[ RadSafe ] AW: AW: AW: Log-log plot for excess breast cancer incidence rate
Rainer.Facius at dlr.de
Rainer.Facius at dlr.de
Sat Jul 23 06:38:20 CDT 2005
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).
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.
Educated guesswork/intuition/visual inspection, all are entirely admissibly techniques to determine fit parameters.
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.
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.
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.
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.)
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.
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). 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 circuits already known.
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. 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.
You might wish to ponder from this perspective the display of the Cardis 1995 data I recently submitted to John Jacobus.
Thank you for stimulating me once more to sharpen up my reasoning.
Truly, with kind regards, Rainer
Von: George Stanford [mailto:gstanford at aya.yale.edu]
Gesendet: Sa 23.07.2005 07:46
An: Facius, Rainer
Cc: radsafe at radlab.nl; Zack.Clayton at epa.state.oh.us; jimm at WPI.EDU; 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
Thanks for your further explanations. I
really do appreciate your patience.
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
thinking about least-squares minimization of
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
understand your new loglog plot
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.
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