- On 19 Oct 2005 at 19:17:43, Stanley110.-a-.aol.com sent the message

Back to the Top

Recently there was considerable discussion of confirming linearity. I

suggested the Lack of Fit test that requires replicate measurements

at each level of the independent variable which I learned from the

discussion is not done in Pk work.

Since then I thought perhaps the following might be useful.

For a linear relationship, y = x^1.

For a near linear relationship, the empirical model, y = x^(1+-a),

can be fitted to the data.

The value of 'a' then represents the deviation from linearity.

Acceptable limits of 'a' might be defined based on the intended

application of the data.

Regards,

Stan Alekman - On 20 Oct 2005 at 14:02:29, "Frederik B. Pruijn" (f.pruijn.at.auckland.ac.nz) sent the message

Back to the Top

The following message was posted to: PharmPK

Dear Stan,

How do you propose to use this empirical model? I assume you would

test your data first to see whether a+/-95%CI (for p<0.05) is within

a pre-defined range (I have seen recommended somewhere a +/- 0.03,

but not clear to me what the convention would be/is). Then, if a +/-

95%CI is indeed within the said range, the data are assumed to be

linear. Would you then pre-set a=0 and re-fit according to y=ax+b? I

think you have omitted the intercept for clarity.

TIA

Frederik Pruijn

Frederik B. Pruijn PhD MSc (Senior Research Fellow)

Experimental Oncology Group

Auckland Cancer Society Research Centre

Faculty of Medical and Health Sciences

The University of Auckland

Private Bag 92019

Auckland

New Zealand

Phone: +64-9-3737 599 x86939 or x86090

Fax: +64-9-3737 571

E-mail: f.pruijn.aaa.auckland.ac.nz - On 20 Oct 2005 at 09:57:07, Peter.Wolna.-at-.merck.de sent the message

Back to the Top

The following message was posted to: PharmPK

Dear Stan,

several approaches to the check of linearity are presented in the

literature. The approach you proposed is known as the "power model".

Other

approaches are for example

y = ax^1 + bx^2 + cx^3 + .....

Deviations from linearity may be considered to be statistically

significant, if the coefficients b, c etc. are different from zero.

A good paper is

Gough K, Hutchinson M, Keene O, Byrom B, Ellis S, Lacey L, McKellar J.

Assessment of dose proportionality: Report from the Statisticians in the

Pharmaceutical Industry / Pharmacokinetics UK Joint Working Party.

Drug Inf J 1995; 29:1039-1048

Regards,

Peter Wolna - On 25 Oct 2005 at 22:57:58, Stanley110.aaa.aol.com sent the message

Back to the Top

Peter,

Thanks for the reference.

When I fit raw data, I always check whether higher orders improve the

model. If not, I stick with a linear model. Of course in my work I

make replicate measurements at each calibrator level so I rely on the

Lack of Fit test for any model I fit. That is the utility of this test.

I fit dissolution processes and others where many controlling factors

come into play. Some fitted models are rather involved expressions

but I never accept one that is not known in the literature for a

physical process I can review and understand. (I am not so arrogant

as to believe that I might observe an original, heretofore unobserved

model.)

The suggestion I made is somewhat different from the power model in

that I propose finding the exponent of x that fits the data best. It

is not likely to be exactly one for true linear relationships but

very close to one. I suggest that the difference between the observed

exponent and one may be considered a deviation from linearity. For

the intended use of the model, a tolerance, the difference from

observed and one must be earlier established. In this way, one may be

comfortable the linear model may be adequate for the specific

application. The tolerance may be established by simulation or simple

trial and error estimations.

This suggestion was addressed to those who posed the question, how

far from linearity may we be with data and safely use a linear

relationship. There were replies based on various statistical

parameters. This suggestion, based on a pre-established tolerance for

the intended application, may meet that need.

Regards,

Stan Alekman

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 "Linearity" as the subject

PharmPK Discussion List Archive Index page

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