[ RadSafe ] Re: AW: Log-log plot for excess breast cancer incidence rate
John Jacobus
crispy_bird at yahoo.com
Thu Jul 21 16:17:24 CDT 2005
George,
The BEIR VII says that leukemia follows the
linear-quadratic model. It is the solid tumors that
follow a linear fit.
--- George Stanford <gstanford at aya.yale.edu> wrote:
---------------------------------
Rainer:
Thanks forthe additional information, and the
two new graphs.
I'm afraidI have to take issue with you on one
point.
Whenfitting a curve to data, one has to use
the observed valuesconsistently. That is what I did
with my fits. The observedresidual background on the
plot that I used is not zero. It isapproximately 25.
It's certainly legitimate to subtract aconstant from
the background, which is what you did. Subtractingthe
entire observed background leads to negative data
points -- noproblem on a linear graph, but awkward in
a logarithmic representation(as you have pointed out).
If youwere to repeat my process with the full
background, the result would bethe same. The LNT
model** fits the hemangioma data within thereported
experimental error limits.
In yourearlier graph, you selected the extreme
(lowest) data point from thelow-dose region to use as
the observed background. That led to theweird result
that you depicted an excess of low-dose cancers --
exactlythe opposite of what we are claiming. If I
understand your newloglog plot
(PrestonHemExcess(1-1000)loglog.gif), you
havecorrected that problem, and the result is the same
as mine -- the LNT fitis within the error limits.
That's something we have to live with-- accept it, and
move on.
Theinterpretation of the other graph
(PrestonHemLowFits.gif) escapesme, since it has lines
with negative slopes labeled "LNT" --clearly not the
conventional LNT -- but, as instructed, I will
refrainfrom asking for an explanation. Maybe it will
dawn on mesometime.
Best,
George
** I can't think of a better term --"model" does
notimply that it's a good model. The quadratic model
isbetter.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
At 08:12 AM 7/20/2005, Rainer.Facius at dlr.de wrote:
George:
Thank you for providing a near perfect example for
what I intended toinstigate with my original note to
E.M. Goldin.
In contrast to what a few others have insinuated, I
did and do notwant anybody to believe in anything,
least of all in my statements butalso neither in fit
parameters nor even in peer review and committees.
Iintended to make them look at the data and generate
their ownconclusions, as you do. The only arbiter of
truth - within the limitedrealm of science – is data.
(BTW, in my view the prime function of peerreview is
to make sure that the provenance of the data and
theirdependability are spelled out as extensively as
necessary and asprecisely as possible, something which
appears to beretreating.)
Yet, I am afraid you have fallen in one of the traps
which I tried tocaution against previously, in
particular with respect to log-logrepresentations.
In the graph to which you added your fit lines and
which you did attach,one reasonable/feasible estimate
of the background HAD ALREADY beensubtracted (note the
ordinate label), namely the incidence rate in
theminimum at [500,1000] mSv so that your term “bkg”
would have to be zeroinstead of 25. In this graph the
straight line D^1 is already a (visual)LNT estimate of
the EXCESS (above the minimum). If you wish to avoid
theextreme values, either minimum or maximum, another
reasonable/feasibleestimate would be the average
between 0 and 1000 mSv, which
is[44.9,51.7,59.3]-95%CI. I attach yet another graph
with this averagealready subtracted as background
(watch the ordinate label). Thereforeagain, the
straight lines are already visual fits for the
respectiveexcess.
By now you have ‘talked’ me into doing what I still
consider a pointlesseffort given the reduced published
data – to perform some formal fits tothe data in the
low exposure range. For that purpose I had to convert
theasymmetric 95% confidence interval into symmetric
standard errors bydividing the confidence range by 4.
For the x-values I took the middle ofthe respective
interval for which the averages were specified. I
fitted alinear quadratic and a linear model to the
data up to 2500 mSv and asecond linear model to the
range relevant for radiation protection, i.e.,below
1000 mSv. I include a copy of the fit statistics
provided by theORIGIN PRO 7.5 program. You may use
them as you like and can make senseof them but please
don't ask for explanations.
I attach the corresponding graph too. It’s up to you
to judge to whatextent this might be considered a case
for LNT with a slope>0.
Whatever the bottom line might be, thank you for your
motivatingcontributions to approach it.
Kind regards, Rainer
Here come the STATISTICS belonging to the fits:
[20.07.2005 12:17 "/DATA/Graph1" (2453571)]
Polynomial Regression for HMSwP_G:
Y = A + B1*X + B2*X^2
Weight given by HMSwP_Gerr error bars.
Parameter Value Error t-Value Prob>|t|
-----------------------------------------------------
A 54.3644 4.22643 12.86297<0.0001
B1 -0.04349 0.03298 -1.31855 0.22882
B2 2.91727E-5 2.57982E-5 1.1308 0.29539
-----------------------------------------------------
R-Square(COD) Adj. R-Square Root-MSE(SD) N
-----------------------------------------------------
0.19915 -0.02966 1.54799 10
-----------------------------------------------------
Parameter LCI UCI
-----------------------------------------------------
A 44.3705 64.35831
B1 -0.12148 0.0345
B2 -3.18303E-5 9.01756E-5
-----------------------------------------------------
ANOVA Table:
-----------------------------------------------------
Degrees of Sum of Mean
Item Freedom Squares Square F Statistic
-----------------------------------------------------
Model 2 4.17129 2.08565 0.87037
Error 7 16.77389 2.39627
Total 9 20.94518
-----------------------------------------------------
Prob>F
-----------------------------------------------------
0.45965
-----------------------------------------------------
[20.07.2005 12:36 "/DATA/Graph1" (2453571)]
Polynomial Regression for HMSwP_G:
Y = A + B1 * X
Weight given by HMSwP_Gerr error bars.
Parameter Value Error t-Value Prob>|t|
-----------------------------------------------------
A 52.1004 3.78641 13.75985<0.0001
B1 -0.01086 0.01626 -0.66819 0.52282
-----------------------------------------------------
R-Square(COD) Adj. R-Square Root-MSE(SD) N
-----------------------------------------------------
0.05286 -0.06553 1.57472 10
-----------------------------------------------------
Parameter LCI UCI
-----------------------------------------------------
A 43.36892 60.83188
B1 -0.04835 0.02663
-----------------------------------------------------
ANOVA Table:
-----------------------------------------------------
Degrees of Sum of Mean
Item Freedom Squares Square F Statistic
-----------------------------------------------------
Model 1 1.10715 1.10715 0.44647
Error 8 19.83803 2.47975
Total 9 20.94518
-----------------------------------------------------
Prob>F
-----------------------------------------------------
0.52282
-----------------------------------------------------
[20.07.2005 13:17 "/Graphs/GHMSwP" (2453571)]
Linear Regression for HMSwP_G:
Y = A + B * X
Weight given by HMSwP_Gerr error bars.
Parameter Value Error t-Value Prob>|t|
-----------------------------------------------------
A 53.64138 2.56982 20.87361 <0.0001
B -0.02791 0.0145 -1.92414 0.33451
-----------------------------------------------------
R R-Square(COD) Adj. R-Square Root-MSE(SD) N
-----------------------------------------------------
-0.43086 0.18564 0.02277 1.80228 7
-----------------------------------------------------
Parameter LCI UCI
-----------------------------------------------------
A 47.03546 60.2473
B -0.06519 0.00938
-----------------------------------------------------
ANOVA Table:
-----------------------------------------------------
Degrees of Sum of Mean
Item Freedom Squares Square F Statistic
-----------------------------------------------------
Model 1 3.70232 3.70232 1.1398
Error 5 16.24109 3.24822
Total 6 19.94341
-----------------------------------------------------
Prob>F
-----------------------------------------------------
0.33451
-----------------------------------------------------
Dr. Rainer Facius
German Aerospace Center
Institute of Aerospace Medicine
Linder Hoehe
51147 Koeln
GERMANY
Voice: +49 2203 601 3147 or 3150
FAX: +49 2203 61970
---------------------------------
Von: George Stanford[mailto:gstanford at aya.yale.edu]
Gesendet: Mittwoch, 20. Juli 2005 08:58
An: Facius, Rainer
Cc: 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: Log-log plot for excess breast cancer
incidencerate
Rainer:
Thanks foryour further clarifications. You
have done a valuable service inpointing out a useful
way to examine this kind of data.
Theattached PDF file (also below) is your
"loglog excess" plot ofhemangiomas, with the functions
(bkg + LNT) and (bkg+LNT^2) superimposed, using as
background the mean extrapolatedvalue of your residual
background (25 on the ordinate scale).
Twofeatures of this representation have
surprised me. First, the LNTcurve remains entirely
within the error bands. This is not to saythat` there
is no threshold -- only that the statistics are
insufficientto demonstrate it clearly. (In your
linear plot of the same data,you have used for the LNT
line a y-intercept that is higher than the
meanextrapolated value of the background, and also, I
think, has a steeperslope).
Second, Ihave to take back what I said about
the quadratic fit not beinggood: It is, in fact very
good (for the dose range covered, atleast).
The bottomline is this: the initial impression
given by the loglog plots isdeceptive -- under
examination, they do not clearly show that LNT iswrong
(this one doesn't, anyway). Neither, of course, do
they showthat LNT is correct -- the fact that the
quadratic fit is much better isan indication of
non-linearity, but the statistics are too poor to
ruleLNT out.
In yourlinear plots, your LNT lines are, of
course, really (bkg + LNT). All of your
representations show indications of thresholds, with
hints ofhormesis, but the demonstration is not nearly
as dramatic as I thought atfirst.
Thank youvery much for a stimulating
discussion.
Bestregards,
George
PrestonHemExcess(1-1000)loglog.gif
PrestonHemLowFits.gif
+++++++++++++++++++
"Every now and then a man's mind is stretched by a new idea and never shrinks back to its original proportion." -- Oliver Wendell Holmes, Jr.
-- John
John Jacobus, MS
Certified Health Physicist
e-mail: crispy_bird at yahoo.com
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