Dear NMusers,
I have a question regarding simulations for a VPC. When a combined residual
error is used it happens that for low concentrations negative values are
simulated. While this is statistically correct, I wonder if it is correct to
use these results for the VPC because the distribution of the observed low
concentrations is truncated by the LLOQ. So the VPC might suggest model
misspecification for lower concentrations. Further, when one wants to use
the model for clinical trial simulation should then the negative (BQL)
values be omitted because they would never appear in reality?
I would like to know how the more experienced NMusers handle this.
Thanks in advance, Andreas.
____________________________
Andreas Lindauer
University of Bonn
Department of Clinical Pharmacy
An der Immenburg 4
D-53121 Bonn
phone:+49 228 73 5781
fax: +49 228 73 9757
Visual predictive check!
Andreas,
There are many ways to create a VPC (come to PAGE this year and hear about them from Mats Karlsson and myself).
In the specific case of using a VPC to simulate both the between subject variability and the residual unidentified variability for comparison with the observations then I would apply the same truncation rules used to create the model. If you have a LLOQ defined and you are in the unfortunate situation of not being able to use values less than LLOQ then I would suggest you truncate the simulations.
If you have honestly reported measurements (i.e. without omitting measurements less than LLOQ) then I would not truncate the simulated values -- I would even accept negative simulated values because if your residual error model was correct then there would be negative measured values.
Best wishes,
Nick
andreas lindauer wrote:
> Dear NMusers,
>
> I have a question regarding simulations for a VPC. When a combined residual error is used it happens that for low concentrations negative values are simulated. While this is statistically correct, I wonder if it is correct to use these results for the VPC because the distribution of the observed low concentrations is truncated by the LLOQ. So the VPC might suggest model misspecification for lower concentrations. Further, when one wants to use the model for clinical trial simulation should then the negative (BQL) values be omitted because they would never appear in reality?
>
> I would like to know how the more experienced NMusers handle this.
>
> Thanks in advance, Andreas.
>
> ____________________________
>
> Andreas Lindauer
>
> University of Bonn
>
> Department of Clinical Pharmacy
>
> An der Immenburg 4
>
> D-53121 Bonn
>
> phone:+49 228 73 5781
>
> fax: +49 228 73 9757
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
[EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:+64(9)373-7090
www.health.auckland.ac.nz/pharmacology/staff/nholford
Andreas,
You've raised an important, but sometimes overlooked, point about model checking using simulation-based methods. As Andrew Gelman points out in the reference below, when comparing simulated vs observed values you need to compare apples to apples. Either incorporate a model for the missing data in the simulation and compare the subset of non-missing data only, or impute the missing observed data and compare the complete (e.g. no-missing data) data sets.
Gelman et al. Multiple Imputation for Model Checking: Completed-Data Plots with Missing and Latent Data. Biometrics 61, 74–85 , March 2005
Marc
Marc R. Gastonguay, Ph.D.
President & CEO, Metrum Research Group LLC [www.metrumrg.com]
Scientific Director, Metrum Institute [www.metruminstitute.org]
Direct: 860-670-0744 Main: 860-735-7043
Email: [EMAIL PROTECTED]
Quoted reply history
On May 23, 2008, at 6:22 AM, andreas lindauer wrote:
> Dear NMusers,
>
> I have a question regarding simulations for a VPC. When a combined residual error is used it happens that for low concentrations negative values are simulated. While this is statistically correct, I wonder if it is correct to use these results for the VPC because the distribution of the observed low concentrations is truncated by the LLOQ. So the VPC might suggest model misspecification for lower concentrations. Further, when one wants to use the model for clinical trial simulation should then the negative (BQL) values be omitted because they would never appear in reality?
>
> I would like to know how the more experienced NMusers handle this.
> Thanks in advance, Andreas.
>
> ____________________________
>
> Andreas Lindauer
>
> University of Bonn
> Department of Clinical Pharmacy
> An der Immenburg 4
> D-53121 Bonn
>
> phone:+49 228 73 5781
> fax: +49 228 73 9757
Andreas,
Your simulations highlight a limitation with the combined (additive +
proportional or slope-intercept) residual error model. The combined
residual error model cannot be the correct model at very low concentrations
since the normal distribution will put non-zero probability mass at
concentrations less than zero if the mean is low relative to its SD. The
purist in me says don't truncate as that will lead to bias in your
simulations although it may be minimal if few observations are simulated
with negative concentrations. A better approach would be to consider an
alternative residual error model that bounds the concentrations to be
positive such as the log-normal residual error model (log-transform both
sides approach) or fit a model that takes into account the censored BQL data
( see Beal, Ways to Fit a PK Model with Some Data Below the Quantification
Limit. JPP 2001;28:481-504).
Ken
Kenneth G. Kowalski
President & CEO
A2PG - Ann Arbor Pharmacometrics Group
110 E. Miller Ave., Garden Suite
Ann Arbor, MI 48104
Work: 734-274-8255
Cell: 248-207-5082
[EMAIL PROTECTED]
Quoted reply history
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On
Behalf Of andreas lindauer
Sent: Friday, May 23, 2008 6:23 AM
To: [email protected]
Subject: [NMusers] Visual predictive check!
Dear NMusers,
I have a question regarding simulations for a VPC. When a combined residual
error is used it happens that for low concentrations negative values are
simulated. While this is statistically correct, I wonder if it is correct to
use these results for the VPC because the distribution of the observed low
concentrations is truncated by the LLOQ. So the VPC might suggest model
misspecification for lower concentrations. Further, when one wants to use
the model for clinical trial simulation should then the negative (BQL)
values be omitted because they would never appear in reality?
I would like to know how the more experienced NMusers handle this.
Thanks in advance, Andreas.
____________________________
Andreas Lindauer
University of Bonn
Department of Clinical Pharmacy
An der Immenburg 4
D-53121 Bonn
phone:+49 228 73 5781
fax: +49 228 73 9757
I prefer to do analysis in log-transformed variables thus avoiding this question entirely. Alternatively, you may try to create an error model that never returns negative values even in the non-transformed variables, but it is more complicated.
One way to compare simulation results with the real data is to remove BQL values from the simulated data set, compare data above LLOQ, but then also compare percent of data that is BQL (in the real and simulated data set). With NM6, you can get expected percent below LLQ (1-PR_Y) using YLO functionality
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
andreas lindauer wrote:
> Dear NMusers,
>
> I have a question regarding simulations for a VPC. When a combined residual error is used it happens that for low concentrations negative values are simulated. While this is statistically correct, I wonder if it is correct to use these results for the VPC because the distribution of the observed low concentrations is truncated by the LLOQ. So the VPC might suggest model misspecification for lower concentrations. Further, when one wants to use the model for clinical trial simulation should then the negative (BQL) values be omitted because they would never appear in reality?
>
> I would like to know how the more experienced NMusers handle this.
>
> Thanks in advance, Andreas.
>
> ____________________________
>
> Andreas Lindauer
>
> University of Bonn
>
> Department of Clinical Pharmacy
>
> An der Immenburg 4
>
> D-53121 Bonn
>
> phone:+49 228 73 5781
>
> fax: +49 228 73 9757
Andreas,
You might want to look at the reference below. Another way of comparing
apples to apples is to present the VPC while also visualizing the
percentage of expected but missing data (e.g. BQL data).
Post TM, Freijer JI, Ploeger BA, Danhof M. Extensions to the Visual
Predictive Check to facilitate model performance evaluation. J
Pharmacokinet Pharmacodyn. 2008 Apr;35(2):185-202
Teun
Teun Post, PharmD
Clinical Pharmacology and Kinetics - PK-PD - M&S
PK-PD Scientist
N.V. Organon, a part of Schering-Plough Corporation
KM2521 - PO Box 20 - 5340 BH - Oss - The Netherlands
T: +31 412 662782
F: +31 412 662506
_____
Quoted reply history
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]
On Behalf Of Gastonguay, Marc
Sent: Friday, 23 May, 2008 13:35
To: andreas lindauer
Cc: [email protected]
Subject: Re: [NMusers] Visual predictive check!
Andreas,
You've raised an important, but sometimes overlooked, point about model
checking using simulation-based methods. As Andrew Gelman points out in
the reference below, when comparing simulated vs observed values you
need to compare apples to apples. Either incorporate a model for the
missing data in the simulation and compare the subset of non-missing
data only, or impute the missing observed data and compare the complete
(e.g. no-missing data) data sets.
Gelman et al. Multiple Imputation for Model Checking: Completed-Data
Plots with Missing and Latent Data. Biometrics 61, 74-85 , March 2005
Marc
Marc R. Gastonguay, Ph.D.
President & CEO, Metrum Research Group LLC [www.metrumrg.com]
Scientific Director, Metrum Institute [www.metruminstitute.org]
Direct: 860-670-0744 Main: 860-735-7043
Email: [EMAIL PROTECTED]
On May 23, 2008, at 6:22 AM, andreas lindauer wrote:
Dear NMusers,
I have a question regarding simulations for a VPC. When a
combined residual error is used it happens that for low concentrations
negative values are simulated. While this is statistically correct, I
wonder if it is correct to use these results for the VPC because the
distribution of the observed low concentrations is truncated by the
LLOQ. So the VPC might suggest model misspecification for lower
concentrations. Further, when one wants to use the model for clinical
trial simulation should then the negative (BQL) values be omitted
because they would never appear in reality?
I would like to know how the more experienced NMusers handle
this.
Thanks in advance, Andreas.
____________________________
Andreas Lindauer
University of Bonn
Department of Clinical Pharmacy
An der Immenburg 4
D-53121 Bonn
phone:+49 228 73 5781
fax: +49 228 73 9757
This message and any attachments are solely for the intended recipient. If you
are not the intended recipient, disclosure, copying, use or distribution of the
information included in this message is prohibited --- Please immediately and
permanently delete.
Ken and All,
The recent paper on JPP "Impact on censoring data below an arbitrary
quantification limit on structural model misspecification" 2008, 35:101-16, by
Byron, Fletcher and Brundage is still fully available on line and it speaks
volumes about bioanalytical motivated LLOQ and pharmacokinetics modeling. Just
for those who haven't read it, I vividly reccomend so.
Cheers
---------------------------------------------------------------
Luis M. Pereira, Ph.D.
Assistant Professor, Pharmacometrics
Massachusetts College of Pharmacy and Health Sciences
Childrens Hospital Boston / Harvard Medical School
179 Longwood Ave, Boston, MA 02115
Phone: (617) 732-2905
Fax: (617) 732-2228
Quoted reply history
________________________________
From: [EMAIL PROTECTED] on behalf of Ken Kowalski
Sent: Fri 5/23/2008 11:22 AM
To: 'Nick Holford'; [email protected]
Subject: RE: [NMusers] Visual predictive check!
Nick,
Yes, I'm making the assumption that a measured concentration cannot be
negative. Educate me about chemical assays. Can you get troughs rather
than peaks in a chromatogram such that the area below zero is integrated and
reported as a negative concentration? If so, what would happen if you
assayed a bunch of pre-dose samples (before drug is administered) where the
true mean concentration is zero? Would we get measured concentrations
symmetrically distributed about zero (with about 50% of the measured
concentrations reported as negative and 50% positive)? If so, then a normal
residual error model may indeed be appropriate.
Ken
Luis,
A very good suggestion. I agree this is an excellent piece of work dealing with the LLOQ problem. It provides a clear example of the benefits of the YLO option in NONMEM for dealing with censored data.
By the way the first author is Wonkyung BYON -- not Byron.
Best wishes,
Nick
[EMAIL PROTECTED] wrote:
> Ken and All,
>
> The recent paper on JPP "Impact on censoring data below an arbitrary quantification limit on structural model misspecification" 2008, 35:101-16, by Byron, Fletcher and Brundage is still fully available on line and it speaks volumes about bioanalytical motivated LLOQ and pharmacokinetics modeling. Just for those who haven't read it, I vividly reccomend so.
>
> Cheers
>
> ---------------------------------------------------------------
> Luis M. Pereira, Ph.D.
> Assistant Professor, Pharmacometrics
> Massachusetts College of Pharmacy and Health Sciences
>
> Childrens Hospital Boston / Harvard Medical School
> 179 Longwood Ave, Boston, MA 02115
> Phone: (617) 732-2905
> Fax: (617) 732-2228
>
> ------------------------------------------------------------------------
> *From:* [EMAIL PROTECTED] on behalf of Ken Kowalski
> *Sent:* Fri 5/23/2008 11:22 AM
> *To:* 'Nick Holford'; [email protected]
> *Subject:* RE: [NMusers] Visual predictive check!
>
> Nick,
>
> Yes, I'm making the assumption that a measured concentration cannot be
> negative. Educate me about chemical assays. Can you get troughs rather
>
> than peaks in a chromatogram such that the area below zero is integrated and
>
> reported as a negative concentration? If so, what would happen if you
>
> assayed a bunch of pre-dose samples (before drug is administered) where the
>
> true mean concentration is zero? Would we get measured concentrations
> symmetrically distributed about zero (with about 50% of the measured
>
> concentrations reported as negative and 50% positive)? If so, then a normal residual error model may indeed be appropriate.
>
> Ken
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
[EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:+64(9)373-7090
www.health.auckland.ac.nz/pharmacology/staff/nholford
Dear Nick,
I do not claim to have much real life experience with HPLC
or LC-MS/MS either. However, I think both these methods
can yield negative concentrations and both have some
measurement noise.
As far as I know, for HPLC-UV and HPLC-Fluorescence
methods photons are converted into an electronic signal
that then becomes the chromatogram. For LC-MS/MS,
ions of a specific mass/charge ratio hit a photomultiplier
tube and thereby create an electric signal. Some MS have
a resolution in the mass/charge ratio of 10^(-5) atomic
units. All those devices that provide an electric signal will
most likely have some level of random background noise.
I think the most likely reason to measure negative
concentrations might not be a negative area or negative
peak height in a chromatogram. Negative conc. might
more likely come from the regression equation of the
calibration row itself:
Drug_conc = intercept + (area_drug / area_IS) * slope
The area denotes the area of the drug of interest and of
the internal standard (IS) in the chromatogram. An IS
is often spiked to all samples at a known concentration.
If you have a chromatogram without noise, then area_drug
will be zero and area_IS will be a large number
(otherwise e.g. the HPLC-injection went wrong and the
sample is likely to be correctly discarded). A truly blank
sample will then have a negative concentration, if the
intercept is negative. As usually not all samples are
measured in one analytical run, one will have several
regression equations in a clinical trial with random
intercepts which may be negative and should be centered
around zero.
Hope we will see more of these negative numbers in our
datasets (-:
Best wishes
Juergen
-----------------------------------------------
Jurgen Bulitta, PhD, Post-doctoral Fellow
ID - Pharmacometrics, University at Buffalo, NY, USA
Phone: +1 716 645 2855 ext. 281, [EMAIL PROTECTED]
Fax: +1 716 645 3693
-----------------------------------------------
-----Ursprüngliche Nachricht-----
Von: "Nick Holford" <[EMAIL PROTECTED]>
Gesendet: 23.05.08 17:54:26
An: [email protected]
Betreff: Re: [NMusers] Visual predictive check!
Ken,
First of all -- I have almost no real world experience of modern
analytical laboratory methods. But I have seen chromatograms from HPLC
machines which have baseline noise. One way to quantitate the sample is
to integrate over an interval at the expected retention time after a
true zero specimen had passed through the system then the resulting area
could be either positive or negative. Another method would be to search
for a positive peak around the expected retention time and center the
integration around that peak -- this would of course lead to a positive
bias.
So if the first (potentially unnbiased) method is used for a series of
pre-dose concs then the resulting distribution should have both negative
and positive values. Whether it was symmetrical or even normal would
depend on the factors that cause the baseline noise.
I suspect that commonly used methods today rely on software that will
have a truncation bias built into it (e.g. using the second method) even
before the LLOQ bias is added.
I have even less experience of mass spectroscopy methods - my naive
understanding is that the mass lines are measured within one atomic
weight unit of resolution so it is unlikely even for true zero samples
that a negative mass would be obtained. So for mass spec assays the
assumption that measurements are non-negative may be true.
Best wishes,
Nick
Ken Kowalski wrote:
> Nick,
>
> Yes, I'm making the assumption that a measured concentration cannot be
> negative. Educate me about chemical assays. Can you get troughs rather
> than peaks in a chromatogram such that the area below zero is integrated and
> reported as a negative concentration? If so, what would happen if you
> assayed a bunch of pre-dose samples (before drug is administered) where the
> true mean concentration is zero? Would we get measured concentrations
> symmetrically distributed about zero (with about 50% of the measured
> concentrations reported as negative and 50% positive)? If so, then a normal
> residual error model may indeed be appropriate.
>
> Ken
>
Quoted reply history
> -----Original Message-----
> From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On
> Behalf Of Nick Holford
> Sent: Friday, May 23, 2008 10:40 AM
> To: [email protected]
> Subject: Re: [NMusers] Visual predictive check!
>
> Ken,
>
> You wrote among other things:
> "The combined residual error model cannot be the correct model at very
> low concentrations since the normal distribution will put non-zero
> probability mass at concentrations less than zero if the mean is low
> relative to its SD."
>
> I think you are making the assumption that *measured* concentrations
> have to be non-negative. In a real world measurement system there will
> be random measurement noise around true zero. Thus a real world
> measurement system would return both negative and positive measurements
> for a true zero. Additive residual error models in theory describe this
> behaviour. Simulations of *measurements* will then quite reasonably
> include negative values.
>
> In the truncated real world of chemical analysis real measurements of
> true zero seem to be always reported as non-negative. Its a pity
> chemical analysts don't seem to understand that this truncation always
> causes measurement bias (whether the LLOQ is 0 or greater).
>
> Best wishes,
>
> Nick
>
> Ken Kowalski wrote:
>
>> Andreas,
>>
>> Your simulations highlight a limitation with the combined (additive +
>> proportional or slope-intercept) residual error model. The combined
>> residual error model cannot be the correct model at very low
>> concentrations since the normal distribution will put non-zero
>> probability mass at concentrations less than zero if the mean is low
>> relative to its SD. The purist in me says don't truncate as that will
>> lead to bias in your simulations although it may be minimal if few
>> observations are simulated with negative concentrations. A better
>> approach would be to consider an alternative residual error model that
>> bounds the concentrations to be positive such as the log-normal
>> residual error model (log-transform both sides approach) or fit a
>> model that takes into account the censored BQL data ( see Beal, Ways
>> to Fit a PK Model with Some Data Below the Quantification Limit. JPP
>> 2001;28:481-504).
>>
>> Ken
>>
>> Kenneth G. Kowalski
>>
>> President & CEO
>>
>> A2PG - Ann Arbor Pharmacometrics Group
>>
>> 110 E. Miller Ave., Garden Suite
>>
>> Ann Arbor, MI 48104
>>
>> Work: 734-274-8255
>>
>> Cell: 248-207-5082
>>
>> [EMAIL PROTECTED]
>>
>> *From:* [EMAIL PROTECTED]
>> [mailto:[EMAIL PROTECTED] *On Behalf Of *andreas lindauer
>> *Sent:* Friday, May 23, 2008 6:23 AM
>> *To:* [email protected]
>> *Subject:* [NMusers] Visual predictive check!
>>
>> Dear NMusers,
>>
>> I have a question regarding simulations for a VPC. When a combined
>> residual error is used it happens that for low concentrations negative
>> values are simulated. While this is statistically correct, I wonder if
>> it is correct to use these results for the VPC because the
>> distribution of the observed low concentrations is truncated by the
>> LLOQ. So the VPC might suggest model misspecification for lower
>> concentrations. Further, when one wants to use the model for clinical
>> trial simulation should then the negative (BQL) values be omitted
>> because they would never appear in reality?
>>
>> I would like to know how the more experienced NMusers handle this.
>>
>> Thanks in advance, Andreas.
>>
>> ____________________________
>>
>> Andreas Lindauer
>>
>> University of Bonn
>>
>> Department of Clinical Pharmacy
>>
>> An der Immenburg 4
>>
>> D-53121 Bonn
>>
>> phone:+49 228 73 5781
>>
>> fax: +49 228 73 9757
>>
>>
>
>
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
[EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:+64(9)373-7090
www.health.auckland.ac.nz/pharmacology/staff/nholford
Nick, Ken
I don't think it's a matter of an integrated area being negative. This is
of course possible but suggests the area dips down below the baseline
rather than rising above it.
I think the problem is much simpler. When analysts create a standard
curve, from which areas are associated with concentrations, then it is
generally assumed:
a) that the curve is linear (a straight line in this case)
b) that you estimate the intercept
The intercept of course is not required to go through zero - and can be
positive or negative. A non-zero intercept provides bias which analysts
(from my take) appear to be concerned about and hence truncate at a higher
value (LLOQ) from which any bias will be minimal. Note the definition of
LLOQ is all about variance not bias. But I do think it's bias that causes
the LLOQ war not variance (there is no case that variance should cause
such heated feelings on PharmPK). The confidence interval around the
slope will reveal a band of random uncertainty of the assay.
So - to clarify.
For me, a true concentration can never be observed and if it could it
would never be negative. An observed concentration predicted from an
assay can certainly be observed and be negative. A model predicted
concentration should therefore also be allowed to be negative, even though
negative concentrations are often perceived as inconvenient! Confusion may
arise regarding the non-equality of true concentration, observed
concentration and predicted concentration. And observed concentration
perhaps should be termed "assay predicted concentration" while predicted
concentration should be "PK model predicted concentration", but this is a
bit of a mouthful.
Regards
Steve
--
Professor Stephen Duffull
School of Pharmacy
University of Otago
PO Box 913
Dunedin
P 03 479 5044
F 03 479 7034
Quoting Nick Holford <[EMAIL PROTECTED]>:
> Ken,
>
> First of all -- I have almost no real world experience of modern
> analytical laboratory methods. But I have seen chromatograms from HPLC
> machines which have baseline noise. One way to quantitate the sample
> is
> to integrate over an interval at the expected retention time after a
> true zero specimen had passed through the system then the resulting
> area
> could be either positive or negative. Another method would be to
> search
> for a positive peak around the expected retention time and center the
> integration around that peak -- this would of course lead to a
> positive
> bias.
>
> So if the first (potentially unnbiased) method is used for a series of
> pre-dose concs then the resulting distribution should have both
> negative
> and positive values. Whether it was symmetrical or even normal would
> depend on the factors that cause the baseline noise.
>
> I suspect that commonly used methods today rely on software that will
> have a truncation bias built into it (e.g. using the second method)
> even
> before the LLOQ bias is added.
>
> I have even less experience of mass spectroscopy methods - my naive
> understanding is that the mass lines are measured within one atomic
> weight unit of resolution so it is unlikely even for true zero samples
> that a negative mass would be obtained. So for mass spec assays the
> assumption that measurements are non-negative may be true.
>
> Best wishes,
>
> Nick
>
> Ken Kowalski wrote:
> > Nick,
> >
> > Yes, I'm making the assumption that a measured concentration cannot
> be
> > negative. Educate me about chemical assays. Can you get troughs
> rather
> > than peaks in a chromatogram such that the area below zero is
> integrated and
> > reported as a negative concentration? If so, what would happen if
> you
> > assayed a bunch of pre-dose samples (before drug is administered)
> where the
> > true mean concentration is zero? Would we get measured
> concentrations
> > symmetrically distributed about zero (with about 50% of the measured
> > concentrations reported as negative and 50% positive)? If so, then a
> normal
> > residual error model may indeed be appropriate.
> >
> > Ken
> >
> > -----Original Message-----
Quoted reply history
> > From: [EMAIL PROTECTED]
> [mailto:[EMAIL PROTECTED] On
> > Behalf Of Nick Holford
> > Sent: Friday, May 23, 2008 10:40 AM
> > To: [email protected]
> > Subject: Re: [NMusers] Visual predictive check!
> >
> > Ken,
> >
> > You wrote among other things:
> > "The combined residual error model cannot be the correct model at
> very
> > low concentrations since the normal distribution will put non-zero
> > probability mass at concentrations less than zero if the mean is low
> > relative to its SD."
> >
> > I think you are making the assumption that *measured* concentrations
> > have to be non-negative. In a real world measurement system there
> will
> > be random measurement noise around true zero. Thus a real world
> > measurement system would return both negative and positive
> measurements
> > for a true zero. Additive residual error models in theory describe
> this
> > behaviour. Simulations of *measurements* will then quite reasonably
> > include negative values.
> >
> > In the truncated real world of chemical analysis real measurements
> of
> > true zero seem to be always reported as non-negative. Its a pity
> > chemical analysts don't seem to understand that this truncation
> always
> > causes measurement bias (whether the LLOQ is 0 or greater).
> >
> > Best wishes,
> >
> > Nick
> >
> > Ken Kowalski wrote:
> >
> >> Andreas,
> >>
> >> Your simulations highlight a limitation with the combined (additive
> +
> >> proportional or slope-intercept) residual error model. The combined
> >> residual error model cannot be the correct model at very low
> >> concentrations since the normal distribution will put non-zero
> >> probability mass at concentrations less than zero if the mean is
> low
> >> relative to its SD. The purist in me says don't truncate as that
> will
> >> lead to bias in your simulations although it may be minimal if few
> >> observations are simulated with negative concentrations. A better
> >> approach would be to consider an alternative residual error model
> that
> >> bounds the concentrations to be positive such as the log-normal
> >> residual error model (log-transform both sides approach) or fit a
> >> model that takes into account the censored BQL data ( see Beal,
> Ways
> >> to Fit a PK Model with Some Data Below the Quantification Limit.
> JPP
> >> 2001;28:481-504).
> >>
> >> Ken
> >>
> >> Kenneth G. Kowalski
> >>
> >> President & CEO
> >>
> >> A2PG - Ann Arbor Pharmacometrics Group
> >>
> >> 110 E. Miller Ave., Garden Suite
> >>
> >> Ann Arbor, MI 48104
> >>
> >> Work: 734-274-8255
> >>
> >> Cell: 248-207-5082
> >>
> >> [EMAIL PROTECTED]
> >>
> >> *From:* [EMAIL PROTECTED]
> >> [mailto:[EMAIL PROTECTED] *On Behalf Of *andreas
> lindauer
> >> *Sent:* Friday, May 23, 2008 6:23 AM
> >> *To:* [email protected]
> >> *Subject:* [NMusers] Visual predictive check!
> >>
> >> Dear NMusers,
> >>
> >> I have a question regarding simulations for a VPC. When a combined
> >> residual error is used it happens that for low concentrations
> negative
> >> values are simulated. While this is statistically correct, I wonder
> if
> >> it is correct to use these results for the VPC because the
> >> distribution of the observed low concentrations is truncated by the
> >> LLOQ. So the VPC might suggest model misspecification for lower
> >> concentrations. Further, when one wants to use the model for
> clinical
> >> trial simulation should then the negative (BQL) values be omitted
> >> because they would never appear in reality?
> >>
> >> I would like to know how the more experienced NMusers handle this.
> >>
> >> Thanks in advance, Andreas.
> >>
> >> ____________________________
> >>
> >> Andreas Lindauer
> >>
> >> University of Bonn
> >>
> >> Department of Clinical Pharmacy
> >>
> >> An der Immenburg 4
> >>
> >> D-53121 Bonn
> >>
> >> phone:+49 228 73 5781
> >>
> >> fax: +49 228 73 9757
> >>
> >>
> >
> >
>
> --
> Nick Holford, Dept Pharmacology & Clinical Pharmacology
> University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
> Zealand
> [EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:+64(9)373-7090
> www.health.auckland.ac.nz/pharmacology/staff/nholford
>
>
>
--
Professor Stephen Duffull
School of Pharmacy
University of Otago
PO Box 913
Dunedin
P 03 479 5044
F 03 479 7034
All,
Would anyone be willing to comment on the applicability, or lack thereof, of
applying the various literature referenced techniques to PD/biomarker data,
including differences in assumptions and practical considerations?
Thank you,
Mark
Mark C. Peterson
Amgen Inc.
One Amgen Center Drive
MS 28-3-B
Thousand Oaks, CA 91320
Quoted reply history
________________________________
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of [EMAIL PROTECTED]
Sent: Saturday, May 24, 2008 4:58 PM
To: [EMAIL PROTECTED]
Cc: [email protected]
Subject: RE: [NMusers] Visual predictive check!
Ken and All,
The recent paper on JPP "Impact on censoring data below an arbitrary
quantification limit on structural model misspecification" 2008, 35:101-16, by
Byron, Fletcher and Brundage is still fully available on line and it speaks
volumes about bioanalytical motivated LLOQ and pharmacokinetics modeling. Just
for those who haven't read it, I vividly reccomend so.
Cheers
---------------------------------------------------------------
Luis M. Pereira, Ph.D.
Assistant Professor, Pharmacometrics
Massachusetts College of Pharmacy and Health Sciences
Childrens Hospital Boston / Harvard Medical School
179 Longwood Ave, Boston, MA 02115
Phone: (617) 732-2905
Fax: (617) 732-2228
________________________________
From: [EMAIL PROTECTED] on behalf of Ken Kowalski
Sent: Fri 5/23/2008 11:22 AM
To: 'Nick Holford'; [email protected]
Subject: RE: [NMusers] Visual predictive check!
Nick,
Yes, I'm making the assumption that a measured concentration cannot be
negative. Educate me about chemical assays. Can you get troughs rather
than peaks in a chromatogram such that the area below zero is integrated and
reported as a negative concentration? If so, what would happen if you
assayed a bunch of pre-dose samples (before drug is administered) where the
true mean concentration is zero? Would we get measured concentrations
symmetrically distributed about zero (with about 50% of the measured
concentrations reported as negative and 50% positive)? If so, then a normal
residual error model may indeed be appropriate.
Ken