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Re: Inflated random effects showed by VPC

From: Nick Holford <n.holford>
Date: Fri, 05 Sep 2014 08:43:53 +1200


To respond to your first sentence. A VPC may show a difference between
the distribution of the observations and the distribution of the
predictions due to misspecification of the fixed effect part of the
model. This includes differences in the lower and upper percentiles
which are often mistakenly thought to just reflect the random effects
part of the model.

Please look at the poster pdf you will find in the following URL. This
uses a rather primitive kind of VPC but nevertheless show clearly how
known fixed effect model misspecification can widen ("inflate") the
lower and upper percentiles of the predictions compared to the observations.

The same pdf may be consulted to see that the so called GOF plots may be
misleading and do not mean the fixed effects are OK.

You could try simulating a dataset using the parameters from your best
model so far then fit that dataset and use the resulting parameters to
construct a VPC. You will then know both the fixed and random effects
parts of the model are correct and can then judge how well the VPC can
confirm the known model structure. You can then try misspecifying the
model and refit the simulated dataset created with a known model and
then see how well the VPC can help diagnose the model misspecification.

Best wishes,


On 5/09/2014 4:15 a.m., Jiang, Yu wrote:
> Dear all,
> I wonder what might cause a pharmacokinetic model to have inflated
> variability. For my model, the GOF plots look reasonably good--meaning
> that the fixed effects are OK. However the prediction corrected VPC
> implemented by PsN indicated severely overestimated variability
> regardless of whether I stratify them into different dose groups or
> analysis them altogether. I have tried all my candidate models, all of
> them have the observed 95th and 5th percentile way off from the
> simulated confidence bands, and for some of them, the observation
> points don't even go into the upper and lower confidence interval bands.
> I checked my eta plots, and I think although they don't look perfectly
> normal, they still looks reasonably symmetrical with a bell shape. Eta
> on V seems to be a little skewed to the right. I don't have much
> experience on PopPK so I might be wrong.
> I think there might three possibilities causing this problem.
> One is that, the true distribution of etas is not normally distributed
> but more like uniformly distributed (or skewed). The estimation step
> have no problem of identifying the right mean and variance for
> parameters even the true underlying distribution is not normal
> distribution. But when it comes to simulation, the simulated
> parameters are draw from the normal distribution with the estimated
> mean and variance. That discrepancy might cause inflated variability
> in simulated parameters and therefore inflated variability in
> simulated observations.
> The other is that there are a few subjects having very large eta
> compared with other subjects, therefore inflated the estimated omega.
> Also all my subjects are dosed based on their weight, height, gender
> and age to achieve a target drug concentration level. They might do a
> very good job making the concentrations to reach the target level so
> all of my observations lies in the middle of the prediction corrected
> VPC plots. I think this is the least likely possibility since I have
> already taken covariate effects into consideration in some of my models..
> I am not sure I am thinking it right. Please correct me if I am wrong.
> Does anyone have any thoughts into this? Has anyone encountered
> similar things before? I truly appreciate any comments or suggestions.
> Yu
> Graduate student in Clinical Pharmaceutical Science
> University of Iowa

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
office:+64(9)923-6730 mobile:NZ +64(21)46 23 53
email: n.holford

Holford SD, Allegaert K, Anderson BJ, Kukanich B, Sousa AB, Steinman A, Pypendop, B., Mehvar, R., Giorgi, M., Holford,N.H.G. Parent-metabolite pharmacokinetic models - tests of assumptions and predictions. Journal of Pharmacology & Clinical Toxicology. 2014;2(2):1023-34.

Ribba B, Holford N, Magni P, Trocóniz I, Gueorguieva I, Girard P, Sarr,C., Elishmereni,M., Kloft,C., Friberg,L. A review of mixed-effects models of tumor growth and effects of anticancer drug treatment for population analysis. CPT: pharmacometrics & systems pharmacology. 2014;Accepted 15-Mar-2014.

Received on Thu Sep 04 2014 - 16:43:53 EDT

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