Rupert,
Thanks for mentioning this issue. I quite agree there would be a problem
if the chemical analyst had not checked for bias over the entire range
of measured concs and adjusted the calibration procedure to remove bias.
The nice thing about creating an assay calibration curve is that the
true value is known and bias is easily estimated. if there is bias then
the calibration model should be modified to account for it. This is one
of the simple ways to reduce the model misspecification I mentioned.
Once the chemical analyst has done the job properly then the remaining
error from the assay will be random at all values of true concentration
and thus the key assumption involved in fitting all the measurements
with a residual error model is satisfied.
Best wishes,
Nick
On 4/10/2014 4:04 a.m., Rupert Austin wrote:
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
*From:*owner-nmus...@globomaxnm.com
[mailto:owner-nmus...@globomaxnm.com] *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
<ellen.siwei...@gmail.com <mailto:ellen.siwei...@gmail.com>> 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:n.holf...@auckland.ac.nz <mailto:n.holf...@auckland.ac.nz>
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.
--
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: n.holf...@auckland.ac.nz
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.
