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]
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.
