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Hi
Could somebody provide a reference that pharmacokinetic parameters
are not normally distributed and thus non-parametric statistics are
more appropriate to use? Bearing in mind even if we do data
transformation, the number of observation in PK studies are usually
too small to conduct a meaningful normality test.
Regards,
Dr. Ibrahim Wasfi
Camelracing Laboratory,
P O Box 253, Abu Dhabi,
UAE
Fax 00971 2 463470
Tel 00971 2 4092522
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[Two replies - db]
X-Sender: whittem.-a-.staff.uiuc.edu
Date: Wed, 26 Jan 2000 08:45:15 -0600
To: PharmPK.-at-.boomer.org
From: Dr Ted Whittem
Subject: Re: PharmPK Reference for PK parameters not normally
distributed
Reference Type: Journal Article
Record Number: 2
Author: Powers, J.; Powers, T.
Year: 1990
Title: Statistical analysis of pharmacokinetic data with special
applications to bioequivalence studies
Journal: Ann Rech Vet
Volume: 21
Issue: Suppl 1
Pages: 87S-92S
Label: 91181833
Keywords: Animal
Biological Availability
Linear Models
*Models, Statistical
*Pharmacokinetics
Statistics
Abstract: The objectives of this investigation are: 1) to describe
techniques for determining the validity of the assumptions; 2) to
suggest data transformations which may validate the use of parametric
procedures; and 3) to describe a non-parametric alternative to the
analysis of variance for crossover designs. Two assumptions common to
all parametric procedures include the underlying normal distribution
of the observations and equality of variances across treatment
groups. Normal probability plots and/or stem and leaf plots are good
diagnostic techniques to address the assumption of normality, while
Bartlett's test is the most common method of determining equality of
variances. To evaluate bioequivalence data, the Food and Drug
Administration suggests the use of analysis of variance for crossover
designs. If the underlying assumptions are valid, the appropriate
statistical models are well known. On the other hand, if the
assumptions are not valid, the investigator has one of two choices:
1) transform the data in such a way as to satisfy the assumptions, or
2) use a non-parametric procedure. Square root or logarithmic
transformations are commonly used in this situation. However, if a
suitable transformation cannot be found, then a non-parametric
procedure should be used. Koch (Biometrics (1972) 28, 577-584)
developed a non-parametric crossover test, which is relatively easy
to apply, but the corresponding power calculations required by the
FDA are less obvious.
Reference Type: Journal Article
Record Number: 3
Author: Powers, J.
Year: 1990
Title: Statistical analysis of pharmacokinetic data
Journal: Journal of Veterinary Pharmacolgy and Therapeutics
Volume: 13
Pages: 113-120
Reference Type: Journal Article
Record Number: 1
Author: Powers, J.D.
Year: 1991
Title: Hypothesis testing of pharmacokinetic parameters
Journal: ACTA Veterinaria Scandinavia Supplement
Volume: 87
Pages: 184-185
Ted Whittem.
--
X-Sender: jelliffe.at.hsc.usc.edu
Date: Wed, 26 Jan 2000 20:18:08 -0800
To: PharmPK.at.boomer.org
From: Roger Jelliffe
Subject: Re: PharmPK Reference for PK parameters not normally
distributed
Dear Ibrahim:
Thanks for your note. It is common for many drugs to have some subjects
that are fast, and others that are slow, metabolizers. The important thing
is not just that nonparametric population models get the most likely
probability density function for the parameters from the raw data in the
population (they do), but also that they permit the use of "multiple model"
dosage design. This approach gets around the limitations of the separation
principle and permits design of dosage regimens which can specifically
predict the degree (weighted squared error, for example) with which any
dosage regimen will fail to achieve a stated target goal. One can then
examine other regimens, and can find the one which specifically minimizes
the weighted squared error with which a target goal can be achieved. This
is new in thePK area. It comes from, and is well known is, the area of
flight control and missile guidance systems, where it is used extensively,
as in the Airbus, the 777, the F16, etc.
You might look at our web site, and also at Clin Pharmacokinetics 34:
57-77, 1998. We feel strongly that the important thing is not what single
number best describes a parameter distribution, but rather what is the most
informed action you can take, based on the population data. Usually this
means being able to develop the most informed dosage regimen. This is
illustrated in that article.
We think this is the strength of the sequence of, first,
determining the
assay error pattern over its entire working range, to fit each population
data point by its Fisher information. Second, the use of the assay error
polynomial and a parametric population model to find the remaining
intraindividual variability, with which to scale the assay error. Then, use
a nonparametric pop model to get the entire joint density, usually one set
of parameter values for each subject, with an estimate of the probability
of each set. Finally, the multiple models in the nonparametric joint
density can be used with multiple model dosage design to get the regimen
which hits the desired targets most precisely.
Hope this helps,
Roger Jelliffe
PharmPK Discussion List Archive Index page
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