LINEAR MODEL

["Fritz A. Seiler" <faseiler@nmia.com>]

In a private e-mail to me, GACarlson@aol.com wrote:

> Perhaps, we are just jousting over semantics, but I teach my students
that x+ y
> = 2 does not pass through the origin, but is still linear.

I think this comment and its resolution may be of a more
general interest, because I hear this argument altogether
too often. So let us see:

Mathematically,  x + y = 2  is the equation of a straight line.
So you are teaching your students right, Glenn.  Take note,
however,  that you are talking about the purely mathematical
property of an equation.
The linear model of radiation carcinogenesis, on the other
hand, is NOT given by any old straight line! It  is given by a
straight line through the origin. Thus the linear model is given
by  y - ax = 0.  Then, and only then, will the often cited model
property be true that twice the dose leads to twice the  risk.
Thus a straight line is one (mathematical) thing, the linear model
of radiation carcinogenesis is quite another (radiobiological)
thing.

Best regards

Fritz

*************************

Fritz A. Seiler, Ph.D.
Principal
Sigma Five Associates
P.O. Box 14006
Albuquerque, NM 87191-4006
Tel.    505-323-7848
Fax.    505-293-3911
e-mail: faseiler@nmia.com

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