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The following message was posted to: PharmPK
Hello All
I have a rather basic question about distribution of pharmacokinetic
data. More often than not in a large dataset, pharmacokinetic
parameters including AUC or apparent clearance follows non-Gaussian
distribution. Not surprisingly drug or metabolite concentrations are
often non-normally distributed. In that case we have the following
options in reporting such values but the question is which method is
the most preferred (and/or correct). Also what is the preferred
method of plotting average concentration versus time plots (with
error bars) when data is non normally distributed?
1. Just report arithmetic mean and SD and perform parametric
statistical tests i.e. t-test or ANOVA without paying attention to
the distribution.
2. Transform the values to natural log, confirm normality and
then perform parametric statistical tests on log transformed data and
report back transformed values for mean and 95% confidence intervals
(SE?).
3. Report median and interquartile range and compare values by
non parametric tests.
I personally prefer the second option for both cross over and case
control studies but I look forward to hear about your opinion on this
subject.
Many thanks
Fatemeh
Fatemeh Akhlaghi, PharmD, PhD
Assistant Professor
Biomedical and Pharmaceutical Sciences (BPS)
University of Rhode Island
125 Fogarty Hall, 41 Lower College Road
Kingston, RI 02881
USA
Phone: (401) 874 9205
Fax: (401) 874 2181
Email: fatemeh.aaa.uri.edu
Laboratory Website: http://www.uri.edu/pharmacy/faculty/aps/akhlaghi/
index
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The following message was posted to: PharmPK
The second option permits the use of the more powerful parametric
statistics. Normalization doesn't necessarily have to be a log
transform - other transforms are valid as well.
James D. Prah, PhD
US EPA
Human Studies Division MD (58B)
Research Triangle Park, NC, 27711
919 966 6244
919 966 6367 FAX
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The following message was posted to: PharmPK
Dear James!
You wrote:
>Normalization doesn't necessarily have to be a log
>transform - other transforms are valid as well.
>
....which is perfectly correct in statistical sense.
Unfortunatelly FDA stated 2001 in 'Guidance for Industry:
Statistical Approaches to Establishing Bioequivalence.'
(http://www.fda.gov/cder/guidance/3616fnl.pdf)
'Sponsors and/or applicants are not encouraged to test
for normality of error distribution after
log-transformation [...].'
I love Jones and Kenward writing (2003):
'No analysis is complete until the assumptions that
have been made in the modeling have been checked.
Among the assumptions are that the repeated measurements
on each subject are independent, normally distributed
random variables with equal variances.
Perhaps the most important advantage of formally fitting
a linear model is that diagnostic information on the
validity of the assumed model can be obtained.
These assumptions can be most easily checked by analyzing
the residuals.'
Great! It's an assumption we made, but we are not allowed
(excuse me: not encouraged) to test it...
European Regulators are not that strict, but it would
be a nice task convincing them about the application
of anything other than a log-transform.
I scared them away many times with nonparametrics,
and now you come up with something else than logs ;-)
best regards,
Helmut
--
Helmut Schuetz
BEBAC
Consultancy Services for Bioequivalence and Bioavailability Studies
Neubaugasse 36/11
1070 Vienna/Austria
tel/fax +43 1 2311746
http://BEBAC.at
Bioequivalence/Bioavailability Forum at http://forum.bebac.at
http://www.goldmark.org/netrants/no-word/attach.html
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The following message was posted to: PharmPK
Fatemah,
Assuming that you have a reasonably large number of subjects (say 100
or more) then you do not have to describe what you see in parametric
terms. You can display the results honestly as a frequency
distribution histogram or an empirical cumulative distribution function.
Parametric predictions (e.g. 90% confidence intervals) can be
provided at the expense of assumptions about the distribution.
If you feel tbe need to do some kind of a test to generate a P value
then its up to you to choose a suitable assumption. If the P value
conclusion is sensitive to the assumption you make (e.g. normal or
log normal) then it suggests the biological difference that is being
examined is not robustly defined by your data.
Examination of a frequency histogram of the distributions
representing the two groups may be more informative than P values for
learning about the biology.
Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
email:n.holford.-a-.auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
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The following message was posted to: PharmPK
Dear Fatemeh,
With respect to your 'multiple-choice question':
> 1. Just report arithmetic mean and SD and perform parametric
> statistical tests i.e. t-test or ANOVA without paying attention to
> the distribution.
If there are indications that the distribution is not normal, I would
not
recommend to do so. But the phrase 'without paying attention to the
distribution' sounds bad! Whenever possible, get at least some idea
about
the distribution. If variability is small, the distribution does not
really
matter, but in case of high variability, it does.
> 2. Transform the values to natural log, confirm normality and
> then perform parametric statistical tests on log transformed data and
> report back transformed values for mean and 95% confidence intervals
> (SE?).
In pharmacokinetics this is the most logical choice, in general.
Please note
that the logarithmic transformation is quite different from any other
transformation. It is not a trick, it is based on the concept that many
variables in biological systems are (at least close to) lognormally
distributed.
> 3. Report median and interquartile range and compare values by
> non parametric tests.
An excellent alternative if good nonparametric tests are available. The
statistical power of nonparametric tests may be slightly less than
parametric tests in the case that the distribution is chosen
correctly, but
may be higher in other cases.
Best regards,
Hans Proost
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
tel. 31-50 363 3292
fax 31-50 363 3247
Email: j.h.proost.-at-.rug.nl
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Just a reminder:
Two issues should be kept in mind when assuming or testing
distribution. 1. Testing normality is often a problem if the data
size is small, which is the case for most of our PK data. Small
sample size can aften pass the test using whatever methods. 2. It is
also difficult to distinguish the normality or lognormality for many
PK data in reality. People interested can run some test for this
either by literature data or their own data. I had some tests years
ago; the results often showed that either distribution was significant.
Also there are intrinsic problems associated with the distribution
assumption for PK parameters. CL, K, t1/2, AUC, V, etc, can be
converted with certain simple functions (x, or /). Therefore, the
assumption of the normality or lognormlity for one parameter will
result in a non-normal distribution of the others. Although the
reciprocal of log-normal still brings in log-normal, the sigma will
be distorted a lot. However, we often simultaneously assume one kind
of distribution, which of course violates the assumptions themselves.
How and what the magnitudes of effect that the violation will bring
in for modeling and statistical testing is case by case, and is higly
dependent on the data itself.
Huadong Tang
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Just a reminder:
Two issues should be kept in mind when assuming or testing
distribution. 1. Testing normality is often a problem if the data
size is small, which is the case for most of our PK data. Small
sample size can aften pass the test using whatever methods. 2. It is
also difficult to distinguish the normality or lognormality for many
PK data in reality. People interested can run some test for this
either by literature data or their own data. I had some tests years
ago; the results often showed that either distribution was significant.
Also there are intrinsic problems associated with the distribution
assumption for PK parameters. CL, K, t1/2, AUC, V, etc, can be
converted with certain simple functions (x, or /). Therefore, the
assumption of the normality or lognormlity for one parameter will
result in a non-normal distribution of the others. Although the
reciprocal of log-normal still brings in log-normal, the sigma will
be distorted a lot. However, we often simultaneously assume one kind
of distribution, which of course violates the assumptions themselves.
How and what the magnitudes of effect that the violation will bring
in for modeling and statistical testing is case by case, and is higly
dependent on the data itself.
Huadong Tang
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The following message was posted to: PharmPK
Dear Dr Tan,
I thought the underlying assumption is that the data come from a
population that is normally distributed; IMHO this is not the equal to
saying that the sample data are normally distributed.
Kind regards,
Frederik Pruijn
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Copyright 1995-2010 David W. A. Bourne (david@boomer.org)