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Re: LINEAR MODEL
My apologies, but the following has no purpose other than to present an
*accurate* record. Dr. Seiler's original public posting to RADSAFE and my
private response regarding "jousting over semantics" are reproduced in full
below.
My comment regarding "jousting over semantics" responded to Dr. Seiler's
correction of "some people [who] think that a linear relationship that does
not go through the origin is still linear."
As Dr. Van Pelt pointedly observed: If Dr. Seiler's definition of "linear"
were correct, we would not refer to a "LNT" model, but, rather, only to a "L"
model.
Glenn
GACarlson@aol.com
In a message dated 05/06/99 6:50:03 PM Central Daylight Time,
faseiler@nmia.com writes:
>
> 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
>
>
===============================
Subj: Re: Radiation hormesis
Date: 05/06/99 2:23:44 PM Central Daylight Time
From: faseiler@nmia.com (Fritz A. Seiler)
Sender: radsafe@romulus.ehs.uiuc.edu
Reply-to: radsafe@romulus.ehs.uiuc.edu
To: radsafe@romulus.ehs.uiuc.edu (Multiple recipients of list)
Dear Glenn,
What I really meant to say is that you do not have to worry
about inadvertently going beyond the hormetic region because
any nonlinear cause-effect relationship needs total accumulated
doses. Nothing else will do! Note also that any model different
from the linear model is by necessity nonlinear. I have to say this
because some people think that a linear relationship that does not
go through the origin is still linear. Not so, it is a 'truncated linear'
and therefore nonlinear in some places.
As for the references, some of the most important are:
1. Seiler, F.A., and J.L. Alvarez, "Definition of a Minimum
Significant Risk," Technol. J. Franklin Inst., 331A, 83-95,
1994.
2. Alvarez, J.L., and F.A. Seiler, "New Approaches to
Low-Dose Risk Modeling," Technol. J. Franklin Inst.,
333A, 33-51, 1996.
3. Seiler, F.A., and J.L. Alvarez, "Use of Nonlinear Dose-
Effect Models to Predict Consequences," Transactions
of the American Nuclear Society, 75, 412-413, 1996.
Joe and I have both spoken at many meetings about the dose
requirements for use with nonlinear dose-effect relationships. I
hope you can find them, otherwise we will have to try some
other method.
Best regards
Fritz
===========================
Subj: Re: Radiation hormesis
Date: 05/06/99 3:20:01 PM Central Daylight Time
From: GACarlson
To: faseiler@nmia.com
Thank you very much for the citations. I will look them up.
In a message dated 5/6/99 2:23:44 PM EST, faseiler@nmia.com writes:
<< What I really meant to say is that you do not have to worry about
inadvertently going beyond the hormetic region because any nonlinear
cause-effect relationship needs total accumulated doses. Nothing else will
do! >>
I realize that the rate of exposure can affect risk, but assume that the
relationship in question is risk versus accumulated dose. In that case, if I
begin with an accumulated dose in the hormetic region (i.e., negative risk)
and continue to add increments of dose, won't I eventually move from negative
risk to positive risk? Surely, I cannot increase accumulated dose
indefinitely and still have negative risk.
<< Note also that any model different from the linear model is by necessity
nonlinear. I have to say this because some people think that a linear
relationship that does not go through the origin is still linear. Not so, it
is a 'truncated linear'
and therefore nonlinear in some places. >>
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. Hormesis
would allow negative risk, but would not consider negative dose. In that
sense, the relationship is "truncated linear" (i.e., truncated at dose = 0).
Thanks again.
Glenn
GACarlson@aol.com
====================
Subj: Re: LINEAR MODEL
Date: 05/06/99 7:43:40 PM Central Daylight Time
From: vanpeltw@idt.net (Wes Van Pelt)
Sender: radsafe@romulus.ehs.uiuc.edu
Reply-to: radsafe@romulus.ehs.uiuc.edu
To: radsafe@romulus.ehs.uiuc.edu (Multiple recipients of list)
"Fritz A. Seiler" wrote:
> 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 and all,
I think I see your point. But, why do we always refer to the "Linear
Non-threshold Model" rather than just the "Liner" model. If what you say is
true, there could be no such thing as a "Linear Threshold" model. And we
should refer to the LNT model as just the L model.
Regards,
Wes
--
Wesley R. Van Pelt, Ph.D., CIH, CHP KF2LG
President, Van Pelt Associates
Radiation Safety and Environmental Radioactivity
mailto:vanpeltw@idt.net http://idt.net/~vanpeltw/
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