Dear Nick, I do not claim to have much real life experience with HPLC or LC-MS/MS either. However, I think both these methods can yield negative concentrations and both have some measurement noise.
As far as I know, for HPLC-UV and HPLC-Fluorescence methods photons are converted into an electronic signal that then becomes the chromatogram. For LC-MS/MS, ions of a specific mass/charge ratio hit a photomultiplier tube and thereby create an electric signal. Some MS have a resolution in the mass/charge ratio of 10^(-5) atomic units. All those devices that provide an electric signal will most likely have some level of random background noise. I think the most likely reason to measure negative concentrations might not be a negative area or negative peak height in a chromatogram. Negative conc. might more likely come from the regression equation of the calibration row itself: Drug_conc = intercept + (area_drug / area_IS) * slope The area denotes the area of the drug of interest and of the internal standard (IS) in the chromatogram. An IS is often spiked to all samples at a known concentration. If you have a chromatogram without noise, then area_drug will be zero and area_IS will be a large number (otherwise e.g. the HPLC-injection went wrong and the sample is likely to be correctly discarded). A truly blank sample will then have a negative concentration, if the intercept is negative. As usually not all samples are measured in one analytical run, one will have several regression equations in a clinical trial with random intercepts which may be negative and should be centered around zero. Hope we will see more of these negative numbers in our datasets (-: Best wishes Juergen ----------------------------------------------- Jurgen Bulitta, PhD, Post-doctoral Fellow ID - Pharmacometrics, University at Buffalo, NY, USA Phone: +1 716 645 2855 ext. 281, [EMAIL PROTECTED] Fax: +1 716 645 3693 ----------------------------------------------- -----Ursprüngliche Nachricht----- Von: "Nick Holford" <[EMAIL PROTECTED]> Gesendet: 23.05.08 17:54:26 An: [email protected] Betreff: Re: [NMusers] Visual predictive check! Ken, First of all -- I have almost no real world experience of modern analytical laboratory methods. But I have seen chromatograms from HPLC machines which have baseline noise. One way to quantitate the sample is to integrate over an interval at the expected retention time after a true zero specimen had passed through the system then the resulting area could be either positive or negative. Another method would be to search for a positive peak around the expected retention time and center the integration around that peak -- this would of course lead to a positive bias. So if the first (potentially unnbiased) method is used for a series of pre-dose concs then the resulting distribution should have both negative and positive values. Whether it was symmetrical or even normal would depend on the factors that cause the baseline noise. I suspect that commonly used methods today rely on software that will have a truncation bias built into it (e.g. using the second method) even before the LLOQ bias is added. I have even less experience of mass spectroscopy methods - my naive understanding is that the mass lines are measured within one atomic weight unit of resolution so it is unlikely even for true zero samples that a negative mass would be obtained. So for mass spec assays the assumption that measurements are non-negative may be true. Best wishes, Nick Ken Kowalski wrote: > Nick, > > Yes, I'm making the assumption that a measured concentration cannot be > negative. Educate me about chemical assays. Can you get troughs rather > than peaks in a chromatogram such that the area below zero is integrated and > reported as a negative concentration? If so, what would happen if you > assayed a bunch of pre-dose samples (before drug is administered) where the > true mean concentration is zero? Would we get measured concentrations > symmetrically distributed about zero (with about 50% of the measured > concentrations reported as negative and 50% positive)? If so, then a normal > residual error model may indeed be appropriate. > > Ken > > -----Original Message----- > From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On > Behalf Of Nick Holford > Sent: Friday, May 23, 2008 10:40 AM > To: [email protected] > Subject: Re: [NMusers] Visual predictive check! > > Ken, > > You wrote among other things: > "The combined residual error model cannot be the correct model at very > low concentrations since the normal distribution will put non-zero > probability mass at concentrations less than zero if the mean is low > relative to its SD." > > I think you are making the assumption that *measured* concentrations > have to be non-negative. In a real world measurement system there will > be random measurement noise around true zero. Thus a real world > measurement system would return both negative and positive measurements > for a true zero. Additive residual error models in theory describe this > behaviour. Simulations of *measurements* will then quite reasonably > include negative values. > > In the truncated real world of chemical analysis real measurements of > true zero seem to be always reported as non-negative. Its a pity > chemical analysts don't seem to understand that this truncation always > causes measurement bias (whether the LLOQ is 0 or greater). > > Best wishes, > > Nick > > Ken Kowalski wrote: > >> Andreas, >> >> Your simulations highlight a limitation with the combined (additive + >> proportional or slope-intercept) residual error model. The combined >> residual error model cannot be the correct model at very low >> concentrations since the normal distribution will put non-zero >> probability mass at concentrations less than zero if the mean is low >> relative to its SD. The purist in me says don't truncate as that will >> lead to bias in your simulations although it may be minimal if few >> observations are simulated with negative concentrations. A better >> approach would be to consider an alternative residual error model that >> bounds the concentrations to be positive such as the log-normal >> residual error model (log-transform both sides approach) or fit a >> model that takes into account the censored BQL data ( see Beal, Ways >> to Fit a PK Model with Some Data Below the Quantification Limit. JPP >> 2001;28:481-504). >> >> Ken >> >> Kenneth G. Kowalski >> >> President & CEO >> >> A2PG - Ann Arbor Pharmacometrics Group >> >> 110 E. Miller Ave., Garden Suite >> >> Ann Arbor, MI 48104 >> >> Work: 734-274-8255 >> >> Cell: 248-207-5082 >> >> [EMAIL PROTECTED] >> >> *From:* [EMAIL PROTECTED] >> [mailto:[EMAIL PROTECTED] *On Behalf Of *andreas lindauer >> *Sent:* Friday, May 23, 2008 6:23 AM >> *To:* [email protected] >> *Subject:* [NMusers] Visual predictive check! >> >> Dear NMusers, >> >> I have a question regarding simulations for a VPC. When a combined >> residual error is used it happens that for low concentrations negative >> values are simulated. While this is statistically correct, I wonder if >> it is correct to use these results for the VPC because the >> distribution of the observed low concentrations is truncated by the >> LLOQ. So the VPC might suggest model misspecification for lower >> concentrations. Further, when one wants to use the model for clinical >> trial simulation should then the negative (BQL) values be omitted >> because they would never appear in reality? >> >> I would like to know how the more experienced NMusers handle this. >> >> Thanks in advance, Andreas. >> >> ____________________________ >> >> Andreas Lindauer >> >> University of Bonn >> >> Department of Clinical Pharmacy >> >> An der Immenburg 4 >> >> D-53121 Bonn >> >> phone:+49 228 73 5781 >> >> fax: +49 228 73 9757 >> >> > > -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand [EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:+64(9)373-7090 www.health.auckland.ac.nz/pharmacology/staff/nholford
