shown in Karlsson & Holford 2008 Slide 27/28 shown
at PAGE last year. Dropout simulation based on the simulated response
(informative missingness) led to good agreement between the observed and
simulated distributions shown in a VPC. Dropout simulation is just an
example of adaptive design and in principle is no different from
adaptive dosing changes to the design.
The second is that the adaptive dosing model that is found to help
describe the observations can now be used with some confidence to
simulate future trials when adaptive dosing is not strictly controlled
but is likely to follow the pattern in the original study. This is not
an unreasonable assumption as we frequently make it for other parts of
the model when doing clinical trial simulations.
This brings me to your question to me. A PC-VPC may help to confirm a
model for describing the data but if it does not simulate using adaptive
dosing, for a trial that used adaptive dosing, then it cannot help
understand what kind of model should be used to simulate adaptive dosing
in a future design. This illustrates an important difference between
empirical (PC-VPC) and mechanism based (adaptive dose simulation).
Results from empirical methods ("confirming") speak to the past while
mechanism based methods ("learning") can help predict the future.
You mention that in your experience that SPCs are not useful for
adaptive dosing studies because of correlation between ETAs and design.
I can understand why NPCs would fail (they have the same problem as VPC
when comparisons are made directly between the distributions of
observations and predictions) but not NPDE. I have struggled with the
properties of NPDE in adaptive design but have no direct experience. I
have recently responded on nmusers to comments from Yaning Wang which
make me think that NPDE should be fine to evaluate adaptive designs
provided the original dosing is used for the simulation. Can you tell us
more about your experiences? Do you have examples that show that NPDE
comes to the wrong conclusion about a model when the original design is
based on adaptive dosing?
Best wishes,
Nick
Karlsson MO, Holford NHG. A Tutorial on Visual Predictive Checks. PAGE
17 (2008) Abstr 1434 [wwwpage-meetingorg/?abstract=1434]. 2008.