# PharmPK Discussion - AXSYM Drug Assay System: Equation For Standard Deviation of Assay

PharmPK Discussion List Archive Index page
• On 31 Aug 2000 at 10:25:47, ml11439.-at-.goodnet.com sent the message
`Discussion Group,      Our hospital has a AxSym system for drug assays (serial number3249). I wanted to know if there was an equation for SD of assay errorfor this system as there is for the Abbott TDX system where:            Gentamicin SD= .02548 + .04948C  + .0020318C2      For gentamicin assays done by the Abbott TDX system, thisformula was published in an article by Jelliffe et al in Therap DrugMonitoring 1993;15:380-393. It is a polynomial equation obtained bypolynomial regression of assay SD versus gentamicin concentration.     Is there a similar equation for the Abbott AxSym system forgentamicin assays and vancomycin assays?                                           Mike Leibold, PharmD, RPh                                           ML11439.-a-.goodnet.om`
Back to the Top

• On 31 Aug 2000 at 15:31:45, "David Nix, Pharm D." (nix.at.Pharmacy.Arizona.EDU) sent the message
`I would argue that the assay variability pattern needs to be establishedfor each laboratory since instruments, assay kits, and conditions willvary. From the equation below:Conc	SD		CV%0.1	0.030448318	30.4483180.2	0.035457272	17.7286360.5	0.05072795	10.145591	0.0769918	7.699188	0.5513552	6.8919410	0.72346		7.234615	1.224835	8.16556666730	3.3385		11.12833333Most labs will accept 10-15% CV.  For gentamicin, it is typical forclinical labs not to report concentrations < 0.5 mcg/ml and not greaterthan 10-15 mcg/ml.  An equation when used, will only apply to the rangeof concentrations used to create the equation.  In this case, theequation predicts that gentamicin concentraitons > 30 mcg/ml could bemeasure, but that is probably not so.In a research setting, a validation needs to be performed for any assayprior to performing an assay on study samples.  The validation usuallyincludes running multiple standard curves in one day (within-day), andrunning standard curves on 3 to 5 different days (between-day) alongwith quality control samples.  The quality control samples are made in asingle batch and frozen.  Thawed QC samples are then ran along with eachassay run.  In the clinical setting, QC samples (commercially available)are included in each assay run.  Ideally, QC concentrations should coverthe range of the standard curve (usually 3 QC's for research).  Oneoften has to add additional QC samples to obtain a good estimate of theassay variability pattern.One major discussion point between those interested in PK modeling andanalytical chemists involves reporting of concentrations below the LMQ,where LMQ is defined by reasonable precision.  The analyticalperspective is that these concentrations are unreliable and should notbe reported.  The PK modeler will often want these concentrations andwill accept lower precision as long as the precision is known.David Nix`
Back to the Top

• On 1 Sep 2000 at 15:30:42, Roger Jelliffe (jelliffe.at.usc.edu) sent the message
`Dear David:         Thanks for your comments, and the data. You are correct thatthe best thing is for each lab to determine its own assay errorpattern. Using our USC*PACK software, the assay error polynomial foryour assay data is that theassay SD = 0.02548 + 0.04948C + 0.002032CSq,where C is the concentration and Csq is the square of theconcentration. The data is very well fitted, and the Rsq isessentially 1.0.         I am following this with a repeat of what I mentioned sometime earlier.         About accuracy and precision. They ARE important. At leastfor potentially toxic drugs, we are not playing with data, we aremodeling it so we can act on it OPTIMALLY, that is, to develop dosageregimens to achieve desired target goals with maximal precision. Itis not just that the assay should be acceptable precise over itsworking range, but also that the error be carefully determined so itcan be used to fit data by its Fisher information. Differentweighting schemes yield different model parameter values. This is oneof the reasons that linear regression on the logs of the levels, withits inappropriate weighting scheme built into the fit, often yieldssignificantly different parameter values compared to weightednonlinear least squares or the MAP Bayesian fitting procedure, asthese can take the correct weighting scheme based on the assay errorpolynomial.         The issue of LOQ is also important here. When we have noother info about the specimen except the measured value itself, thenthere most certainly IS a LOQ. However, when we do most PK work, thatis not the case. We know, with reasonable precision, when the doseswere given and when the samples were obtained. So we know the drug isreally present. Even simple linear models show us that the lastmolecule is theoretically never excreted. So, instead of having toask, as we must in toxicological work, if the drug is PRESENT OR NOT,and having therefore to develop a LOQ, we know the drug is present.The question being asked is not the same as in toxicology. It isinstead - HOW MUCH drug is present?         Now comes the question of weighting the data optimally. Mostpeople agree that weighting data by its Fisher information isappropriate - the reciprocal of the variance of the data point. Itworks quite well. The point is that when you determine the assayerror and express it as a polynomial function of the concentration,that important relationship continues over the entire range of theassay, down to and including the blank, if you set it up correctly.This point is discussed in more detail in an article in Therap DrugMonit 15:380-393, 1993, especially the section on Evaluating theCredibility of Population Parameter Values and Serum Level Data, pp.386-391.         Thus, not only should one determine if the assay issufficiently precise or not, but even after that decision is made,there remains the issue of fitting the data correctly by its Fisherinformation. Determining the assay error polynomial in this way is acost effective way to do this. It has the fringe benefit that thereis no LOQ for PK work.Hope this helps. The polynomials are easy to fit, and many softwarepackages can do it just fine.Very best regards,Roger JelliffeRoger W. Jelliffe, M.D. Professor of Medicine, USCUSC Laboratory of Applied Pharmacokinetics2250 Alcazar St, Los Angeles CA 90033, USAPhone (323)442-1300, fax (323)442-1302, email=  jelliffe.-at-.hsc.usc.eduOur web site=  http://www.usc.edu/hsc/lab_apk****`
Back to the Top

• On 3 Sep 2000 at 14:09:44, ml11439.at.goodnet.com sent the message
`Discussion group,      As per our previous email, our hospital has a AxSym system for drug assays(serial number 3249). I wanted to know if there was an equation for SD of assayerror for this system as there is for the Abbott TDX gentamicin assay where:                     SD= .02548 + .04948C  + .0020318C2     (Jelliffe et al in Therap Drug Monitoring 1993;15:380-393)     Using data supplied from the AXSYM package inserts forgentamicin, tobramycin and vancomycin, the following equations werederived by polynomial regressing using Excel's Solver:POLYNOMIAL REGRESSION GENTAMCIN SD ASSAYCOEFFICIENTS		SD**	 GENTAMICIN CONC	Predicted SD0.023608		0.067	1			0.0670.043155		0.2	4			0.2000150.000237		0.384	8			0.3839920EQUATION: SD= .023608 + .043155(C)  + .000237(C*C)			SS equation minimized			2.79E-10POLYNOMIAL REGRESSION TOBRAMYCIN SD ASSAYCOEFFICIENTS		SD**	 TOBRAMYCIN CONC	Predicted SD0.006848		0.042	1			0.0420010.03144		        0.192  	4		        0.1920140.003713		0.496	8			0.4959920EQUATION: SD= .006848 + .03144(C)  + .003713(C*C)			SS equation minimized			2.6E-10POLYNOMIAL REGRESSION VANCOMYCIN SD ASSAYCOEFFICIENTS		SD**	 VANCOMYCIN CONC	Predicted SD0.221368		0.3195	7.5			0.3193150.010327		1.029	35			1.0290680.000364		3.045	75			3.0449840EQUATION: SD= .221368 + .010327(C)  + .000364(C*C)			SS equation minimized			3.93E-08** SD deviation supplied by manufacturer's package insert for each AXSYMassay for the specified concentrations.     Is this data analysis consistent with your knowledge of this process?Or, do you know of other equations, or should we still individualize thisprocess by determining our own standard deviations for drug assays byperforming quadruplicate assays at each of the above concentrations?                                           Mike Leibold, PharmD, RPhML11439.at.goodnet.com`
Back to the Top

• On 4 Sep 2000 at 15:10:24, James Wright (J.G.Wright.aaa.ncl.ac.uk) sent the message
`Dear Roger and Mike,I would like to see some confidence intervals on those coefficients beforeI went any further, which acknowledge that the SDs you are fitting arecrudely determined.  The popular quadruplicate is nowhere near enough toestimate variability - this is like assessing population variability fromfour patients.James Wright`
Back to the Top

Want to post a follow-up message on this topic? If this link does not work with your browser send a follow-up message to PharmPK@boomer.org with "AXSYM Drug Assay System: Equation For Standard Deviation of Assay" as the subject

Copyright 1995-2010 David W. A. Bourne (david@boomer.org)