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Dear Pharmacokineticists,
I am a Masters by Research student who is studying pharmacokinetic
data of cancer drugs in humans. My background is Statistics, and some of the
things you may take for granted, we don't. I have a question:
I would like to know whether, in general, an intercept is fitted to
a HPLC standard 'curve'. I see that sometimes it is forced through the
origin and then sometimes it is not. It appears that the intercept is also
often not significant in the regression, however this is usually
insufficient grounds for removing it. It's better to have a physical
reasoning. As far as I've been told, no-one knows what happens between the
lowest measurable concentration and zero. It's definitely not a straight
line. But at zero concentration, the peak should be zero (obviously),
however that again is insufficient grounds for removing the intecept. It
also appears that fitting an intercept allows a better fit to the three or
four values that make up a 'standard'.
Direct replies appreciated.
Master Luke...
Checkin' the stats
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In our company, there are strict guidelines about not forcing the intercept
through zero. The range of quantification is bounded by nonzero
calibration standards. Weighted linear regression is used to fit the arnge
if an unweighted fit is unsatisfactory. The limit of quantification is the
lowestcalibration standard that, upon back-calculation, gives satisfactory
precision and accuracy results.
A useful general guide may be found in J. Pharm. Sci. 81(3):309-312,
1992, or J. AOAC Int. 75(1):19A-26A, 1992.
Varun Garg
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On Dec. 7, Luke asked "I would like to know whether, in general, an intercept
is fitted to a HPLC standard 'curve'."
Dear Luke,
A standard curve is valid only between the lowest and highest concentrations.
The regresion should not be forced through the origin (how do you know the
curve is linear below the lowest standard concentration) nor should the
standard curve be extrapolated below the lowest concentration - or above the
highest. Thus, the intercept of a standard curve is unimportant. To estimate
concentrations lower than your lowest standard, you must choose a new lower
standard concentration and include it in your standard curve.
Jo Cato
Allen.E.Cato.-at-.Abbott.com
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Hi Dear Master,
With regard to including or excluding the intercept from the Std. curve,
you should consider the magnitude of the intercept compared to the ratio
of drug/IS for the lowest concentration that you have in your std.calib.
curve. In general, if the intercept is 10 times smaller than the
mentioned ratio, one can simply omitte that from the estimation of
concentration of the unknown samples. However, if the intercept is
relatively high and/or inclusion of intercept decreases the error of
estimation of unknown samples within a run, one should consider the
intercept.
M.Vakily
Faculty of Pharmacy and Pharmaceutical Sc.
University of Alberta
Edmonton, Alberta
Canada
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I'm not certain if this is helpful or not. I am currently in a
pharmacometrics fellowship and still learning, but here goes..
I have had the pleasure of attending Dr. Roger Jelliffe's Population
PK/PD course. One of the books he gives out is about characterizing
the error patterns of assays. It's whole title is 'Pharmacoinformatics:
Equations for Serum Drug Assay Error Patterns; Implications for
Therapeutic Drug Monitoring and Dosage.' It talks about polynomial
descriptions of assay error.
Hope it's on the right path. Dr. Jelliffe's address is Laboratory of
Applied Pharmacokinetics, USC (CSC 134B), 2250 Alcazar St., L.A.,
CA. 90033. Phone (213) 342-1300, email jelliffe.aaa.hsc.usc.edu.
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There are 'right answers' here but probably the most important thing to
do is what has already been done here i.e. to think about your
particular problem and ask if an intercept is reasonable. I agree that
the theoretical predicition is that the peak should be zero when conc is
zero but it is possible to have a systematic error at zero e.g. by not
calibrating the machine properly. But I think the main issue here is the
nature of the error model not the structural model. An error model that
predicts the variance of the peak at each conc can be constructed that
say makes the variance proportional to the predicted peak squared plus
an additive component which allows for the error (mean zero) at a conc
of zero. Software that allows this and other more flexible variants of
this error model has been around for a while but I
dont know if many conc analysts (as opposed to data analysts) are aware
of that.
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, Private Bag 92019, Auckland, New Zealand
email:n.holford.-at-.auckland.ac.nz http://www.phm.auckland.ac.nz
Tel:+64 (9) 373-7599 x 6730 Fax:373-7556
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Thanks for all the responses regarding whether an intercept should
be fitted to a HPLC curve. I recieved about 14, and will reply to each one
in time. It appears that there is stronger grounds for keeping the intercept.
Lukas Zdanius
School of Statistics
Master Luke...
Checkin' the stats
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I am sure the audience of this discussion group would appreciate reading
some of the responses to your query which were mailed directly to you and
not posted on the listserv. Anyone out there who agrees??
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