Dear all,
I would like to share with you and get people's opinions on a recent issue I
had.
I have a data set of 46 patients, orally dosed, with very dense sampling
during absorption (0.25h, 0.5h, 0.75h, 1h, 1.5h, 2h, 3h, 4h, 6h, 8h, 12h,
24h, 36h), Cmax at around 4 hours.
During modelling, I found that the residual error was not evenly
distributed. Plotting CWRES against time after dose, the result looked like
an "hourglass" shape. I.e. A wide spread during absorption, narrower near
Cmax time, then wider at later time points.
My thinking was as follows: Residual error contains both the assay / model
spec. error, and the error in recorded observation time. When the gradient
of the PK curve is large, any error in recorded observation time equals a
large error in the recorded concentration, whereas if the gradient is small
then the recorded concentration error will be small.
I "split" the residual error into its assay/model spec and time-error parts
in the $ERROR block:
$ERROR
GRAD = KA*A(2) - K20*A(3)
IF (GRAD.LT.0) GRAD = -1*GRAD
C_1 = A(3)/V ; Concentration in the
central compartment
IPRED = C_1
SD = SQRT(EPROP*C_1**2) ; Standard deviation of
predicted concentration
Y=IPRED+SD*(1+val*GRAD)*EPS(1)
Note: Sigma is fixed to one and EPROP is estimated as a theta. Here, GRAD is
the right hand side of the differential equation for A(3), in order to
recover the gradient. Val is estimated by NONMEM.
This approach vastly improved the model fit (OFV drop of around 350!). All
GOF plots, VPCs, NPCs, NPDEs, individual fits looked good. This got me
thinking, and I tried this approach on some of my other popPK models. I
found for the simpler models, the result was nearly always a significant
improvement in the model fit. For the more complicated models, NONMEM had
trouble finishing the runs.
I struggled to find any approach like this in the literature, which leads me
to believe that there is something wrong, as it is a relatively simple
concept. Please, what are peoples thoughts on this?
Thanks,
Jon
Jon Moss, PhD
Modeller
BAST Inc Limited
Loughborough Innovation Centre
Charnwood Wing
Holywell Park
Ashby Road
Loughborough, LE11 3AQ, UK
Tel: +44 (0)1509 222908
Splitting the residual error
Dear Jon,
As you point out the concept of residual error magnitude being dependent on
anything else than the prediction itself is a straightforward. Yet it is, I
think underused and that is why you may not see it much in the literature. In
addition to what you mention, a large component is that model misspecification
is not a homogeneous process. It is likely that most of our models are more
specified for absorption than disposition. Absorption contains many processes
that are discrete and difficult to easily capture in simple models.
For most compunds, the absolute gradient is much higher during the absorption
phase than the distribution phase and that is probably a contributing factor to
what experience. You would probably get as good an improvement if you had a
separate error magnitude during the absorption phase.
The model you mentioned with were outlined in the 1998 article below. I also
add some other articles for the case you're further interested in residual
error modeling.
Best regards,
Mats
1.
A strategy for residual error modeling incorporating scedasticity of variance
and distribution http://www.ncbi.nlm.nih.gov/pubmed/26679003
Dosne AG, Bergstrand M, Karlsson MO.
J Pharmacokinet Pharmacodyn. 2016 Apr;43(2):137-51. doi:
10.1007/s10928-015-9460-y. Epub 2015 Dec 17.
PMID: 26679003 [PubMed - in process] Free PMC Article
Similar
http://www.ncbi.nlm.nih.gov/pubmed?linkname=pubmed_pubmed&from_uid=26679003
2.
The impact of misspecification of residual error or correlation structure on
the type I error rate for covariate
http://www.ncbi.nlm.nih.gov/pubmed/19219538
Silber HE, Kjellsson MC, Karlsson MO.
J Pharmacokinet Pharmacodyn. 2009 Feb;36(1):81-99. doi:
10.1007/s10928-009-9112-1. Epub 2009 Feb 14.
PMID: 19219538 [PubMed - indexed for MEDLINE]
Similar
http://www.ncbi.nlm.nih.gov/pubmed?linkname=pubmed_pubmed&from_uid=19219538
3.
Three new residual error models for population PK/PD
http://www.ncbi.nlm.nih.gov/pubmed/8733951
Karlsson MO, Beal SL, Sheiner LB.
J Pharmacokinet Biopharm. 1995 Dec;23(6):651-72.
PMID: 8733951 [PubMed - indexed for MEDLINE]
Similar
http://www.ncbi.nlm.nih.gov/pubmed?linkname=pubmed_pubmed&from_uid=8733951
4.
Assumption testing in population pharmacokinetic models: illustrated with an
analysis of moxonidine data from congestive heart failure
http://www.ncbi.nlm.nih.gov/pubmed/9795882
Karlsson MO, Jonsson EN, Wiltse CG, Wade JR.
J Pharmacokinet Biopharm. 1998 Apr;26(2):207-46.
PMID:
9795882
Mats Karlsson, PhD
Professor of Pharmacometrics
Dept of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
75124 Uppsala
Phone: +46 18 4714105
Fax + 46 18 4714003
http://www.farmbio.uu.se/research/researchgroups/pharmacometrics/
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Jonathan Moss
Sent: Friday, May 13, 2016 11:37 AM
To: [email protected]
Subject: [NMusers] Splitting the residual error
Dear all,
I would like to share with you and get people's opinions on a recent issue I
had.
I have a data set of 46 patients, orally dosed, with very dense sampling during
absorption (0.25h, 0.5h, 0.75h, 1h, 1.5h, 2h, 3h, 4h, 6h, 8h, 12h, 24h, 36h),
Cmax at around 4 hours.
During modelling, I found that the residual error was not evenly distributed.
Plotting CWRES against time after dose, the result looked like an "hourglass"
shape. I.e. A wide spread during absorption, narrower near Cmax time, then
wider at later time points.
My thinking was as follows: Residual error contains both the assay / model
spec. error, and the error in recorded observation time. When the gradient of
the PK curve is large, any error in recorded observation time equals a large
error in the recorded concentration, whereas if the gradient is small then the
recorded concentration error will be small.
I "split" the residual error into its assay/model spec and time-error parts in
the $ERROR block:
$ERROR
GRAD = KA*A(2) - K20*A(3)
IF (GRAD.LT.0) GRAD = -1*GRAD
C_1 = A(3)/V ; Concentration in the
central compartment
IPRED = C_1
SD = SQRT(EPROP*C_1**2) ; Standard deviation of
predicted concentration
Y=IPRED+SD*(1+val*GRAD)*EPS(1)
Note: Sigma is fixed to one and EPROP is estimated as a theta. Here, GRAD is
the right hand side of the differential equation for A(3), in order to recover
the gradient. Val is estimated by NONMEM.
This approach vastly improved the model fit (OFV drop of around 350!). All GOF
plots, VPCs, NPCs, NPDEs, individual fits looked good. This got me thinking,
and I tried this approach on some of my other popPK models. I found for the
simpler models, the result was nearly always a significant improvement in the
model fit. For the more complicated models, NONMEM had trouble finishing the
runs.
I struggled to find any approach like this in the literature, which leads me to
believe that there is something wrong, as it is a relatively simple concept.
Please, what are peoples thoughts on this?
Thanks,
Jon
Jon Moss, PhD
Modeller
BAST Inc Limited
Loughborough Innovation Centre
Charnwood Wing
Holywell Park
Ashby Road
Loughborough, LE11 3AQ, UK
Tel: +44 (0)1509 222908
Dear Jon,
We routinely use separate residual errors during absorption and later (say, a larger error in the first X hours), although I do not remember whether we published any of those models.
Regards,
Katya
Ekaterina Gibiansky, Ph.D.
CEO&CSO, QuantPharm LLC
Web:www.quantpharm.com
Email:[email protected]
Quoted reply history
On 5/13/2016 6:37 AM, Mats Karlsson wrote:
> Dear Jon,
>
> As you point out the concept of residual error magnitude being dependent on anything else than the prediction itself is a straightforward. Yet it is, I think underused and that is why you may not see it much in the literature. In addition to what you mention, a large component is that model misspecification is not a homogeneous process. It is likely that most of our models are more specified for absorption than disposition. Absorption contains many processes that are discrete and difficult to easily capture in simple models.
>
> For most compunds, the absolute gradient is much higher during the absorption phase than the distribution phase and that is probably a contributing factor to what experience. You would probably get as good an improvement if you had a separate error magnitude during the absorption phase.
>
> The model you mentioned with were outlined in the 1998 article below. I also add some other articles for the case you’re further interested in residual error modeling.
>
> Best regards,
>
> Mats
>
> 1.
>
> A strategy for residual error modeling incorporating scedasticity of variance and distribution shape. < http://www.ncbi.nlm.nih.gov/pubmed/26679003 >
>
> Dosne AG, Bergstrand M, Karlsson MO.
>
> J Pharmacokinet Pharmacodyn. 2016 Apr;43(2):137-51. doi: 10.1007/s10928-015-9460-y. Epub 2015 Dec 17.
>
> PMID: 26679003 [PubMed - in process]*Free PMC Article *
>
> Similar articles < http://www.ncbi.nlm.nih.gov/pubmed?linkname=pubmed_pubmed&from_uid=26679003 >
>
> 2.
>
> The impact of misspecification of residual error or correlation structure on the type I error rate for covariate inclusion. < http://www.ncbi.nlm.nih.gov/pubmed/19219538 >
>
> Silber HE, Kjellsson MC, Karlsson MO.
>
> J Pharmacokinet Pharmacodyn. 2009 Feb;36(1):81-99. doi: 10.1007/s10928-009-9112-1. Epub 2009 Feb 14.
>
> PMID: 19219538 [PubMed - indexed for MEDLINE]
>
> Similar articles < http://www.ncbi.nlm.nih.gov/pubmed?linkname=pubmed_pubmed&from_uid=19219538 >
>
> 3.
>
> Three new residual error models for population PK/PD analyses. < http://www.ncbi.nlm.nih.gov/pubmed/8733951 >
>
> Karlsson MO, Beal SL, Sheiner LB.
>
> J Pharmacokinet Biopharm. 1995 Dec;23(6):651-72.
>
> PMID: 8733951 [PubMed - indexed for MEDLINE]
>
> Similar articles < http://www.ncbi.nlm.nih.gov/pubmed?linkname=pubmed_pubmed&from_uid=8733951 >
>
> 4.
>
> Assumption testing in population pharmacokinetic models: illustrated with an analysis of moxonidine data from congestive heart failure patients. < http://www.ncbi.nlm.nih.gov/pubmed/9795882 >
>
> *Karlsson MO*, Jonsson EN, Wiltse CG, Wade JR.
>
> J Pharmacokinet Biopharm. 1998 Apr;26(2):207-46.
>
> PMID:
>
> 9795882
>
> Mats Karlsson, PhD
>
> Professor of Pharmacometrics
>
> Dept of Pharmaceutical Biosciences
>
> Faculty of Pharmacy
>
> Uppsala University
>
> Box 591
>
> 75124 Uppsala
>
> Phone: +46 18 4714105
>
> Fax + 46 18 4714003
>
> www.farmbio.uu.se/research/researchgroups/pharmacometrics/ < http://www.farmbio.uu.se/research/researchgroups/pharmacometrics/ >
>
> *From:* [email protected] [ mailto: [email protected] ] *On Behalf Of *Jonathan Moss
>
> *Sent:* Friday, May 13, 2016 11:37 AM
> *To:* [email protected]
> *Subject:* [NMusers] Splitting the residual error
>
> Dear all,
>
> I would like to share with you and get people’s opinions on a recent issue I had.
>
> I have a data set of 46 patients, orally dosed, with very dense sampling during absorption (0.25h, 0.5h, 0.75h, 1h, 1.5h, 2h, 3h, 4h, 6h, 8h, 12h, 24h, 36h), Cmax at around 4 hours.
>
> During modelling, I found that the residual error was not evenly distributed. Plotting CWRES against time after dose, the result looked like an “hourglass” shape. I.e. A wide spread during absorption, narrower near Cmax time, then wider at later time points.
>
> My thinking was as follows: Residual error contains both the assay / model spec. error, and the error in recorded observation time. When the gradient of the PK curve is large, any error in recorded observation time equals a large error in the recorded concentration, whereas if the gradient is small then the recorded concentration error will be small.
>
> I “split” the residual error into its assay/model spec and time-error parts in the $ERROR block:
>
> $ERROR
>
> GRAD = KA*A(2) - K20*A(3)
>
> IF (GRAD.LT.0) GRAD = -1*GRAD
>
> C_1 = A(3)/V ; Concentration in the central compartment
>
> IPRED = C_1
>
> SD = SQRT(EPROP*C_1**2) ; Standard deviation of predicted concentration
>
> Y=IPRED+SD*(1+val*GRAD)*EPS(1)
>
> Note: Sigma is fixed to one and EPROP is estimated as a theta. Here, GRAD is the right hand side of the differential equation for A(3), in order to recover the gradient. Val is estimated by NONMEM.
>
> This approach vastly improved the model fit (OFV drop of around 350!). All GOF plots, VPCs, NPCs, NPDEs, individual fits looked good. This got me thinking, and I tried this approach on some of my other popPK models. I found for the simpler models, the result was nearly always a significant improvement in the model fit. For the more complicated models, NONMEM had trouble finishing the runs.
>
> I struggled to find any approach like this in the literature, which leads me to believe that there is something wrong, as it is a relatively simple concept. Please, what are peoples thoughts on this?
>
> Thanks,
>
> Jon
>
> *Jon Moss, PhD*
>
> Modeller
>
> *BAST Inc Limited*
>
> Loughborough Innovation Centre
>
> Charnwood Wing
>
> Holywell Park
>
> Ashby Road
>
> Loughborough, LE11 3AQ, UK
>
> Tel: +44 (0)1509 222908
Steve,
In papers 3 and 4 below, we outlined and tested a few different models for
separating error models for absorption and disposition based on time or partial
derivatives versus time or Ka. Overall message is *that* you do it is more
important than *how* you do it. I typically choose a simple way of doing it,
like allowing a separate residual error magnitude up until a little after Tmax.
Best regards,
Mats
Mats Karlsson, PhD
Professor of Pharmacometrics
Dept of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
75124 Uppsala
Phone: +46 18 4714105
Fax + 46 18 4714003
http://www.farmbio.uu.se/research/researchgroups/pharmacometrics/
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Ekaterina Gibiansky
Sent: Saturday, May 14, 2016 12:13 AM
To: Stephen Duffull; Andre Jackson; nmusers
Subject: Re: [NMusers] Splitting the residual error
Hi Steve and Andre,
No, nothing fancy, I did not even estimate the time of the switch. Something
like this:
ITAD=1
IF(TAD.LE.4) ITAD=THETA(10)
Y=F + (F*ITAD*ERR(1)+ERR(2))
ITAD can also include differences in populations, e.g. Phase 1 versus Phase 2-3
data, or healthy versus patients, etc.
The number for switch usually is pretty obvious from the data, but yes
estimating it would be nicer.
Regards,
Katya
On 5/13/2016 4:33 PM, Stephen Duffull wrote:
Hi Katya
Are they discrete models with estimated transition times (e.g. error model 1
from 0 to 2 hours, then error model 2 etc) or continuous models (two models
who's weighting is time dependent) that overlap?
We do the former as a diagnostic but not the latter at this point. But I have
pondered.
Cheers
Steve
From: [email protected]<mailto:[email protected]>
[mailto:[email protected]] On Behalf Of Ekaterina Gibiansky
Sent: Saturday, 14 May 2016 2:07 a.m.
To: Jonathan Moss <[email protected]><mailto:[email protected]>;
[email protected]<mailto:[email protected]>
Subject: Re: [NMusers] Splitting the residual error
Dear Jon,
We routinely use separate residual errors during absorption and later (say, a
larger error in the first X hours), although I do not remember whether we
published any of those models.
Regards,
Katya
Ekaterina Gibiansky, Ph.D.
CEO&CSO, QuantPharm LLC
Web:www.quantpharm.com
Email:[email protected]<mailto:Email:[email protected]>
On 5/13/2016 6:37 AM, Mats Karlsson wrote:
Dear Jon,
As you point out the concept of residual error magnitude being dependent on
anything else than the prediction itself is a straightforward. Yet it is, I
think underused and that is why you may not see it much in the literature. In
addition to what you mention, a large component is that model misspecification
is not a homogeneous process. It is likely that most of our models are more
specified for absorption than disposition. Absorption contains many processes
that are discrete and difficult to easily capture in simple models.
For most compunds, the absolute gradient is much higher during the absorption
phase than the distribution phase and that is probably a contributing factor to
what experience. You would probably get as good an improvement if you had a
separate error magnitude during the absorption phase.
The model you mentioned with were outlined in the 1998 article below. I also
add some other articles for the case you're further interested in residual
error modeling.
Best regards,
Mats
1.
A strategy for residual error modeling incorporating scedasticity of variance
and distribution http://www.ncbi.nlm.nih.gov/pubmed/26679003
Dosne AG, Bergstrand M, Karlsson MO.
J Pharmacokinet Pharmacodyn. 2016 Apr;43(2):137-51. doi:
10.1007/s10928-015-9460-y. Epub 2015 Dec 17.
PMID: 26679003 [PubMed - in process] Free PMC Article
Similar
http://www.ncbi.nlm.nih.gov/pubmed?linkname=pubmed_pubmed&from_uid=26679003
2.
The impact of misspecification of residual error or correlation structure on
the type I error rate for covariate
http://www.ncbi.nlm.nih.gov/pubmed/19219538
Silber HE, Kjellsson MC, Karlsson MO.
J Pharmacokinet Pharmacodyn. 2009 Feb;36(1):81-99. doi:
10.1007/s10928-009-9112-1. Epub 2009 Feb 14.
PMID: 19219538 [PubMed - indexed for MEDLINE]
Similar
http://www.ncbi.nlm.nih.gov/pubmed?linkname=pubmed_pubmed&from_uid=19219538
3.
Three new residual error models for population PK/PD
http://www.ncbi.nlm.nih.gov/pubmed/8733951
Karlsson MO, Beal SL, Sheiner LB.
J Pharmacokinet Biopharm. 1995 Dec;23(6):651-72.
PMID: 8733951 [PubMed - indexed for MEDLINE]
Similar
http://www.ncbi.nlm.nih.gov/pubmed?linkname=pubmed_pubmed&from_uid=8733951
4.
Assumption testing in population pharmacokinetic models: illustrated with an
analysis of moxonidine data from congestive heart failure
http://www.ncbi.nlm.nih.gov/pubmed/9795882
Karlsson MO, Jonsson EN, Wiltse CG, Wade JR.
J Pharmacokinet Biopharm. 1998 Apr;26(2):207-46.
PMID:
9795882
Mats Karlsson, PhD
Professor of Pharmacometrics
Dept of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
75124 Uppsala
Phone: +46 18 4714105
Fax + 46 18 4714003
http://www.farmbio.uu.se/research/researchgroups/pharmacometrics/
From: [email protected]<mailto:[email protected]>
[mailto:[email protected]] On Behalf Of Jonathan Moss
Sent: Friday, May 13, 2016 11:37 AM
To: [email protected]<mailto:[email protected]>
Subject: [NMusers] Splitting the residual error
Dear all,
I would like to share with you and get people's opinions on a recent issue I
had.
I have a data set of 46 patients, orally dosed, with very dense sampling during
absorption (0.25h, 0.5h, 0.75h, 1h, 1.5h, 2h, 3h, 4h, 6h, 8h, 12h, 24h, 36h),
Cmax at around 4 hours.
During modelling, I found that the residual error was not evenly distributed.
Plotting CWRES against time after dose, the result looked like an "hourglass"
shape. I.e. A wide spread during absorption, narrower near Cmax time, then
wider at later time points.
My thinking was as follows: Residual error contains both the assay / model
spec. error, and the error in recorded observation time. When the gradient of
the PK curve is large, any error in recorded observation time equals a large
error in the recorded concentration, whereas if the gradient is small then the
recorded concentration error will be small.
I "split" the residual error into its assay/model spec and time-error parts in
the $ERROR block:
$ERROR
GRAD = KA*A(2) - K20*A(3)
IF (GRAD.LT.0) GRAD = -1*GRAD
C_1 = A(3)/V ; Concentration in the
central compartment
IPRED = C_1
SD = SQRT(EPROP*C_1**2) ; Standard deviation of
predicted concentration
Y=IPRED+SD*(1+val*GRAD)*EPS(1)
Note: Sigma is fixed to one and EPROP is estimated as a theta. Here, GRAD is
the right hand side of the differential equation for A(3), in order to recover
the gradient. Val is estimated by NONMEM.
This approach vastly improved the model fit (OFV drop of around 350!). All GOF
plots, VPCs, NPCs, NPDEs, individual fits looked good. This got me thinking,
and I tried this approach on some of my other popPK models. I found for the
simpler models, the result was nearly always a significant improvement in the
model fit. For the more complicated models, NONMEM had trouble finishing the
runs.
I struggled to find any approach like this in the literature, which leads me to
believe that there is something wrong, as it is a relatively simple concept.
Please, what are peoples thoughts on this?
Thanks,
Jon
Jon Moss, PhD
Modeller
BAST Inc Limited
Loughborough Innovation Centre
Charnwood Wing
Holywell Park
Ashby Road
Loughborough, LE11 3AQ, UK
Tel: +44 (0)1509 222908