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

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• 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 number
3249). I wanted to know if there was an equation for SD of assay error
for 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, this
formula was published in an article by Jelliffe et al in Therap Drug
Monitoring 1993;15:380-393. It is a polynomial equation obtained by
polynomial regression of assay SD versus gentamicin concentration.

Is there a similar equation for the Abbott AxSym system for
gentamicin assays and vancomycin assays?

Mike Leibold, PharmD, RPh
ML11439.-a-.goodnet.om

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• 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 established
for each laboratory since instruments, assay kits, and conditions will
vary.

From the equation below:
Conc SD CV%
0.1 0.030448318 30.448318
0.2 0.035457272 17.728636
0.5 0.05072795 10.14559
1 0.0769918 7.69918
8 0.5513552 6.89194
10 0.72346 7.2346
15 1.224835 8.165566667
30 3.3385 11.12833333

Most labs will accept 10-15% CV. For gentamicin, it is typical for
clinical labs not to report concentrations < 0.5 mcg/ml and not greater
than 10-15 mcg/ml. An equation when used, will only apply to the range
of concentrations used to create the equation. In this case, the
equation predicts that gentamicin concentraitons > 30 mcg/ml could be
measure, but that is probably not so.

In a research setting, a validation needs to be performed for any assay
prior to performing an assay on study samples. The validation usually
includes running multiple standard curves in one day (within-day), and
running standard curves on 3 to 5 different days (between-day) along
with quality control samples. The quality control samples are made in a
single batch and frozen. Thawed QC samples are then ran along with each
assay run. In the clinical setting, QC samples (commercially available)
are included in each assay run. Ideally, QC concentrations should cover
the range of the standard curve (usually 3 QC's for research). One
often has to add additional QC samples to obtain a good estimate of the
assay variability pattern.

One major discussion point between those interested in PK modeling and
analytical chemists involves reporting of concentrations below the LMQ,
where LMQ is defined by reasonable precision. The analytical
perspective is that these concentrations are unreliable and should not
be reported. The PK modeler will often want these concentrations and
will accept lower precision as long as the precision is known.

David Nix

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• On 1 Sep 2000 at 15:30:42, Roger Jelliffe (jelliffe.at.usc.edu) sent the message

Dear David:

the best thing is for each lab to determine its own assay error
pattern. Using our USC*PACK software, the assay error polynomial for
your assay data is that the

assay SD = 0.02548 + 0.04948C + 0.002032CSq,

where C is the concentration and Csq is the square of the
concentration. The data is very well fitted, and the Rsq is
essentially 1.0.

I am following this with a repeat of what I mentioned some
time earlier.

About accuracy and precision. They ARE important. At least
for potentially toxic drugs, we are not playing with data, we are
modeling it so we can act on it OPTIMALLY, that is, to develop dosage
regimens to achieve desired target goals with maximal precision. It
is not just that the assay should be acceptable precise over its
working range, but also that the error be carefully determined so it
can be used to fit data by its Fisher information. Different
weighting schemes yield different model parameter values. This is one
of the reasons that linear regression on the logs of the levels, with
its inappropriate weighting scheme built into the fit, often yields
significantly different parameter values compared to weighted
nonlinear least squares or the MAP Bayesian fitting procedure, as
these can take the correct weighting scheme based on the assay error
polynomial.

The issue of LOQ is also important here. When we have no
other info about the specimen except the measured value itself, then
there most certainly IS a LOQ. However, when we do most PK work, that
is not the case. We know, with reasonable precision, when the doses
were given and when the samples were obtained. So we know the drug is
really present. Even simple linear models show us that the last
molecule is theoretically never excreted. So, instead of having to
ask, 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 is
instead - HOW MUCH drug is present?

Now comes the question of weighting the data optimally. Most
people agree that weighting data by its Fisher information is
appropriate - the reciprocal of the variance of the data point. It
works quite well. The point is that when you determine the assay
error and express it as a polynomial function of the concentration,
that important relationship continues over the entire range of the
assay, down to and including the blank, if you set it up correctly.
This point is discussed in more detail in an article in Therap Drug
Monit 15:380-393, 1993, especially the section on Evaluating the
Credibility of Population Parameter Values and Serum Level Data, pp.
386-391.

Thus, not only should one determine if the assay is
sufficiently precise or not, but even after that decision is made,
there remains the issue of fitting the data correctly by its Fisher
information. Determining the assay error polynomial in this way is a
cost effective way to do this. It has the fringe benefit that there
is no LOQ for PK work.

Hope this helps. The polynomials are easy to fit, and many software
packages can do it just fine.

Very best regards,

Roger Jelliffe
Roger W. Jelliffe, M.D. Professor of Medicine, USC
USC Laboratory of Applied Pharmacokinetics
2250 Alcazar St, Los Angeles CA 90033, USA
Phone (323)442-1300, fax (323)442-1302, email= jelliffe.-at-.hsc.usc.edu
Our web site= http://www.usc.edu/hsc/lab_apk
****

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• 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 assay
error 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 for
gentamicin, tobramycin and vancomycin, the following equations were
derived by polynomial regressing using Excel's Solver:

POLYNOMIAL REGRESSION GENTAMCIN SD ASSAY
COEFFICIENTS SD** GENTAMICIN CONC Predicted SD
0.023608 0.067 1 0.067
0.043155 0.2 4 0.200015
0.000237 0.384 8 0.383992
0

EQUATION: SD= .023608 + .043155(C) + .000237(C*C)
SS equation minimized
2.79E-10

POLYNOMIAL REGRESSION TOBRAMYCIN SD ASSAY

COEFFICIENTS SD** TOBRAMYCIN CONC Predicted SD
0.006848 0.042 1 0.042001
0.03144 0.192 4 0.192014
0.003713 0.496 8 0.495992
0

EQUATION: SD= .006848 + .03144(C) + .003713(C*C)
SS equation minimized
2.6E-10

POLYNOMIAL REGRESSION VANCOMYCIN SD ASSAY

COEFFICIENTS SD** VANCOMYCIN CONC Predicted SD
0.221368 0.3195 7.5 0.319315
0.010327 1.029 35 1.029068
0.000364 3.045 75 3.044984
0

EQUATION: SD= .221368 + .010327(C) + .000364(C*C)
SS equation minimized
3.93E-08

** SD deviation supplied by manufacturer's package insert for each AXSYM
assay 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 this
process by determining our own standard deviations for drug assays by
performing quadruplicate assays at each of the above concentrations?

Mike Leibold, PharmD, RPh
ML11439.at.goodnet.com

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• 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 before
I went any further, which acknowledge that the SDs you are fitting are
crudely determined. The popular quadruplicate is nowhere near enough to
estimate variability - this is like assessing population variability from
four patients.

James Wright

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