Dear NM users:
I have a dataset where some of the concentrations are reported as negative
values. I believe that the concentrations were calculated using a standard
curve.
My instinct is to impute all the negative values to zero, but worry that it
will introduce bias.
A 2nd thought is using the absolute value of the lowest (negative)
concentration as LLOQ. All the concentrations below LLOQ will be treated as
zero. By doing this, some positive and negative values both will be zero
out which will help to cancel some of the unevenness that the 1st method
may introduce.
I believe that the 2nd method is better but wonder if there is any other
better way to do it. Any comments will be greatly appreciated.
Thank you in advance.
Siwei
Negative DV values
hi Siwei,
you should include the BLOQ data as they are, i.e. negative. Any other
approach would decrease precision (e.g. M3 likelihood-based) and/or induce
bias (e.g. LLOQ/2 or LLOQ=0). I've done some simulations on this a while
ago to show this (
http://page-meeting.org/pdf_assets/2413-PAGE_2010_poster_LLOQ_v1.pdf), but
it should be intuitive too.
best regards,
Ron
----------------------------------------------
Ron Keizer, PharmD PhD
Dept. of Bioengineering & Therapeutic Sciences
University of California San Francisco (UCSF)
----------------------------------------------
Quoted reply history
On Thu, Oct 2, 2014 at 2:10 PM, siwei Dai <[email protected]> wrote:
> Dear NM users:
>
> I have a dataset where some of the concentrations are reported as negative
> values. I believe that the concentrations were calculated using a standard
> curve.
>
> My instinct is to impute all the negative values to zero, but worry that
> it will introduce bias.
>
> A 2nd thought is using the absolute value of the lowest (negative)
> concentration as LLOQ. All the concentrations below LLOQ will be treated as
> zero. By doing this, some positive and negative values both will be zero
> out which will help to cancel some of the unevenness that the 1st method
> may introduce.
>
> I believe that the 2nd method is better but wonder if there is any other
> better way to do it. Any comments will be greatly appreciated.
>
> Thank you in advance.
>
> Siwei
>
Siwei,
I agree with Ron. Using the measurements you have is better than trying to use a work around such as likelihood or imputation based methods. Some negative measurement values are exactly what you should expect if the true concentration is zero (or 'close' to zero) when there is background measurement error noise.
As far as I know all common methods of measurement (HPLC, MS) have background noise. You can account for this noise when you model your data by including an additive term in the residual error model. The additive error estimate will also include other sources of residual error that are independent of concentration eg. due to model misspecification.
Here is a reference to a publication which used measured concentrations that included negative measured values. Note that a negative measured value does not mean the actual concentration was negative!
Patel K, Choy SS, Hicks KO, Melink TJ, Holford NH, Wilson WR. A combined pharmacokinetic model for the hypoxia-targeted prodrug PR-104A in humans, dogs, rats and mice predicts species differences in clearance and toxicity. Cancer Chemother Pharmacol. 2011;67(5):1145-55.
Best wishes,
Nick
Quoted reply history
On 3/10/2014 11:07 a.m., Ron Keizer wrote:
> hi Siwei,
>
> you should include the BLOQ data as they are, i.e. negative. Any other approach would decrease precision (e.g. M3 likelihood-based) and/or induce bias (e.g. LLOQ/2 or LLOQ=0). I've done some simulations on this a while ago to show this ( http://page-meeting.org/pdf_assets/2413-PAGE_2010_poster_LLOQ_v1.pdf ), but it should be intuitive too.
>
> best regards,
> Ron
>
> ----------------------------------------------
> Ron Keizer, PharmD PhD
> Dept. of Bioengineering & Therapeutic Sciences
> University of California San Francisco (UCSF)
> ----------------------------------------------
>
> On Thu, Oct 2, 2014 at 2:10 PM, siwei Dai < [email protected] < mailto: [email protected] >> wrote:
>
> Dear NM users:
>
> I have a dataset where some of the concentrations are reported as
> negative values. I believe that the concentrations were
> calculated using a standard curve.
>
> My instinct is to impute all the negative values to zero, but
> worry that it will introduce bias.
>
> A 2nd thought is using the absolute value of the lowest (negative)
> concentration as LLOQ. All the concentrations below LLOQ will be
> treated as zero. By doing this, some positive and negative values
> both will be zero out which will help to cancel some of the
> unevenness that the 1st method may introduce.
>
> I believe that the 2nd method is better but wonder if there is any
> other better way to do it. Any comments will be greatly appreciated.
>
> Thank you in advance.
>
> Siwei
--
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.
Hi, Ron & Nick:
Thank you very much for your helpful suggestions! I will look into those
references.
Regards,
Siwei
Quoted reply history
On Fri, Oct 3, 2014 at 12:27 AM, Nick Holford <[email protected]>
wrote:
> Siwei,
>
> I agree with Ron. Using the measurements you have is better than trying to
> use a work around such as likelihood or imputation based methods. Some
> negative measurement values are exactly what you should expect if the true
> concentration is zero (or 'close' to zero) when there is background
> measurement error noise.
>
> As far as I know all common methods of measurement (HPLC, MS) have
> background noise. You can account for this noise when you model your data
> by including an additive term in the residual error model. The additive
> error estimate will also include other sources of residual error that are
> independent of concentration eg. due to model misspecification.
>
> Here is a reference to a publication which used measured concentrations
> that included negative measured values. Note that a negative measured value
> does not mean the actual concentration was negative!
>
> Patel K, Choy SS, Hicks KO, Melink TJ, Holford NH, Wilson WR. A combined
> pharmacokinetic model for the hypoxia-targeted prodrug PR-104A in humans,
> dogs, rats and mice predicts species differences in clearance and toxicity.
> Cancer Chemother Pharmacol. 2011;67(5):1145-55.
>
> Best wishes,
>
> Nick
>
> On 3/10/2014 11:07 a.m., Ron Keizer wrote:
>
> hi Siwei,
> you should include the BLOQ data as they are, i.e. negative. Any other
> approach would decrease precision (e.g. M3 likelihood-based) and/or induce
> bias (e.g. LLOQ/2 or LLOQ=0). I've done some simulations on this a while
> ago to show this (
> http://page-meeting.org/pdf_assets/2413-PAGE_2010_poster_LLOQ_v1.pdf),
> but it should be intuitive too.
> best regards,
> Ron
>
> ----------------------------------------------
> Ron Keizer, PharmD PhD
> Dept. of Bioengineering & Therapeutic Sciences
> University of California San Francisco (UCSF)
> ----------------------------------------------
>
> On Thu, Oct 2, 2014 at 2:10 PM, siwei Dai <[email protected]>
> wrote:
>
>> Dear NM users:
>>
>> I have a dataset where some of the concentrations are reported as
>> negative values. I believe that the concentrations were calculated using a
>> standard curve.
>>
>> My instinct is to impute all the negative values to zero, but worry
>> that it will introduce bias.
>>
>> A 2nd thought is using the absolute value of the lowest (negative)
>> concentration as LLOQ. All the concentrations below LLOQ will be treated as
>> zero. By doing this, some positive and negative values both will be zero
>> out which will help to cancel some of the unevenness that the 1st method
>> may introduce.
>>
>> I believe that the 2nd method is better but wonder if there is any
>> other better way to do it. Any comments will be greatly appreciated.
>>
>> Thank you in advance.
>>
>> Siwei
>>
>
>
> --
> 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.
>
>
Siwei,
I have to disagree with Nick and Ron’s suggestion to include, without further
question, the negative concentration values in your model. Yes, HPLC/UV and
HPLC/MS methods contain background noise, and if it is purely random you can
account for it in your model by including a suitable residual error term as
Nick suggests. But, when concentrations are measured below the LLOQ, the
background noise could contain components of both random and systematic error
and the data could be severely biased. For example, a calibration plot of
instrument response versus concentration of known standard samples may have
been shown to be nicely linear over the range of the assay from LLOQ to ULOQ,
but use of the concentration values below the LLOQ means that the observed
linear relationship has been assumed to continue below the LLOQ, and has been
extrapolated. If the linear relationship actually breaks down below the LLOQ,
which is a frequent problem from my previous experiences in the world of
HPLC/UV and HPLC/MS quantification, then the data below LLOQ will become
increasingly biased the lower they get, eventually leading in some situations
to “negative” concentrations. As far as I can tell, Ron’s simulation and
modelling study only included random noise in the simulated concentrations,
hence inclusion of the concentrations below LLOQ along with a suitable model
for the random error helped to usefully inform the parameters of the model.
However, if bias is also present in the data below LLOQ then including that
data is likely to misinform your model.
My suggested rough solution to your problem: Include all data that are up to
say 3-fold below the LLOQ and perhaps try a different error model for those
data. All data more than 3-fold below the LLOQ (and especially those negative
values) should be treated with something like the M3 likelihood method.
Regards,
Rupert
Rupert Austin, PhD
Senior Scientist
BAST Inc Limited
Holywell Park
Ashby Road
Loughborough, LE11 3AQ, UK
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Nick Holford
Sent: 03 October 2014 05:27
To: nmusers
Subject: Re: [NMusers] Negative DV values
Siwei,
I agree with Ron. Using the measurements you have is better than trying to use
a work around such as likelihood or imputation based methods. Some negative
measurement values are exactly what you should expect if the true concentration
is zero (or 'close' to zero) when there is background measurement error noise.
As far as I know all common methods of measurement (HPLC, MS) have background
noise. You can account for this noise when you model your data by including an
additive term in the residual error model. The additive error estimate will
also include other sources of residual error that are independent of
concentration eg. due to model misspecification.
Here is a reference to a publication which used measured concentrations that
included negative measured values. Note that a negative measured value does not
mean the actual concentration was negative!
Patel K, Choy SS, Hicks KO, Melink TJ, Holford NH, Wilson WR. A combined
pharmacokinetic model for the hypoxia-targeted prodrug PR-104A in humans, dogs,
rats and mice predicts species differences in clearance and toxicity. Cancer
Chemother Pharmacol. 2011;67(5):1145-55.
Best wishes,
Nick
On 3/10/2014 11:07 a.m., Ron Keizer wrote:
hi Siwei,
you should include the BLOQ data as they are, i.e. negative. Any other approach
would decrease precision (e.g. M3 likelihood-based) and/or induce bias (e.g.
LLOQ/2 or LLOQ=0). I've done some simulations on this a while ago to show this
( http://page-meeting.org/pdf_assets/2413-PAGE_2010_poster_LLOQ_v1.pdf), but it
should be intuitive too.
best regards,
Ron
----------------------------------------------
Ron Keizer, PharmD PhD
Dept. of Bioengineering & Therapeutic Sciences
University of California San Francisco (UCSF)
----------------------------------------------
On Thu, Oct 2, 2014 at 2:10 PM, siwei Dai <[email protected]
<mailto:[email protected]> > wrote:
Dear NM users:
I have a dataset where some of the concentrations are reported as negative
values. I believe that the concentrations were calculated using a standard
curve.
My instinct is to impute all the negative values to zero, but worry that it
will introduce bias.
A 2nd thought is using the absolute value of the lowest (negative)
concentration as LLOQ. All the concentrations below LLOQ will be treated as
zero. By doing this, some positive and negative values both will be zero out
which will help to cancel some of the unevenness that the 1st method may
introduce.
I believe that the 2nd method is better but wonder if there is any other better
way to do it. Any comments will be greatly appreciated.
Thank you in advance.
Siwei
--
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] <mailto:[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.