# [ RadSafe ] Re: AW: AW: AW: Log-log plot for excess breast cancer incidence rate

George Stanford gstanford at aya.yale.edu
Sat Jul 23 11:26:53 CDT 2005

```Rainer:

We might or might not be converging.  I intersperse some comments
below

At 06:38 AM 7/23/2005, Rainer.Facius at dlr.de wrote:
>George:
>
>Thank you for challenging again my views. After dwelling too long on
>technicalities we finally have hit substance.
>
>Yet, first once more some minor technicalities:
>
>  The legend 'polynomial' is automatically - and utterly appropriately -
> generated by my ORIGIN software.
>Y = const is a polynomial of order zero, also a LNT line with slope zero.
>Y = A + B*X is a polynomial of order one, a general LNT through (0,A).

Point well taken.  What I meant, of course, was polynomial of
order greater than one.

>You do constrain the general LNT by imposing the independent requirement
>that B>0; it would be your obligation to rationalize/defend this extra
>precondition. That this is tacitly assumed in radiation protection does
>not qualify as rationale.

I am not the one constraining LNT, which is the linear extension
to low doses of known effects of doses high enough to produce an observable
and measurable cancer rate.  The "LNT line" is, by definition, zero at the
left end and greater than zero at the other.  That gives it a positive
slope.  How can that be "an extra precondition"?  It's built into the
definition.  If there is no data from doses high enough to induce cancer,
it is not possible to generate a meaningful LNT line.  If B is negative,
the line might be straight (linear), but it is not -- cannot be -- LNT.  To
repeat, "Linear" and "LNT" are not synonyms, and cannot be treated as
synonymous while still communicating clearly.

>Educated guesswork/intuition/visual inspection, all are entirely
>admissibly techniques to determine fit parameters.

Yes and no.  You aren't allowed to choose arbitrarily which data
points to accept and which ones to ignore.  Specifically, your background
estimate must be consistent with the (extrapolated) mean of ALL the
low-dose data.  You must not use an outlier as the basis.

>No matter how I 'guesstimate' parameter values, only the comparison
>afterwards of associated likelihoods/chi-squares etc. allows me to make
>rational choices among them (BTW there may be instances where I would like
>to know a maximum chi-squares solution). The maximum likelihood technique
>is just a convenient formal technical shortcut to such an optimum choice.

I submit that the use of formal statistical procedures for curve
fitting means that you are NOT "guesstimating" parameter values.  The
purpose of such procedures is to determine the parameter values that best
fit the data.  No guesswork is involved at all.  When you do guesstimate to
shortcut the formal procedures, what you are doing is trying to predict the
result that the formal procedures would produce.  That is certainly a
legitimate approximation -- but your best guess must be an unbiased
approximation of what the formal fitting procedure would produce.  That's
the only leeway you have.

>Yet, as is often the case in empirical science in general, in epidemiology
>usually, and patently in this case, the likelihoods for different
>estimates may be probabilistically indistinguishable. Then pragmatics may
>legitimately come into play. To what end do I need the information carried
>by the parameters? By which most economical means do I want to implement
>them? And here the real methodological difference between my and your
>approach towards these data surfaces.

Can't say that I fully follow that.  It sounds as though you
advocate choosing your parameter values to give you the result that you
want -- but I don't believe that you would do that.

>Barring accidental overexposures, the exposures whose cancer risk I want
>to assess in radiation protection only rarely exceed say 500 mSv, for a
>whole professional career! Barring reliable theoretical knowledge, I am
>stuck with empirical information only. Given empirical information in the
>exposure range I am concerned with, this empirical information is the most
>reliable assessment I can make at all. Barring empirical information in
>the wanted exposure range, I may look to information in adjacent data
>intervals. Then I must be prepared for the fact that extrapolation into my
>wanted range can lead me off the mark by any amount. If I have empirical
>information in the wanted data range and in adjacent intervals AND IF they
>are concordant, I can consolidate my assessment of the wanted range by
>uniting them. That's the way how science cerates, promotes, and utilizes
>objective knowledge from data - and in the final analysis from data only.

This seems to be off-topic.  I would be the last person to advise
you to base your professional decisions on LNT.  The focus of my remarks
has been how to accurately compare the LNT model with whatever empirical
data is available.

>Applying this to the Preston data, my evaluation is:
>
>Do we have theoretical knowledge? Emphatically NO!
>
>Do we have empirical information? Yes, although of limited quality!
>
>Does the information pertain to the wanted exposure range? Yes!
>
>Is there information in adjacent intervals? Yes!
>
>Does the information match? No, I must not unite them! (Laboratory
>information on relevant mechanisms being accumulated in the last decade(s)
>increasingly shows that they definitely cannot match.)

I assume that "match" refers to the extent to which the LNT model
fails to match the data.  I am no fan of LNT.  However, your rendition of
the data from Preston et al  is indeed consistent with LNT.  LNT is not the
best fit, certainly, but it falls largely within the rather broad
experimental uncertainty limits, as you show them.

>Hence, the most objective assessment I can accomplish is by analysing
>those data which cover the exposure range I have to assess - and BTW were
>obtained under the appropriate exposure conditions as well! Departing from
>this procedure by, e.g., using data from adjacent but discordant intervals
>or obtained under different conditions cannot but DETERIORATE further the
>already limited quality of my appraisal regarding the wanted exposure range.

decisions, and I have no argument with what you say.

>Your assertion that I have to select exposure intervals where a
>positive(!) "excess is clearly evident" is simply coercing the postulated
>end result that there must be a positive excess into the analysis thereby
>enforcing the preconceived postulate to reproduce itself, NO MATTER what
>the data show (which in this case do show a negative excess). . . .

I don't follow this.  What I am saying is that, unless there is
data from doses high enough to cause an observable cancer rate, there is no
basis for generating an LNT fit.   I am most emphatically NOT saying that
you should base your low-dose-range professional decisions on such
high-dose data.

>. . . The naïve rationale behind apparently is: x g/kg of Digitalis
>purpurea drug is 100% lethal, so x*0.6 g/kg is 60% lethal, the latter
>being actually the most beneficial therapeutic dose. I cannot help but
>express my utter disability to grasp the naïveté of applying such 'linear
>thinking' to the realm of biological systems with their still unfathomable
>complexity as revealed by the numerous highly non-linear regulatory

I agree fully.  You are arguing here against LNT, not against what
I have been saying.

>A most striking point in case is the line LNTsub(EAR Preston pooled) which
>you justly find mystifying.
>
>It is drawn with the slope of (9.5,13.4,17) 95% CI per 10^4 PY per Gy as
>given in the last row "Simple Pooled Model" of table 10 "Excess Absolute
>Rate Estimates for Cohorts and the Simple Pooled Model" by Preston 2002.
>As offset/background I choose the incidence rate in the first interval. . . .

Here you have committed a no-no.  You have used a y-intercept of
about 62 for the LNT line, on the basis of one data point, whereas both the
linear and loglog plots of the data show clearly that a statistical fitting
process would put the intercept somewhere near 51.

Because this graph does not show the higher-dose range, one has no
way to assess the validity of the assigned slope.  You say you used
Preston's pooled-data slope (presumably because he gives no slope for the
HMG data you are plotting) -- but why would you do that?  As you point out
below, the pooled data are irrelevant to this particular plot.  On the
other hand, there are higher-dose HMG data, which you have plotted in other
graphs.  If you are going to do an honest LNT fit to the HMG data, you have
no choice but to base the slope of the LNT line on the available high-dose
HMG data, where there does seem to be a definite increase in cancer
rate.  That line in your plot has an erroneous intercept and a meaningless
slope.

>. . .  It is a wonderful exemplification of your recipe "The LNT line MUST
>be the best one-parameter (slope) fit to the high-dose excess" with the
>added 'benefit' of pooling with irrelevant data, i.e. high dose rate
>exposures like A-bomb survivors. That is the evidence which Preston's
>comment addresses which I reproduce in the graphs. It is also the basis
>for BEIR VII-2's assessment of breast cancer risk, as the copy from their
>report as transmitted to you with John Jacobus's recent comment testifies.

My "recipe" does not and did not prescribe the incorporation of
irrelevant data.  The only point I have been addressing is the comparison
of LNT with data.  Here you are criticizing Preston and BEIR VII, not
anything that I have said, or even implied.  I think you are perhaps
correct, but that's another topic.

>You might wish to ponder from this perspective the display of the Cardis
>1995 data I recently submitted to John Jacobus.

Unfortunately, any attachments you sent to John did not come along
with the Radsafe transmission.  I note that the Radsafe rules permit PDF
attachments only.

>Thank you for stimulating me once more to sharpen up my reasoning.

You're welcome.

>Truly, with kind regards, Rainer

And the same from here.  George

George S. Stanford
Reactor physicist
Retired from Argonne National Laboratory

________________________________

Von: George Stanford [mailto:gstanford at aya.yale.edu]
Gesendet: Sa 23.07.2005 07:46
An: Facius, Rainer
jjcohen at prodigy.net; jmarshall.reber at comcast.net; frantaj at aecl.ca;
jaro-10kbq at sympatico.ca; Jim_Hardeman at dnr.state.ga.us; hflong at pacbell.net;
maurysis at ev1.net; crispy_bird at yahoo.com; merklejg at ornl.gov
Betreff: Re: AW: AW: Log-log plot for excess breast cancer incidence rate

Rainer:

Thanks for your further explanations.  I

The observed cancer rate consists of two
components: (1) a background rate; (2) an "excess"
rate (positive or negative) due to radiation.  The
LNT hypothesis is that excess cancers can be
predicted by extrapolating linearly from
moderately high doses back to the origin (linear
plot).  In fitting the LNT model to observed
cancer-rate data (CR), then, there are two
parameters (as you say), and only two.  One of
them is the y-value (bkg) of a horizontal line
representing the background.

The other parameter is the slope of the LNT
representation of the excess, where "excess" is
defined as (CR - bkg).  Call it CRx.  The slope of
that straight line is determined by two
requirements: (a) the line must pass through the
origin (zero excess at zero dose), and (b) it must
pass through the values of CRx at dose rates high
enough that the excess is clearly evident.

The fitting process is very simple, and can
usefully be done by eyeball, without so much as
residuals.  Please note that the term "polynomial
fit" immediately rules out the possibility of
fitting to the LNT model, and therefore cannot be
used to refute that model.

The value of the parameter bkg MUST be the
the y-intercept of the horizontal line that best
fits the observed low-dose rates.  It would not be
representative to use any other guess, because the
resulting slope of the LNT line would be wrong.  I
respectfully suggest that you do not have freedom
to make some other choice.  You would be leaving
yourself open to the charge that you selected the
"background" arbitrarily to suit your purposes.

Also, you seem to using "LNT" as though it
were a synonym for "linear," but it's not.  It's
the term used to refer to the particular linear
model for radiation damage defined above.  The LNT
line MUST be the best one-parameter (slope) fit to
the high-dose excess.  Any other usage of "LNT"
will not be understood, and will only confuse the
reader. Thus, on the linear and loglog plots you
just sent, none of the curves labeled "LNT"
qualifies for that designation.  The rose-colored
curve labeled "LNT EAR Preston pooled" is a
particular mystery, since it does not fit any of
the data at all, although it does come fairly
close at very low dose rates.

Your LQ fit, on the other hand, looks
excellent, with an appropriate y-intercept and
good match to the data.  It's clearly better than
a properly done LNT fit -- although, as shown in
the picture that I sent you earlier, had you used
the comparable procedure for your "LNT" fit, you
would find that the curve falls within the error
bands (except, perhaps, for the low point at 750
mGy) -- as you, too showed in one of your graphs:
To repeat from my preceding transmission, "If I
(PrestonHemExcess(1-1000)loglog.gif),
you have corrected [the background] problem, and
the result is the same as mine -- the LNT fit is
within the error limits.  That's something we have
to live with -- accept it, and move on."

I hope this helps.

Best wishes,

George

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