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In a post-graduate pharmacokinetic course, we have taught that plasma
half-life is not a normally distributed parameter. Texts such as
Goodman & Gilman, however, report plasma t1/2 for various drugs, as well
as, +/- some value (suggesting they have just reported the mean & SD
result of all t1/2's identified). The concern with this type of
reporting is the
that when we use this mean result as our priors (converted to a ke), for
such PK programs as USCPAK, we essentially overestimate the average
half-life for a drug within a population. Would anyone know by chance
who published this observation originally?
Regards,
Robert Ariano, PharmD, BCPS
Department of Pharmacy,
St.Boniface General Hospital,
Winnipeg, MB, Canada
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[db - a few replies]
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Date: Fri, 13 Feb 1998 14:28:11 -0600
To: PharmPK.-at-.pharm.cpb.uokhsc.edu,
Multiple recipients of PharmPK - Sent by
From: "Hugh A. Semple"
Subject: Re: PharmPK Half-life of drug elimination
I think the following paper is where I first saw this topic discussed:
Lam FC, Hung CT, Perrier DG. Estimation of variance for harmonic mean
half-lives. J. Pharm. Sci. 1985; 74 (2):229-231.
Hope this helps.
Hugh
Hugh A. Semple, D.V.M., Ph.D.
Associate Professor of Pharmacy
College of Pharmacy & Nutrition
University of Saskatchewan
110 Science Place
Saskatoon, Saskatchewan
CANADA S7N 5C9
Phone (306)966-6365
FAX (306) 966-6377
"To me, the forest was peace and loneliness and freedom to think
and feel as I pleased. It was tangible nobility and it struck into my being
without literary interference. Later in life,when I was far from the
forest, I found the same thing in music."
Robertson Davies, from "The Cunning Man", 1994
---
From: "Thomas Senderovitz"
To:
Subject: Sv: PharmPK Half-life of drug elimination
Date: Fri, 11 Jul 1997 23:52:37 +0200
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Hello,
First of all i would like to state that reporting a mean +/- a value, which
could be a SD or SEM is not a good idea. IF a parameter is normally
distributed, the mean +/- 2SD would be more appropriate.
Then the next question. I do not think anyone can state that this and this
parameter is NEVER normally distributed. It really depends of the sample
size. Many of the PK parameteres you find in i.e. G&G are from rather SMALL
populations (and some of these "populations" are in fact healthy
volunteers). Under these circumstances you could argue that using
nonmarapetric statistics to describe your data is more correct ( such as
median and range). In reallity, in practical lift, I do not really think
this makes such a big difference, but as far as i know, no really good
trials have ever investigated the clinical consequences of using parametric
statistics instead of nonparametric statistical methods. I would rather
rocus on the PK values themselves - are they really POPULATION values?
Often the answer is no.
I hope these remarks are of some value!
Thomas Senderovitz, MD.
Clinical Pharmacology Unit
Bispebjerg Hospital
University of Copenhagen
E-mail: senderovitz.at.dadlnet.dk
---
Date: Mon, 16 Feb 1998 10:15:51 -0500
From: "Dr. William Webster"
Subject: Re: PharmPK Half-life of drug elimination
To: PharmPK.aaa.pharm.cpb.uokhsc.edu
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Construct a data set with ke's from say 0.1 to 0.00001 & then calc ulate
corresponding half-lives (Use spread sheet). Average each collum & see
that (ln(2)/ mean of the ke does not equal mean of the half life.
However, half-life may have normal distribution of error if the studies
averaged each subject's half life & did not predict average half life from
average ke.
The best model will have the ke parameter as a variable and not t1/2. Why
not do a comparison study of two different methods with the same data set.
The bottom line is how you apply results -- The more the data points, the
less the weight of the priors.\
Hope this helps.
W. Webster, Pharm.D., BCPS
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"reporting a mean +/- a value, which could be a SD or SEM "
does not necessarily describe a normal distribution. It is simply the
1st (mean) and 2nd moment (variability) of the unknown distribution,
which may further be characterized by the 3rd (skewness) and 4th
(kurtosis) moments. If the results for skewness and kurtosis do not
contradict the assumption of a normal distribution you may accept the
assumption of a normal distribution. In this case, the 95 % confidence
interval is given as mean +- 2 SD.
This topic is discussed in detail by:
William H. Press et al., Numerical recipes in C, 1988, Cambridge
University Press, p 472-475
regards
Willi
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Would someone please post an exact mathematical definition of
what is meant by half-life in the message below. I am not sure if it has to
do with the error in parameter estimation or with mean residence time.
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Dear Drs. Semple and Senderovitz:
About using means + SD's, etc, for PK parameter values. In my
experience
many PK parameter distributions are significantly skewed to the right. This
is why it has been common for people to use lognormal distributions for
parameters. In addition, two or more subpopulations may be invloved, such
as fast and slow metabolizers of a drug.
One of the strengths of the nonparametric method of population
modeling is
that it makes absolutely no assumptioms about the shape of the distribution
of any of the parameters. Frequently the mean is significantly higher than
the median, and sometimes is close to the 75th percentile. Warren Dodge
examined this question in newborns receiving gentamicin, and found that
when mean pk parameter values were used, the resulting serum levels were
usually higher than predicted. When median valued were used, the measured
levels were better centered about the predicteions (Drug Invest 5: 206-211,
1993.
The real problem is how to develop dosage regimens that achieve target
goals most precisely. The problem with any method that obtains a single
best estimator of the parameter values is that there is only one version of
the patient, and that the dosage regimen computed to achieve the desired
target goal is assumed to achieve it exactly. There is no way to examine
the probability of missing the goal, or by how much.
Oe of the strengths of the nonparametric population models is that they
provide a discrete joint density ( a collection of discrete support points,
approximately one for each patient studied in making the original
population model. Instead of summarizing everything to get a mean or
median, for example, the collection of support points in the pop model,
when used as the Bayesian prior for developing the initial regimen, can be
used. Each support point provides a collectioon of parameter estimates
which can be used to predict subsequent levels regulting from a candidate
dosage regimen. The method can also detect unsuspected subpopulations
without further aid from other descriptors of covariates.
At the time a target goal is desired, one can compute, for each support
point, what the predicted error is in the achievement of the goal. Since
each support point also has its own estimated probability, one can now
compute the expected weighted squared error with which that particular
regimen fails to achieve the goal. One can then examine other regimens
until the one is found which specifically minimizes the expected weighted
squared error with which the goal is achieved.
This new "multiple model" method is a more precise method of hitting a
target goal than any single point set of parameter values, as it is
specifically designed to minimize the error with which the target goal is
achieved. This has been described by Bayard, Milman, and Schumitzky in Int.
J. Biomed Comput. 36: 103-115, 1994, by Taright, Mentre, Mallet, et al in
Therap. Drug. Monit. 16: 258-69, 1994, and more recently by Jelliffe,
Schumitzky, Bayard, et al in Clin. Pharmacokinet. 34; 57-77, 1998. Our
group is in the process of implementing a clinical software package based
on this new method.
The bottom line is that we want to be able to hit a desired target goal
with the greatest possible precision. Nonparametric population models
provide the structure for this, coupled with using the multiple model
method of developing dosage regimens. That has been our primary motivation
for using nonparametric population models.
Very best regards,
Roger Jelliffe
************************************************
Roger W. Jelliffe, M.D.
USC Lab of Applied Pharmacokinetics
CSC 134-B, 2250 Alcazar St, Los Angeles CA 90033
Phone (213)342-1300, Fax (213)342-1302
email=jelliffe.at.hsc.usc.edu
************************************************
Take a look at our Web page for announcements of
new software and upcoming workshops and events!!
It is http://www.usc.edu/hsc/lab_apk/
************************************************
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[two replies - db]
Date: Thu, 19 Feb 1998 14:08:29 -0800
From: "Dr.Robert E. Ariano"
Reply-To: rariano.aaa.mail.sbgh.mb.ca
Organization: St.Boniface General Hospital, Department of Pharmacy
Mime-Version: 1.0
To: PharmPK.-at-.pharm.cpb.uokhsc.edu
Subject: Re: PharmPK Re: Half-life of drug elimination
Hi Brad:
In response to your request for a definition:
"Half-life expresses the period of time required for the amount or
concentration of a drug to decrease by one-half".
Rob Ariano, PharmD, BCPS
Department of Pharmacy,
St.Boniface General Hospital,
Winnipeg, MB, Canada
---
From: Hans Proost
Organization: Pharmacy Dept Groningen University
To: PharmPK.-at-.pharm.cpb.uokhsc.edu
Date: Fri, 20 Feb 1998 14:36:33 CET
Subject: Re: PharmPK Half-life of drug elimination
X-Confirm-Reading-To: "Hans Proost"
X-pmrqc: 1
Priority: normal
To the PharmPK group:
With respect to the distribution of half-lives: as indicated by Dr.
Jelliffe, assuming a log-normal distribution may be more appropriate
than a normal distribution. Actually, we know that many 'biological'
measures are log-normally distributed; at least, they are 'more log-
normal' than 'normal' (in case of bimodial distributions, both the
log-normal and the normal assumption will be incorrect as well; see
Dr. Jelliffe's message).
Apart from being a distribution which may be expected to be more
closely to the true distribution, an attractive advantage of the log-
normal is that we don't need to care about the difference in the
distribution of rate constants and half-lives: they follow the same
distribution, and their mean values obey the rule
'half-life = ln(2) / k'.
Another advantage is, of course, that we never get negative,
'impossible' values for expected values and confidence intervals.
The disadvantages are (1) a slightly more complicated procedure in
the calculations, which cannot be done as easily as in case of a
normal distribution, in most software packages, and (2) you have to
justify the use of the log-normal distribution: The use of a normal
distribution is so widespread in our world that you can use it without
a sound justification (i.e., it seems to be generally accepted in
scientific papers); in general, you are expected to demonstrate
that the distribution does not deviate significantly from a normal
distribution; in general, this 'proof' is quite easy if you don't have
too much data. However, this does not imply that the distribution
have been shown to be normally distributed.
As you may understand from this, I have a strong preference for the
log-normal distribution, and I promote its use wherever possible
(and justified!).
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Groningen, The Netherlands
tel. 31-50 363 3292
fax 31-50 363 3247
Email: j.h.proost.aaa.farm.rug.nl
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Greetings!
Could someone recommend simulation software currently available
forPharmK & PharmDynamics calculations suitable for nursing courses?
Thank you in advance.
Regards,
Susil
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Date: Fri, 13 Mar 1998 17:51:53 -0600
From: "Dr. Gamal Hussein" <
Reply-To: GHussein-clinPharm.at.worldnet.att.net
MIME-Version: 1.0
To: PharmPK.-at-.pharm.cpb.uokhsc.edu
Subject: Re: PharmPK Re: AW: Half-life of drug elimination
Dear Susil:
Try "Practical Pharmacokinetics" program, you can get a free copy from
this site http://www.ClinPharmInt.com/
Gamal
Gamal Hussein, Pharm.D. at http://www.ClinPharmInt.com/Hussein.htm
Associate Professor of Pharmacy
Northeast Louisiana University-Pharmacy School
Associate Professor of Neurology
Louisiana State University-Medical School
Clinical Coordinator of Clinical Pharmacy/Pharmacology Program
The Medical Center of Louisiana at New Orleans
http://www.ClinPharmInt.com/Orleans.htm
A free demo of the following programs is currently available
for evaluation. Click on the program title to download it. Our goal is
to provide the best tools for education and practice. Thanks for
visiting.
Design your own computerized interactive tests in minutes. This program
converts exams (files) written with any word processing programs to a
computerized/self-grading exam. It is also an excellent tool to
generate unlimited number of interactive case study. It is equipped
with a calculator, a calendar, and an instructor-defined password. It
also provides cumulative statistical reports on class/student
performance.
This is the winner of the 1996 American Association of Colleges of
Pharmacy-Innovation in Teaching Competition. It was designed for the
teaching and practice of clinical pharmacokinetics. It is currently
used by educators and clinicians in more than 45 countries worldwide.
The following programs will be available very soon. Please, e
mail us if you have an interest in them.
---
X-Sender: jelliffe.-a-.hsc.usc.edu
Date: Fri, 13 Mar 1998 16:50:53 -0800
To: PharmPK.-at-.pharm.cpb.uokhsc.edu
From: Roger Jelliffe <
Subject: Re: PharmPK Re: AW: Half-life of drug elimination
Mime-Version: 1.0
Dear Susil:
You might consider the USC*PACK software. You can get info about it
from our web site below. There are also several other good packages
available, such as TDMS, MW/Pharm, and the Abbottbase software.
Roger Jelliffe
************************************************
Roger W. Jelliffe, M.D.
USC Lab of Applied Pharmacokinetics
CSC 134-B, 2250 Alcazar St, Los Angeles CA 90033
Phone (213)342-1300, Fax (213)342-1302
email=3Djelliffe.-a-.hsc.usc.edu
************************************************
Take a look at our Web page for announcements of=20
new software and upcoming workshops and events!!
It is http://www.usc.edu/hsc/lab_apk/
************************************************
---
Date: Mon, 16 Mar 1998 12:52:54 -0500
From: kwatson <
Subject: PharmPK Re: AW: Half-life of drug elimination
Sender: kwatson <
To: "INTERNET:PharmPK.aaa.pharm.cpb.uokhsc.edu"
<
MIME-Version: 1.0
We currently sell a software called WinNonlin. It is the new standard
in pharmacokinetic, pharmacodynamic and noncompartmental analysis. Its
intuitive interface and flexible framework facilitates the use of this powerful
application and provide seamless interfacing with other
software and hardware. If you would like to see a demo of the software, please
send me your name and address and I will gladly send it out to you.=20
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Dear Susil,
Also of interest, you might look into "PK Solutions 2.0", an easy,
interactive and complete noncompartmental pharmacokinetics data analysis
system designed for researchers and educators. The program offers the bonus
feature of running in Excel providing unparalleled easy of use, data
exchange flexibility, and cross-platform compatibility. A demo is available
along with a free listing of 75 noncompartmental equations at our web site:
http://www.bright.net/~dfarrier
David S. Farrier, Ph.D.
Summit Research Services
Pharmacokinetics and Metabolism Software
1374 Hillcrest Drive
Ashland, OH 44805
Tel: 419-289-9207
Web: www.bright.net/~dfarrier
Email: dfarrier.-at-.bright.net
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