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The following message was posted to: PharmPK
Hi,
Can anyone help me to interpret the results for these normality tests?
I know, based on histograms that the distribution is not normal.
Thank you
Vlase Laurian
Dept. Pharm. Technol. & Biopharmaceutics
Faculty of Pharmacy
Cluj-Napoca
Romania
Tests of Normality
Kolmogorov-Smirnov Shapiro-Wilk
TRATAMEN Statistic df Sig. Statistic df Sig.
R_AUC 1.00 .383 18 .000 .601 18 .010
2.00 .316 18 .000 .650 18 .010
R_CMAX 1.00 .231 18 .012 .775 18 .010
2.00 .344 18 .000 .695 18 .010
** This is an upper bound of the true significance.
a Lilliefors Significance Correction
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The following message was posted to: PharmPK
Vlase Laurian wrote:
> Hi,
> Can anyone help me to interpret the results for these normality tests?
> I know, based on histograms that the distribution is not normal.
> Thank you
> Vlase Laurian
>
[...]
> Tests of Normality
> Kolmogorov-Smirnov Shapiro-Wilk
> TRATAMEN Statistic df Sig. Statistic df Sig.
>
> R_AUC 1.00 .383 18 .000 .601 18 .010
> 2.00 .316 18 .000 .650 18 .010
> R_CMAX 1.00 .231 18 .012 .775 18 .010
> 2.00 .344 18 .000 .695 18 .010
>
> ** This is an upper bound of the true significance.
> a Lilliefors Significance Correction
>
Dear Vlase,
the Kolmogorov-Smirnov test is poor in terms of statistical power with
sample sizes generally applied in BE studies. The Shapiro-Wilk test is
the better choice. From the table you gave I guess that you applied the
tests separatelly on test/reference treatments (1/2 ?).
In my opinion this is not correct. One of the main assumptions of ANOVA
is the normality (0,sigma) of errors, which are approximated in the
sample by studentized residuals.
Imagine the simple (and artificial) case of test and reference
treatments following both (the same) triangular distribution (which
clearly is not normal). If you take differences (or use the ratio...)
you will end up with normally distributed residuals. And this is what
we assumed in the model, so the ANOVA is valid.
If you additionally test both treatments for normality this is fine,
but what you have to test are the residuals...
I would suggest the following procedure:
o) lay down a statistical protocol describing what you plan to do (and
adhere to that protocol!)
o) run the ANOVA and calculate studentized intra- and (not so
important) inter-subject residuals
o) test these residuals for normality (according to the protocol; only
one test, otherwise you will run into problems with multiplicity and
contradictory results) and outliers (to be excluded only if you can
justify errors in the clinical and/or analytical conduct of the study)
o) if non-normality of residuals is detected, use a nonparametric
method (e.g., Wilcoxon-Mann-Whitney) instead of ANOVA
Good luck!
Helmut
--
Helmut Schütz Biokinet GmbH / Dept Biostatistics
Neubaugasse 36/11 Nattergasse 4
A-1070 Vienna/Austria A-1170 Vienna/Austria
tel/fax +43 1 9713935 tel +43 1 4856969 62
no cell phone ;-) fax +43 1 4856969 90
http://www.goldmark.org/netrants/no-word/attach.html
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The following message was posted to: PharmPK
Helmut's advise is good. A transformation of the data might be worth
considering to help normalise the error, before resorting to a
nonparametric
method,
Kim
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Dear Vlase,
In your recent mail you wrote:
"Can anyone help me to interpret the results for these normality tests?
I know, based on histograms that the distribution is not normal."
Tests of Normality
Kolmogorov-Smirnov
Shapiro-Wilk
TRATAMEN Statistic df Sig. Statistic df Sig.
R_AUC 1.00 .383 18 .000 .601 18 .010
2.00 .316 18 .000 .650 18 .010
R_CMAX 1.00 .231 18 .012 .775 18 .010
2.00 .344 18 .000 .695 18 .010
You applied 2 different statistical methods to test for normality. The
interpretation of the results of the 2 methods is evident. Both methods
indicate with high confidence that the data of both treatments are not
normally distributed. This is what you already knew based on your
visual inspection of the data.
However, more important than applying a statistical test is a very
clear explanation of the data under consideration as well as precise
statement of the goal(s). It would be helpful to get this information.
Additionally, the distribution of PK parameters like AUC and Cmax has
been addressed rather often in the literature and I feel that there's a
consensus that they are log-normally distributed. In this case you
would just take logarithms of the individual data before they enter any
statistical testing, without any tests regarding the distributional
form. Sequential statistical testing is a problematic task and should
be discouraged if possible.
Best regards,
Martin
Martin M. Schumacher, Ph.D.
Principal Scientist
Novartis Pharma AG
BioMarker Development (BMD)
WKL-136.1.19
CH-4002 Basel
Switzerland
Tel. +41 - 61 696 1030 (direct)
Fax +41 - 61 696 6212
Email martin.schumacher.aaa.pharma.novartis.com
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The following message was posted to: PharmPK
Dear Kim, dear Martin,
I think I have to be more precise. I agree that parameters like AUC and
Cmax are most likely log-normally distributed, so a transformation
should be the starting point.
But I disagree with Martin's "... just take logarithms of the
individual data before they enter any statistical testing, without any
tests regarding the distributional form." I know that this procedure
(not testing for normality after transformation) is stated in the
recent FDA guideline, but it's still very bad statistical practice. We
have to test our assumptions (in ANOVA additivity of effects, normal
distribution of errors, independence of subjects, etc....) before we
apply a statistical method, and if some of them are violated, we have
to take measures and not only close our eyes and continue...
If we decide to go for a nonparametric method, this is not sequential
testing, since we have not calculated the ANOVA confidence limits, and
the alpha-level is still intact.
Best regards,
Helmut
Helmut Schütz Biokinet GmbH / Dept Biostatistics
Neubaugasse 36/11 Nattergasse 4
A-1070 Vienna/Austria A-1170 Vienna/Austria
tel/fax +43 1 9713935 tel +43 1 4856969 62
no cell phone ;-) fax +43 1 4856969 90
http://www.goldmark.org/netrants/no-word/attach.html
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This suggestion is not logical, since the fundamental
assumptions of nonparametric statistics indicate that data
distribution is not part of the underlying principles of the
test(s). Normalization of data sets only applies to the use of
parametric tests to try and achieve something resembling a
Gaussian distribution. Bad data are not salvaged by statistical
contortions. If you keep transforming data by various
mathematical contortions, eventually you will find a way to
get a statistically significant result, but the process is invalid
because of the repeated analysis of the data without
partitioning the finding of a difference by chance.
The best suggestion is to redesign the experiment and
to power it adequately to be able to detect a difference by a
statistical approach that is prospective and scientifically
justifiable.
Dan Sitar, University of Manitoba
Daniel S. Sitar, PhD
Professor and Head
Department of Pharmacology and Therapeutics
sitar.-a-.ms.UManitoba.ca
Tel: 204-789-3532 FAX: 204-789-3932
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The following message was posted to: PharmPK
Having suggested the possibility of a transformation I'd like to
strongly
qualify it. When you visualise the data (eg plot it) you should make
sure
that you do it in units which makes most sense to you / most sense
biologically. If you do not then your ability to judge quality of fit
etc
are severely compromised, and poor conclusions can result. This often
means
that you have to untransform your data in order to visualise it.
People became accustomed to all kinds of transformations as a matter of
course in the old days, often so that a simple linear regression can
yield
key parameter estimates (pre computers). Often this was done
irrespective
of error distribution. There is no excuse for this nowadays as the
parameters can be fitted directly without transformation, but in many
applications the habit dies hard.
The good news is that ANOVA is remakably robust to most breaches of the
key
assumptions listed by Helmut. But as Helmut indicates, historical
knowledge
of the likely distributional form of a variable is valuable. In fact
it may
be at least as good a basis for deciding on a transformation as a
statistical test of Normality, especially if sample numbers are low,
Regards,
Kim
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Copyright 1995-2010 David W. A. Bourne (david@boomer.org)