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Hello there,
I have been mentoring one of my colleagues on the principles of
noncompartmental analysis. They have training in statistics so, for
better or worse, I skipped the usual MRT = AUMC/AUC approach and instead
showed them that the concentration-time curve could be converted to a
probability curve by dividing each concentration by the AUC and then
replotting. They were then comfortable that classical statistical
moment theory could be applied to calculate the mean of the distribution
(MRT) straight from the raw first moment curve.
During the conversation, one of their questions made me hesitate, so I
wanted to check with you to make sure I wasn't misleading them.
"What is the meaning of the probability curve, calculated from the PK
curve?"
My answer was that it was that each point represented the probability of
finding drug in plasma at that particular time.
Does that sound right?
As statisticians they were disappointed that we didn't have much use for
higher statistical moments (for variance, skewness and kurtosis) in PK,
but when I pointed out the potential errors resulting in multiplying a
24-hr concentration by 24^4, and the huge area extrapolations that would
likely be needed for the higher moments, they could see the practical
limitations.
All the very best,
Bernard
Bernard Murray, Ph.D.
Senior Research Scientist, Drug Metabolism
Gilead Sciences
[Reminds me an applied math course I helped to teach many years ago. In
one example the
mathematics instructor turned the PK equation into stochastic events - db]
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The following message was posted to: PharmPK
Dear Bernard:
I don't understand. What good does noncompartmental modeling do for
you that real compartmental modeling does not do better, especially
nonparametric population modeling? How do you plan to use these models?
How
do you use them, for example, to develop dosage regimens of drugs for
maximally precise dosage regimens as with nonparametric models and
multiple
model dosage design? Can you help me?
Some references
1. Jelliffe R, Schumitzky A, Bayard D, Milman M, Van Guilder M, Wang
X,
Jiang F, Barbaut X, and Maire P: Model-Based, Goal-Oriented,
Individualized
Drug Therapy: Linkage of Population Modeling, New "Multiple Model"
Dosage
Design, Bayesian Feedback, and Individualized Target Goals. Clin.
Pharmacokinet. 34: 57-77, 1998.
2. Jelliffe R: Goal-Oriented, Model-Based Drug Regimens: Setting
Individualized Goals for each Patient. Therap. Drug Monit. 22: 325-329,
2000.
3. Jelliffe R, Bayard D, Milman M, Van Guilder M, and Schumitzky A:
Achieving Target Goals most Precisely using Nonparametric Compartmental
Models and "Multiple Model" Design of Dosage Regimens. Therap. Drug
Monit.
22: 346-353, 2000.
4. Leary, R., Jelliffe R., Schumitzky, A., and Van Guilder, M An
adaptive grid non-parametric approach to pharmacokinetic and
dynamic(PK/PD)
population models, 14-th IEEE Symposium on Computer Based Medical
Systems,
389-394, 2001.
5. Jelliffe R: Estimation of Creatinine Clearance in Patients with
Unstable Renal Function, without a Urine Specimen. Am. J. Nephrology,
22:
320-324, 2002.
6. Bayard D, and Jelliffe R: A Bayesian Approach to Tracking Patients
having Changing Pharmacokinetic Parameters. J. Pharmacokin. Pharmacodyn.
31
(1): 75-107, 2004.
7. Bustad A, Terziivanov D, Leary R, Port R, Schumitzky A, and Jelliffe
R: Parametric and Nonparametric Population Methods: Their Comparative
Performance in Analysing a Clinical Data Set and Two Monte Carlo
Simulation
Studies. Clin. Pharmacokinet., 45: 365-383, 2006.
8. Macdonald I, Staatz C, Jelliffe R, and Thomson A: Evaluation and
Comparison of Simple Multiple Model, Richer Data Multiple Model, and
Sequential Interacting Multiple Model (IMM) Bayesian Analyses of
Gentamicin
and Vancomycin Data Collected From Patients Undergoing Cardiothoracic
Surgery. Ther. Drug Monit. 30:67-74, 2008.
9. Jelliffe R, Schumitzky A, Bayard D, Leary R, Botnen A, Van Guilder
M, Bustad A, and Neely M: Human Genetic variation, Population
Pharmacokinetic - Dynamic Models, Bayesian feedback control, and
Maximally
precise Individualized drug dosage regimens. Current Pharmacogenomics
and
Personalized Medicine, 7: 249-262, 2009.
10. Neely M, van Guilder M, Yamada W, Schumitzky A, and Jelliffe R:
Accurate Detection of Outliers and Subpopulations with Pmetrics, a
Nonparametric and Parametric Pharmacometric Modeling and Simulation
Package
for R. Therap. Drug Monit. 34: 467-476, 2012.
11. Tatarinova T, Neely M, Bartroff J, van Guilder M, Walter Yamada W,
Bayard D, Jelliffe R, Leary R, Chubatiuk A, and Schumitzky A: Two
General
Methods for Population Pharmacokinetic Modeling: Non-Parametric Adaptive
Grid and Non-Parametric Bayesian. J. Pharmacokin. Pharmacodyn, in press.
Very best regards,
Roger Jelliffe
Roger W. Jelliffe, M.D., F.C.P., F.A.A.P.S.
Professor of Medicine,
Founder and Co-Director, Laboratory of Applied Pharmacokinetics
www.lapk.org
USC Keck School of Medicine
2250 Alcazar St, Room 134-B
Los Angeles CA 90033
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The following message was posted to: PharmPK
Hi, Bernard:
AUC normalized concentration curve (Ct/AUC) can be described as follows
(assuming F=1 for simplicity):
Ct/AUC=Ct/(Dose/CL)=Ct/(Dose/(V*K))=(Ct*V/Dose)*K
Ct*V/Dose is the fraction of drug molecules remaining (alive) in the
body at time t. This is the same as survival function in statistics,
S(t), proportion of people still alive at time t. K is approximately the
fraction of drug (relative to the drug amount at time t) eliminated from
the body within a small time interval (I like this way of interpreting K
because K can always be converted to a <1 number by scaling time to a
very small unit, such as min, sec, to make K intuitively meaningful.
E.g. K=1/hr can be expressed as 0.0167/min, meaning approximately 1.67%
of remaining drug molecules is eliminated within 1 min). In survival
statistics, K is the same as hazard or conditional failure rate (h), the
fraction of people (relative to the people alive at time t) dying within
a small time interval. Then (Ct*V/Dose)*K is the fraction of drug
molecules (relative to the total dose) eliminated at time t (within a
small time interval around time t). To make it more consistent with the
statistical description, (Ct*V/Dose)*K is the fraction of drug molecules
(relative to the total dose) that has a residence time (survival in the
body) of t because this fraction of drug molecules are not eliminated
(die) until time t. This is the same as the density function or
unconditional failure rate, f(t), in survival statistics. And it is well
known f(t)=S(t)*h. So at each t, Ct/AUC is just like a histogram summary
(expressed as proportion) of drug molecules with different residence
times. E.g. at Ct/AUC=0.1 at 2 hours means that 10% of drug molecules
survived up to 2 hours (residence time=2). Ct/AUC=0.2 at 10 hours means
that 20% of drug molecules survived up to 10 hours (residence time=10).
Therefore, the raw Ct/AUC can be used to calculate the mean residence
time. I hope this will help your colleagues to understand this PK
concept better. There is a close link between PK and survival
statistics. PK is basically a description of the drug molecules
surviving in the body.
David:
Any first order process can be described as a random walk process. The
rate constant can be interpreted as the probability of moving to another
state (compartment) and 1-rate constant is the probability of staying at
the current state (compartment). Of course, the rate constant needs to
be converted to a <1 number as described above to make this
interpretation meaningful.
Thanks
Yaning
Yaning Wang, Ph.D.
Associate Director for Science
Division of Pharmacometrics
Office of Clinical Pharmacology
Office of Translational Science
Center for Drug Evaluation and Research
U.S. Food and Drug Administration
"The contents of this message are mine personally and do not necessarily
reflect any position of the Government or the Food and Drug
Administration."
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The following message was posted to: PharmPK
Hello Roger,
I understand your concern about inappropriate use of NCA, but in this
case it is being applied to nonclinical studies, either to early
discovery pharmacokinetics or to toxicokinetics. The aim is only to
have simple, objective measures of exposure (AUC, Cmax etc.) and
persistence (MRT). My colleague's question was largely triggered by
curiosity as to how MRT calculations were performed. There are some
nice papers on the use of higher statistical moments in pharmacokinetics
(e.g. Weiss & Pang, J Pharmacokin Biopharm, 20: 253-278 [1992]) but, for
reasons I mentioned before, they are not routinely applicable.
I can assure you that we switch to compartmental modeling for
development candidate molecules, or for those used in nonclinical
pharmacodynamic models. It is unfortunate that we don't have time to
develop and validate more sophisticated models for some of our more
"interesting" compounds.
Thank you very much for the literature review. I'll pass that to my
colleague and I am sure that there will be future mentoring sessions on
that topic.
All the very best,
Bernard
Bernard Murray, Ph.D.
Senior Research Scientist, Drug Metabolism
Gilead Sciences
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Yaning: Thank you for your informative and thought provoking commentary
concerning the significance of the AUC normalized concentration curve Ct/AUC.
Could I ask you to enlarge upon it a little to include the significance
of
Cmax/AUC inf quotient.
Thanks
Angus McLean Ph.D.
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The following message was posted to: PharmPK
Angus:
Following "Ct/AUC is just like a histogram summary (expressed as proportion) of
drug molecules with different residence times", Cmax(observed)/AUC is the peak
of this histogram, representing the largest fraction of drug molecules with a
specific residence time: Tmax (observed).
Thanks
Yaning
Yaning Wang, Ph.D.
Associate Director for Science
Division of Pharmacometrics
Office of Clinical Pharmacology
Office of Translational Science
Center for Drug Evaluation and Research
U.S. Food and Drug Administration
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Yaning: As you are aware Ct/AUC has the dimension of time. Therefore
could I say that Cmax(observed)/AUC is the peak of the Ct/AUC histogram
and represents the time of occurrence of the largest fraction of drug
molecules with a specific residence time (Tmax (observed).
Do you agree with this way of putting it?
Angus McLean
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