Submitted for publication in
J. Radiol. Prot, July 2002

Response to “The potential for bias in Cohen’s ecological analysis of lung cancer and residential radon”

I
am writing in response to the critique by Lubin [1] of my test of the linear-no
threshold theory (hereafter LNT). That paper has been cited as providing an
explanation for the discrepancy between my observational findings and the
predictions of LNT, thus negating my test. Therefore, to stay within the length
restrictions on Letters-to-the-Editor, I limit my comments to addressing that
issue.

In
the simplified form adopted by Lubin, my procedure [2] starts with the lung
cancer mortality risk for an individual male, m’, expressed in the BEIR-IV
version [3] of LNT as

m_{s}’ = a_{s} (1 + b r’) smokers

m_{n}’ = a_{n} (1 + b r’) non-smokers

where r’ is his radon exposure, and a and b are
constants given in BEIR-IV.

Mathematically summing the experiences of all
males in a county, leads to

m
= [S a_{s} + (1 – S) a_{n}
] (1 + b r)

where m is the county lung cancer mortality
rate, r is the average radon exposure in the county, and S is the fraction of
adult males in the county that smoke cigarettes. Defining the important symbol
R as

R
= a_{s} / a_{n}

and applying minor corrections, this may be expressed as

M
= m / a_{n} [R S + (1 – S)]
= A + B r (1)

where M is defined by the equation on the left,
and A and B are constants, with A close to 1.0 and, according to BEIR-IV,

B
= +7 LNT
– theory (2a)

In units of % per 37 Bq/m^{3 } (% per pCi/L).

Data
on M and r are available for 1601 U.S. counties and I use them to test the LNT
theory by fitting them to Eqn. (1) to determine an observational value of B.
The result is

B
= -7.3 (+/-0.56) Observation (2b)

which is discrepant with the LNT-theory
prediction, (2a), by 26 standard deviations.

The
Scientific Method requires that theories be tested, where possible, with
observational data, and that any discrepancies between observation and
predictions of the theory must be given
at least a possible explanation that is not implausible; failing that, the
theory is invalid. In a series of papers, I have attempted to find such a
possible plausible explanation for the discrepancy between (2a) and (2b),
including evaluations of suggestions offered by others, but none of these
explanations has been successful.

Lubin’s
recent suggestion [1] is that the discrepancy can be explained by systematic
differences in average radon exposure to smokers, r_{s} and non-smokers, r_{n.} within each
county. I previously treated this general suggestion [4] by defining the
effective average radon exposure, r_{e} , as

r_{e} = [R S r_{s} + (1-S) r_{n} ]
/ [R S + (1 – S)]

where the two terms in the numerator are the
weighted radon exposures to smokers and non-smokers, and the denominator is the
sum of the weightings. This differs from the measured county average radon
exposure, r

r
= S r_{s} + (1 – S) r_{n}

If r_{s} and r_{n} are not
equal, r_{e} instead of r
should be used to fit the data with Eqn. (1), which would change the
observational value of B, and thus hopefully eliminate the discrepancy between
(2a) and (2b). Up to this point, these are the same as the procedures used by
Lubin [1].

I
defined [4]

x
= r_{s} / r_{n}

and treated as variable parameters the national
average value of x, the width of the distribution of x-values among U.S.
counties, and the correlation between x and r. I explored the effects of
varying these parameters within and well beyond their plausible ranges, but the
maximal effect was to change the observational value of B from B = -7.3 to B =
-4.3, still very discrepant with the LNT theory value, B = +7. I concluded that
possible systematic differences between radon exposures to smokers and
non-smokers could not explain the discrepancy between (2a) and (2b).

Lubin’s
paper [1] that I am responding to here demonstrates that the discrepancy
between (2a) and (2b) can be explained if both R and x vary in a systematic way
with r. In particular, this requires that R decreases in a systematic way with
increasing r to 65% of its value at low r, and that x varies with r in a very
complex way, some samples of which are in the following Table derived from Fig.
2 of Reference 1:

r 30 50 75 90 110 150 200

x 7 2.7 1.0 2.2 1.0 0.36 0.27

The behavior for r < 30, which includes
about 20% of our data, is even more complex, but I could not read the plot with
sufficient accuracy to list values here.

Lubin’s
paper [1] does not address the issue of plausibility. But it is extremely
important to recognize that “The Scientific Method” requires that an
explanation be found for the discrepancy between predictions of the theory and
observation that is __not implausible__. We therefore now consider the
plausibility of Lubin’s proposed explanation.

The
quantity R is the ratio of lung cancer risks for smokers and non-smokers,
irrespective of their exposure to radon. It is applicable to individuals.
According to Lubin’s proposal, the ratio of these risks is lower if they live
in a county with high average radon levels than if they live in a county with
low average radon levels, even if they have the same personal exposure to
radon, or even if they have no personal exposure to radon. Surely an
individual’s risk depends on his personal exposure to radon, not on the average
exposure to people in his county of residence. The variation of R with r
proposed in Reference 1 is therefore completely implausible.

Average radon exposure in a county, r, depends on geological factors, house characteristics, and ventilation practices (e.g. window opening). The only way I can imagine these being systematically different for smokers and non-smokers, thus affecting the value of x, is in ventilation practices. But it seems inconceivable that these can vary systematically and very sharply over a very wide range with average radon exposure in the county, especially since these average radon levels were not known to the people controlling the ventilation. The systematic variation of x with r illustrated in the above Table is surely completely implausible.

__Importance of plausibility__

Quite aside from its importance in applying The Scientific Method, plausibility is of utmost importance in all epidemiological studies. For example, the choice of confounding factors to be considered in a study is based completely on plausibility considerations; a plausible confounding factor that is not considered can easily invalidate any such study. It is therefore difficult to understand how such wild violations of plausibility could have escaped consideration in Reference 1.

References:

[1] Lubin, J H 2002 The potential for bias in Cohen’s ecological analysis of lung cancer and residential radon J. Radiol. Prot. 22:141-148

[2] Cohen, B L 1995 Test of the linear-no threshold theory of radiation carcinogenesis for inhaled radon decay products Health Phys. 68:157-174

[3] National Academy of Sciences Committee on Biological Effects of Ionizing Radiation 1988 Health risks of radon and other internally deposited alpha emitters (BEIR-IV) Washington, DC; National Academy Press

[4] Cohen, B L 1998 Response to Lubin’s proposed explanations of our discrepancy Health Phys. 75:18-22