Hi,
I realized after I sent the comment below about mixture model
**simulations** that Mats was no doubt referring to the problem of
separating the two sub-populations in the **observed** data using
MIXEST. This will of course be problematic for generating prediction
percentiles for the 2 populations as Mats pointed out when there is
shrinkage of the EBEs which lead to the 'decision' about MIXEST.
This is an example of why one must be cautious interpreting a VPC when
the observed data is not 'correct' for comparison with the simulation
predictions. Another example is when there is data missing in the
observations which is not missing completely at random (e.g. dropouts
due to adverse effects). Adding a dropout model to the VPC simulation
can help sometimes in 'correcting' the simulation so that it matches the
observed data better.
Mats, can you suggest a way to try to correct for the Bayesian shrinkage
problem for obtaining MIXEST?
Nick
Nick Holford wrote:
Mats,
A VPC relies on simulation alone - there is no estimation step.
Presumably if the population estimate of the % of poor metabolizers is
5% then NONMEM will simulate 5% of the population as a poor
metaboliser. There is no Bayesian 'posthoc' step hidden in the way
that NONMEM does simulations is there? I had assumed (but have never
checked) that if one tabulates the value of MIXEST obtained when using
$SIM that the proportion of MIXEST values would not be biased compared
to the population value.
Nck
Mats Karlsson wrote:
Hi Leonid,
I would not do it for just the reason you mention. I would not want to
condition my VPC on the model results. Especially as we know that the
subpopulation assignment suffer from the same problems as other
empirical
Bayes estimates. "Shrinkage" when it comes to subpopulation
assignment will
have the consequence that the larger of (two) subpopulations having a
higher
fraction of POSTHOC assignments than the Pmix estimate for that
subpopulation. This is expected and I have often seen it. So you may
well
have a situation when the population estimate of poor metabolizers is
5%,
but only 2% are allocated to this subpopulation by the EBE step.
Best regards,
Mats
Mats Karlsson, PhD
Professor of Pharmacometrics
Dept of Pharmaceutical Biosciences
Uppsala University
Box 591
751 24 Uppsala Sweden
phone: +46 18 4714105
fax: +46 18 471 4003
-----Original Message-----
From: Leonid Gibiansky [mailto:[email protected]] Sent:
Tuesday, April 14, 2009 9:06 PM
To: Mats Karlsson
Cc: 'Satyendra Suryawanshi'; [email protected]
Subject: Re: [NMusers] VPC with Mixture Model
Hi Mats,
Could you elaborate why you would not stratify based on the
subpopulations? It seems perfectly reasonable for me to simulate from
the model (including random assignment of subpopulations), and then
compare "apples to apples": observed subpopulation versus simulated
subpopulations. In your example of 5% poor metabolizers, I would plot
observed poor metabolizers (as assigned by the model) versus
simulated poor metabolizers (as simulated from the model). Indeed,
poor metabolizers assignment would be defined by the model, so this
VPC will be conditioned on the model posthoc EST prediction, but the
remaining parts of the model would be tested by this procedure. If
the model is good, VPC should provide good results. It is unclear to
me how sensitive this procedure is to model misspecification (in
general, I think VPC is less sensitive to model misspecification than
other model diagnostics)
Thanks
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
Mats Karlsson wrote:
Dear Satyendra,
Interesting question. I don't think there is much written about
this, but I may be wrong. What I would not do is to try to stratify
based on estimated subpopulation allocation ("EST"). Rather I would
use the same VPCs as if there had been no mixture model. Possibly
what you could do is be more careful in your choice of prediction
intervals to display. For example, if you have a subpopulation of
poor metabolizers of about 5%, displaying only median and
interquartile range PIs may not be a good idea.
Best regards,
Mats
Mats Karlsson, PhD
Professor of Pharmacometrics
Dept of Pharmaceutical Biosciences
Uppsala University
Box 591
751 24 Uppsala Sweden
phone: +46 18 4714105
fax: +46 18 471 4003
*From:* [email protected]
[mailto:[email protected]] *On Behalf Of *Satyendra
Suryawanshi
*Sent:* Tuesday, April 14, 2009 6:50 PM
*To:* [email protected]
*Subject:* [NMusers] VPC with Mixture Model
Dear all,
I have a Mixture Model with 2 subpopulation. Now I want to check its
prediction. One way to see this is a Visual Predictive Check. My
question is, How to perform visual predictive check with mixture model?
I will be thankful for your suggestion and references.
Best regards
Satyendra Suryawanshi, PhD
University of Tennessee Health Science Center
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
[email protected] tel:+64(9)923-6730 fax:+64(9)373-7090
mobile: +33 64 271-6369 (Apr 6-Jul 17 2009)
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
