Re: FW: PPC
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:
> ________________________________________
Quoted reply history
> 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: [email protected]
> 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