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.
