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I never saw anyone recommends or uses weighting in the terminal phase estimation when doing
non-compartment analysis (NCA) in any textbook or literature before.Recently, I saw one of our
collaborator using 1/Y^2 (Y: observed values) in the terminal phase estimation when he did the NCA
by Phoenix WinNonlin. The reason he gave is listed below:
"The plasma concentration at the end of elimination phase is subject to the noise and inherently
carries higher variation than the study samples in the PK profile. The bioanalysis typically
applies weighted linear regression (1/x or 1/x^2) to overcome this variation. In the estimation of
the elimination rate constant, we applied the same strategy in using weighted linear regression (1/x
or 1/x2). This approach will minimize the impact of the high concentration samples on the
regression. This issue is more prominent in the compartment analysis, and often we will not see a
random distribution of the residue."
I know weighting by the reciprocal the predicted values (1/yhat or 1/yhat^2) is generally
recommended in compartment analysis, however I suspect whether it is necessary for NCA. In my humble
opinion, for NCA, as less as the modeling assumption should be made. But how is this applied to
terminal phase estimation?
I appreciate any comment or literature recommendation on this issue.
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Gary: weighted linear regression can be useful for any regression analysis. It depends on the
points you have. In the specific case you cite you would have to look at the goodness of fit of the
regression line first using ordinary least squares regression and then compare with the weighted
option to see what is the best fit. That comparison will tell you whether the weighting is helping
your fit to the line better or not. If "yes" if not the use the ordinary least regression. See the
work below for some background. This technique comes from engineering and it can be very useful.
Application of a variance-stabilizing transformation approach to linear regression of calibration
Angus M. McLean, Donald A. Ruggirello, Christopher Banfield, Mario A. Gonzalez, Meir Bialer. Article
first published online: 18 SEP 2006, DOI: 10.1002/jps.2600791112
Journal of Pharmaceutical Sciences, Volume 79, Issue 11, pages 1005–1008, November 1990
Hope this helps,
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Your collaborator is wrong. There is no need to weight the data in the terminal phase when doing an
NCA analysis. The heteroscedasticity in the data is controlled for by using log-linear regression.
Think of it this way. If
Observed Concentration = True Concentration*Exp(random noise)
then the variability of the observed data would appear log-normal. Variability would increase with
During the termination phase when you take the log-transform
Ln(observed) = Ln(true) + noise
Hence, by taking the log-transform the noise becomes a constant and so there is no need to weight
the data. You can simply use OLS. I hope this helps clarify things.
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Dear Gary and Peter:
Why use weighting? Because there are real errors involved. One wants to give weight to data
according to its credibility. If the lab assay data is Gaussian, and it usually is, Then the proper
measure of precision is the reciprocal of the assay variance at any result. This is well known
. It represents measurement noise. Then, if you fit the data, there is another source of noise,
and that is process noise, due to the uncertainties in the differential equations themselves. People
are beginning to describe this correctly, but nothing is widely published on this as yet. Instead,
one currently can estimate this other noise source as if it were an additive source of measurement
noise. Not correct, but better than nothing.
Fitting data is not an art. One does not mess with mother nature. One should not explore
weighting schemes simply to get a better fit. If one assumes a constant assay variance, as many do
in fitting logs of serum concentrations, as Dr. Bonate suggests, then you run into the problem of
BLQ, and his assumption becomes no longer true, as you encounter the region of machine noise. Better
to fit a polynomial to the assay data, so you can also know the machine noise. You might see
Jelliffe RW, Schumitzky A, Van Guilder M, Liu M, Hu L, Maire P, Gomis P, Barbaut X, and Tahani B:
Individualizing Drug Dosage Regimens: Roles of Population Pharmacokinetic and Dynamic Models,
Bayesian Fitting, and Adaptive Control. Therapeutic Drug Monitoring, 15: 380-393, 1993.
This issue has been around for so long.
All the best for the Holidays,
Roger W. Jelliffe, M.D., F.C.P., F.A.A.P.S.
Professor of Medicine Emeritus
Founder and Director Emeritus, Laboratory of Applied Pharmacokinetics
USC Keck School of Medicine
Children's Hospital of Los Angeles
4650 Sunset Blvd
Los Angeles CA 90027
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