- On 27 Feb 2006 at 11:23:16, Dr Fatemeh Akhlaghi (fatemeh.aaa.uri.edu) sent the message

Back to the Top

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 - On 27 Feb 2006 at 13:06:36, Prah.James.-a-.epamail.epa.gov sent the message

Back to the Top

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 - On 1 Mar 2006 at 22:10:47, =?ISO-8859-1?Q?Helmut_Sch=FCtz?= (helmut.schuetz.at.bebac.at) sent the message

Back to the Top

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 - On 2 Mar 2006 at 11:05:18, Nick Holford (n.holford.aaa.auckland.ac.nz) sent the message

Back to the Top

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/ - On 6 Mar 2006 at 10:00:58, "Hans Proost" (j.h.proost.-a-.rug.nl) sent the message

Back to the Top

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 - On 31 Mar 2006 at 16:20:31, "Huadong Tang" (TangH3.-at-.wyeth.com) sent the message

Back to the Top

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 - On 31 Mar 2006 at 16:20:31, "Huadong Tang" (TangH3.-at-.wyeth.com) sent the message

Back to the Top

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 - On 3 Apr 2006 at 09:57:35, "Frederik B. Pruijn" (f.pruijn.aaa.auckland.ac.nz) sent the message

Back to the Top

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

Want to post a follow-up message on this topic? If this link does not work with your browser send a follow-up message to PharmPK@boomer.org with "Normal distribution of PK data" as the subject

PharmPK Discussion List Archive Index page

Copyright 1995-2010 David W. A. Bourne (david@boomer.org)