- On 31 Aug 2000 at 10:25:47, ml11439.-at-.goodnet.com sent the message

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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 - On 31 Aug 2000 at 15:31:45, "David Nix, Pharm D." (nix.at.Pharmacy.Arizona.EDU) sent the message

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

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Dear David:

Thanks for your comments, and the data. You are correct that

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

**** - On 3 Sep 2000 at 14:09:44, ml11439.at.goodnet.com sent the message

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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 - On 4 Sep 2000 at 15:10:24, James Wright (J.G.Wright.aaa.ncl.ac.uk) sent the message

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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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