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
Inflated random effects showed by VPC
Dear Yu,
Did you explore block Omega structures to investigate potential correlations
among the random effects? If you assumed a diagonal Omega structure where
the random effects are assumed to be independent when they are indeed
correlated this can inflate the between-subject variability in your
simulations of the concentrations. For example, if the IIV random effects
for CL and V are highly correlated but you simulate assuming these random
effects are independent then you will likely simulate some extreme
combinations of subject-specific values of CL and V that may not be
represented in your data.
Ken
Kenneth G. Kowalski
President & CEO
A2PG - Ann Arbor Pharmacometrics Group, Inc.
110 Miller Ave., Garden Suite
Ann Arbor, MI 48104
Work: 734-274-8255
Cell: 248-207-5082
Fax: 734-913-0230
<mailto:[email protected]> [email protected]
http://www.a2pg.com www.a2pg.com
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Jiang, Yu
Sent: Thursday, September 04, 2014 12:15 PM
To: [email protected]
Subject: [NMusers] Inflated random effects showed by VPC
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
Dear You,
pVPC sometimes inflates variability especially if some of the measurements are near BQL. Look at simple VPC, may be using concentrations normalized by dose (if the system is linear).
Sometimes is the very useful to clean the data. Look on the individual plots where you have DV, IPRED and PRED superimposed, and dose times marked. For subjects where you have large discrepancies between IPRED and PRED, look at whether DVs are consistent or you have some outliers. You can also look at observations with large abs(CWRES) to see whether they should be removed (not because they have high CWRES but due to some timing or dosing errors that could be obvious from looking on the plots)
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
Quoted reply history
On 9/4/2014 12:15 PM, 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
>
> No virus found in this message.
> Checked by AVG - www.avg.com http://www.avg.com
> Version: 2014.0.4765 / Virus Database: 4015/8153 - Release Date: 09/04/14
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
--
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: [email protected]
http://holford.fmhs.auckland.ac.nz/
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.