Re: 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
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
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Nick Holford, Professor Clinical Pharmacology
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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.