Re: Inflated random effects showed by VPC
Jiang,
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.
http://www.page-meeting.org/default.asp?abstract=738
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,
Nick
Quoted reply history
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
--
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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.