Paul,
The procedure you describe is a way of producing a posterior predictive
check but I don't know of any good examples of its use. A simpler way of
doing a PPC samples the population parameter estimates from a
distribution centered on the final estimates with a variance-covariance
based on the estimated standard errors and their correlation. VPCs are
not posterior predictive checks because they do not take account of the
posterior distribution of the parameter estimates (i.e. the final
estimates with their uncertainty). A VPC typically ignores the parameter
uncertainty and uses what has been called the degenerate posterior
distribution (See Yano Y, Beal SL, Sheiner LB. Evaluating
pharmacokinetic/pharmacodynamic models using the posterior predictive
check. J Pharmacokinet Pharmacodyn. 2001;28(2):171-92 for terminology,
methods and examples).
When I spoke of uncertainty I did not mean random variability (OMEGA and
SIGMA). A VPC will simulate observations using the final THETA, OMEGA
and SIGMA estimates.
You can calculate distribution statistics for your observations (such as
median and 90% intervals) by combining the observations (one per
individual) at each time point to create an empirical distribution. The
statistics are then determined from this empirical distribution. In
order to get sufficient numbers of points (at least 10 is desirable) you
may need to bin observations into time intervals e.g. 0-30 mins, 30-60
mins etc.
Nick
Paul Matthew Westwood wrote:
________________________________________
From: Paul Matthew Westwood
Sent: 22 July 2008 13:20
To: Nick Holford
Subject: RE: [NMusers] PPC
Nick,
Thanks for your reply and apologies once again for another confusing email. I
think I am using VPC, which as I understand it is simulating n datasets using
the final parameter estimates gained from the final model, and then taking the
median and 90% confidence interval (for example) for each simulated
concentration and comparing these to the real concentrations. Whereas, PPC is
where you then run the final model through the simulated datasets and compare
selected statistics of these new runs with the original. Is this correct? You
mentioned including uncertainty on the parameter estimates in the simulated
datasets. Would one usually not include uncertainty (fixing the error terms to
zero) in the simulated datasets? Doing this with mine obviously produced much
better concentrations with no negative values and no 'significant' outliers.
Another thing you mentioned is comparing the median of the simulated
concentrations with the median of the original dataset concentrations, but as
there is only one sample for any particular time point would this indicate the
unsuitability of VPC (and furthermore PPC) for this model?
Thanks again,
Paul.
________________________________________
From: [EMAIL PROTECTED] [EMAIL PROTECTED] On Behalf Of Nick Holford [EMAIL
PROTECTED]
Sent: 22 July 2008 10:30
To: nmusers@globomaxnm.com
Subject: Re: [NMusers] PPC
Paul,
Its not clear to me if you did a VPC (visual predictive check) using
just the final estimates of the parameters) or tried to do a posterior
predictive check (PPC) including uncertainty on the parameter estimates
in the simulation.
I dont have any experience with PPC but I dont think its helpful for
model evaluation. Its more of a tool for understanding uncertainties of
predictions for future studies.
I assume you dont have complications like informative dropout processes
to complicate the simulation so if you did a VPC and the median of the
predictions doesnt match the median of the observations then your model
needs more work.
Some negative concs are OK but 'impossibly high values' point to
problems with your model.
So I think you can safely say the VPC has worked very well -- it has
told you that you need to think more about your model. You might find
some ideas in these references:
1. Tod M, Jullien V, Pons G. Facilitation of drug evaluation in
children by population methods and modelling. Clin Pharmacokinet.
2008;47(4):231-43.
2. Anderson BJ, Holford NH. Mechanism-Based Concepts of Size and
Maturity in Pharmacokinetics. Annu Rev Pharmacol Toxicol. 2008;48:303-32.
Nick
Paul Matthew Westwood wrote:
Hello all,
I wonder if someone can give me some tips on PPC.
I am working on a midazolam dataset with a pediatric population, and have
decided to use PPC as a model validation technique. The dataset I am modelling
has up to 43 patients, at different ages, different weights, different times of
dosing and sampling, and different doses. I simulated 100 datasets using NONMEM
VI, fixing all parameters to the final estimates from the model. The simulated
datasets produced had a large proportion of negative concentrations, and also a
few impossibly large concentration values. Also the median, 5th and 95th
percentiles were not very promising, and the resulting graphs not very clean.
Firstly, can I use PPC with any degree of confidence with a dataset such as
this, and if so, do I omit the negative concentration values from the analysis?
Thanks in advance for any help given.
Paul Westwood,
PhD Student,
QUB,
Belfast.
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
[EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:+64(9)373-7090
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
[EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:+64(9)373-7090
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
