- On 25 Jan 2000 at 23:58:45, "Dr.Ibrahim Wasfi" (iawasfi.-at-.emirates.net.ae) sent the message

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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 - On 26 Jan 2000 at 23:58:59, David_Bourne (david.-a-.boomer.org) sent the message

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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

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