Chapter 20.2 in “Standard Handbook of Environmental Science,
Health, and Technology” J.H. Lehr (Editor), McGraw-Hill (New York); 2000

TEST OF THE VALIDITY OF THE LINEAR-NO THRESHOLD THEORY OF
RADIATION CARCINOGENESIS WITH A SURVEY OF RADON LEVELS IN U.S. HOMES

Bernard L. COHEN

University of Pittsburgh, Pittsburgh, PA 15260, USA

__Introduction__

__ __All estimates of the cancer risk from low level radiation are
based on the linear-no threshold theory (LNT) which is based solely on largely
discredited concepts of radiation carcinogenesis, with no experimental
verification in the low dose region of the most important applications.. These
risk estimates are now leading to the expenditure of tens of billions of
dollars to protect against dangers whose existence is highly questionable. It
is therefore of utmost importance to test the validity of this theory.

A definitive
answer to the validity of LNT in the low dose region must be based on human
data, but to obtain statistically indisputable data requires much larger
numbers of subjects than can be obtained from occupational, accidental, or
medical exposures. The obvious source
is natural radiation. If one attempts
to use natural gamma radiation, which varies somewhat with geography, one is
faced with the problem that LNT predicts that only a few percent of cancers are
due to natural radiation; whereas there are unexplained differences of tens of
percent for different geographic areas.
For example, the percentage of all deaths that are from cancer varies in
U.S. from 22% in New England to 17% in the Rocky Mountain States (where
radiation levels are highest). Another
problem is that gamma ray backgrounds vary principally with geographic regions,
and there are also many potential confounding factors that may vary with
geography. Nevertheless, there have
been attempts to study effects of gamma ray background on cancer rates, and in
general either no effect or an inverse relationship has been found. For example, no excess cancer has been found
in the high radiation areas of India or Brazil. But all such effects can easily be explained by potential
confounding factors.

A much more
favorable situation is available for radon in homes. According to LNT, it is responsible for at least 10% of all lung
cancers, and a known confounder, cigarette smoking, is responsible for nearly
all of the rest. Another advantage is
that levels of radon in homes vary much more widely than natural gamma
radiation.

There have been
numerous case-control studies of the relationship between radon in homes and
lung cancer but the results from different studies have been inconsistent and
this work has given no statistically significant information on the validity of
LNT in the low dose region which we define here as below 5 pCi/L which
corresponds to 20-50 cSv (whole body equivalent dose) over a lifetime. A
different approach, specifically designed for testing LNT, was carried out by
the present author and is described in the following sections.

__Original 1995 paper__

My group at
University of Pittsburgh developed an elaborate study designed specifically to
test LNT (1). We briefly review it here. We compiled hundreds of thousands of radon measurements from
several sources to give the average radon level, r, in homes for 1729 U.S.
counties, well over half of all U.S. counties and comprising about 90% of the
total U.S. population. Plots of
age-adjusted lung cancer mortality rates, m, vs these r are shown in Fig. 1
where, rather than showing individual points for each county, we have grouped
them into intervals of r (shown on the base-line along with the number of
counties in each group) and we plot the mean value of m for each group, its
standard deviation indicated by the error bars, and the first and third quartiles
of the distribution. Note that when
there is a large number of counties in an interval, the standard deviation of
the mean is quite small. We see, in Fig. 1a,c, a clear tendency for m to __de__crease
with increasing r, in sharp contrast to the __in__crease expected from the
supposition that radon can cause lung cancer, shown by the line labelled
“Theory”.

One obvious
problem is migration: people do not spend their whole lives and receive all of
their radon exposure in their county of residence at time of death where their
cause of death is recorded. However, it
is easy to correct the theoretical prediction for this, and the “Theory” lines
in Fig. 1 have been so corrected. As
part of this correction, data for Florida, California, and Arizona, where many
people move after retirement,
have been deleted, reducing the number of counties to 1601. (This deletion does not affect the results.)

A more serious
problem is that this is an “ecological study”, relating the average risk of
groups of people (county populations) to their average exposure dose. Since
most dose-response relationships have a “threshold” below which there is little
or no risk, the disease rate depends largely on the fraction of the population
that is exposed above this threshold, which is not necessarily closely related
to the __average__ dose which may be far below the threshold. Thus, in
general, the average dose does __not__ determine the average risk, and to
assume otherwise is what epidemiologists call “the ecological fallacy”.
However, it is easily shown that the ecological fallacy does not apply in
testing a linear-no threshold theory (LNT). This is familiar from the well
known fact that, according to LNT,
population dose in person-rem determines the number of deaths;
person-rem divided by the population gives the average dose, and number of
deaths divided by the population gives the mortality rate which is the average
risk. These are the quantities plotted in Fig. 1. Other problems with ecological studies have been discussed in the
epidemiology literature, but these have also been investigated and found not to
be applicable to our study. The most important of these problems are discussed
below.

Epidemiologists
normally study the mortality risk to individuals, m’, from their exposure dose,
r’, so we start from that premise using the BEIR-IV version of LNT (in
simplified form; full treatment in Ref.1).

m’ = a_{n }( 1 + b r’) non-smokers

m’ = a_{s }( 1 + b r’ ) smokers

where a_{n} and a_{s} are constants determined
from national lung cancer rates, and b is a constant determined from studies of
miners exposed to high radon levels.

Summing these
over all people in the county and dividing by the population gives

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

where m and r have the county average definitions given above in
the presentation of Fig. 1, and S is the smoking prevalence--the fraction of
the adult population that is smokers. Eq. (1) is the prediction of the LNT
theory we are testing here (we also show that
our test applies not only to the BEIR-IV version but to all other LNT theories);
note that it is derived by rigorous mathematics from the risk to individuals,
with no problem from the ecological fallacy.

The bracketed
term in Eq.(1), which we call m_{0, }contains the information on
smoking prevalence, so m/m_{0} may be thought of as the lung cancer
rate corrected for smoking. Fig. 1b,d show m/m_{0} vs r. We fit the
data (I.e. all 1601 points) to

m/m_{0} = A + B r (2)

deriving values of B . The theory lines are from Eq. (1) with
slight renormalization. It is clear from Fig. 1b,d that there is a huge
discrepancy between measurements and theory. The theory predicts B = +7.3% per
pCi/L, whereas the data are fit by B = -7.3 (+/- 0.6) and -8.3 (+/- 0.8) % per
pCi/L for males and females respectively. We see that there is a discrepancy between
theory and observation of about 20 standard deviations; we call this “our
discrepancy”.

All explanations
for our discrepancy that we could develop or that have been suggested by others
have been tested and found to be grossly inadequate. We review some of the details of this process here.

There may be some
question about the radon measurements, but three independent sources of radon
data, our own measurements, EPA measurements, and measurements sponsored by
various states governments, have been used and each gives essentially the same
results. These three sets of data correlate well with one another, and by
comparing them, we can estimate the uncertainties in each and in our combined
data set; these indicate that uncertainties in the radon data are not a
problem.

Another potential
problem is in our values of smoking prevalence,S. Three different and
independent sources of data on smoking prevalence were used, and all result in
essentially the same discrepancy with LNT seen in Fig. 1b,d. Nevertheless,
since cigarette smoking is such an important cause of lung cancer, one might
think that uncertainties in S-values can frustrate our efforts. Analysis shows
that the situation is not nearly so unfavorable. The relative importance of
smoking and radon for affecting the variation of lung cancer rates among U.S.
Counties may be estimated by use of the BEIR-IV theory. For males, the width of
the distribution of S-values, as measured by the standard deviation (SD) for
that distribution, is 13.3% of the mean, and according to BEIR-IV a difference
of 13.3% in S would cause a difference in lung cancer rates of 11.3%; whereas
the SD in the width of the distribution of radon levels for U.S. Counties is
58% of the mean which, according to BEIR-IV, would cause a difference in lung
cancer rates of 6.6%. Thus, the importance of smoking for determining
variations in lung cancer rates among counties is less than twice (11.3/6.6)
that of radon. Smoking is not as dominant a factor as one might intuitively
think it is.

Even more
important for our purposes is the fact that smoking prevalence, S, can only
influence our results to the extent that it is correlated with the average
radon levels in counties. Thus we are facing a straightforward __quantitative__
question: How strong a correlation between S and r, CORR-r, would be necessary
to explain our discrepancy. If we use our best estimate of the width of the
distribution of S-values for U.S. counties, even a perfect negative correlation
between radon and smoking prevalence, CORR-r = -1.0, eliminates only half of
the discrepancy. If the width of the S-value distribution is doubled, making it
as wide as the distribution of lung cancer rates, which is the largest credible
width since other factors surely contribute to lung cancer rates, an
essentially perfect negative correlation, CORR-r = -0.90, would be required to explain the discrepancy
and to cut the discrepancy in half requires Corr-r = - 0.62.

How plausible is
such a large |CORR-r|? There is no obvious direct relationship between S and r,
so the most reasonable source of a correlation is through confounding by
socioeconomic variables (SEV). We studied 54 different SEV to find their
correlation with r, including population characteristics, vital statistics,
medical care, social characteristics, education, housing, economics, government
involvements, etc. The largest |CORR-r| was 0.37, the next largest was 0.30,
and for 49 of the 54 SEV, |CORR-r| was less than 0.20. Thus a |CORR-r| for
smoking prevalence, S, even approaching 0.90, or even 0.62, seems completely incredible. We conclude
that errors in our S-values can do little to explain our discrepancy.

In another
largely unrelated study (2), we found that the strong correlation between radon
exposure and lung cancer mortality (with or without S as a covariate), albeit
negative rather than positive, is unique to lung cancer; no remotely comparable
correlation was found for any of the other 32 cancer sites. We conclude that the observed behavior is
not something that can easily occur by chance.

To investigate
effects of a potential confounding variable, data are stratified into quintiles
on the values of that variable, and a regression analysis is done separately
for each stratum. Since the potential
confounder has nearly the same value for all counties in a given stratum, its
confounding effect is greatly reduced in these analyses. An average of the slopes, B, of the regression lines for the five quintiles
then gives a value for B which is largely free of the confounding under
investigation.

This test was
carried out for the 54 socioeconomic variables mentioned above, and none was
found to be a significant confounder.
In all 540 regression analyses (54 variables x 5 quintiles x 2 sexes),
the slopes, B, were negative and the average B value for the five quintiles was
always close to the value for the entire data set. Incidently, this means that
the negative correlation between lung cancer rates and radon exposure is found
if we consider only the very urban counties, or if we consider only the very
rural counties; if we consider only the richest counties, or if we consider
only the poorest; if we consider only the counties with the best medical care,
or if we consider only those with the poorest medical care; and so forth for all
54 socioeconomic variables. It is also
found for all strata in between, as, for example, considering only counties of
average urban-rural balance, or considering only counties of average wealth, or
considering only counties of average medical care, etc.

The possibility
of confounding by combinations of socioeconomic variables was studied by
multiple regression analyses and found not to be an important potential
explanation for the discrepancy.

The
stratification method was used to investigate the possibility of confounding by
geography, by considering only counties in each separate geographical region,
but the results were similar for each region. The stratification method was
also used to investigate the possibility of confounding by physical features such
as altitude, temperature, precipitation, wind, and cloudiness, but these
factors were of no help in explaining the discrepancy. The negative slope and
gross discrepancy with LNT theory is found if we consider only the wettest
areas, or if we consider only the driest; if we consider only the warmest
areas, or if we consider only the coolest; if we consider only the sunniest, or
if we consider only the cloudiest; etc

The effects of
the two principal recognized factors that correlate with both radon and smoking
were calculated in detail: (1) urban people smoke 20% more but average 25%
lower radon exposures than rural people; (2) houses of smokers have 10% lower
average radon levels than houses of non-smokers. These were found to explain only 3% of the discrepancy. Since they are typical of the largest
confounding effects one can plausibly expect, it is extremely difficult to
imagine a confounding effect that can explain the discrepancy. Requirements on such an unrecognized
confounder were listed, and they make its existence seem extremely implausible.

__Updates on original paper__

Our 1995 paper
was based on lung cancer rates for 1970-1979, the latest age adjusted data
available at that time. Recently, age adjusted lung cancer rates for 1979-1994
have become available. When these are used, the slopes, B, are changed from
-7.3 to -7.7 % per pCi/L for males, and from -8.3 to -8.2 for females. Since
there are more lung cancer cases included, the standard deviations of these
B-values are reduced, increasing the discrepancy with the predictions of LNT to
about 30 standard deviations.

The 54
socioeconomic variables (SEV) used in the original paper were from the 1980
Census. About 450 new SEV from the 1990 Census have now been introduced and
investigated in substantial depth. None of these SEV had |CORR-r| >0.45, and
extensive stratification studies led to the conclusion that none of these
additional SEV can help to explain our discrepancy.

__The Ecological Study issue__

Most criticisms
of our study have been based on generalized criticisms of ecological studies.
The most important of these is called “cross level bias” (3). On this basis, in
a presentation to NCRP (Feb.17, 1998), Jay Lubin dismissed my work as useless
by a mathematical demonstration showing that an ecological study does not do an
adequate job in handling a confounding factor. This problem was addressed in some detail in Ref, 1 and 4 where I
describe it as “the ecological fallacy for confounding factors (CF)”. The
classical “ecological fallacy” arises from the fact that the average dose does
not, in general, determine the average risk, but I avoid this problem by
designing my study as a test of the linear-no threshold theory (LNT) -- in LNT,
the average dose __does__ determine the average risk. Use of separate and
independent risks for smokers and non-smokers avoids this problem for smoking
prevalence. However, this problem does arise for other CF -- the average value
of a CF does not adequately determine its confounding effects, as demonstrated
mathematically by Lubin.

For example,
consider annual income as a CF that might confound the radon vs lung cancer
relationship -- maybe very poor people have lower radon levels and for
unrelated reasons, have higher lung cancer rates than others. As Lubin’s
demonstration shows, average income is not necessarily a measure of what
fraction of the population is very poor. A case-control study, in principle,
selects cases and controls of matched incomes (although this is not always
done, and is still less frequently done well).

My approach to
this problem is to use a large number of CFs. For the example under discussion,
I use as CF the fraction of the population in various income brackets,
<$5000/y, $5000-$10,000/y, ..........., >$150,000/y (10 intervals in
all). In addition, I consider combinations of adjacent brackets, and other
related characteristics such as the fraction of the population that is below
the poverty line, the percent unemployment, etc.

We have found that smoking prevalence, which is very strongly
correlated with lung cancer, must have at least a 35% correlation (Corr-r =
-0.6) with radon to have a significant effect, but none of the above CF have a
correlation larger than 7%. This is convincing evidence that income is not an
important confounder of the lung cancer vs radon relationship.

It is not
difficult to devise a model in which cross level bias could nullify our
results, verifying Lubin’s mathematical proof. For example, we might suppose
that those with an income that is an integral multiple of $700 have 50 times
lower radon and 50 times higher lung cancer rates than average. I have no data
to show that this is not the case. But such a model is not acceptable for two
reasons:

(1) It is not
plausible

(2) It would also
not be taken care of in case-control studies (they don’t match incomes
with that precision).

What is needed is a model that avoids these two limitations. These
limitations are effectively corollaries to Lubin’s mathematical proof.

Of course annual
income is not the only CF that must be considered.. Another example is age
distribution. Case-control studies match cases and controls by age, and as
Lubin’s mathematical demonstration shows, average age in a county does not
handle this problem in our study. Of course I do use age-adjusted mortality
rates which take care of the gross aspects of that problem, but there are
limitations in the age-adjustment process. My solution is to use as CF the
percent of the population in each age bracket, <1y, 1-2y, ......., 80-84Y,
>85y, 31 age brackets in all, and to also use combinations of adjacent age
brackets. None of these age brackets had correlations with radon above 4% with
the exception of the >85y bracket where the correlation was 7.7 %.. This was
further investigated by stratification, using five strata of 320 counties each
and determining the slopes, B, (cf. Eq. (2) above) of the lung cancer vs radon
relationship for each stratum. As we go from the stratum with the lowest to the
stratum with the highest percent of population with age >85y, Bvalues for
males were -10.1, -6.4, -6.1, -4.7, and -7.2 % per pCi/L, and for females they
were -6.3, -2.0, -9.1, -3.5, -10.7 % per pCi/L, whereas LNT predicts B=+7.3%
per pCi/L. Since the value of B is negative and grossly discrepant with the LNT
prediction for all cases, and there is no consistent trend in its variations, I
conclude that the correlation between radon and elderly people cannot explain
our discrepancy. I can’t prove this mathematically, but I can’t concoct a
not-implausible model in which variations of radon and lung cancer with age
helps substantially to explain our discrepancy. As Lubin’s proof shows, it is
possible to concoct a model to explain our discrepancy --e.g. we might assume
that those born on the first day of a month have 50 times higher radon levels
and 50 times lower lung cancer rates than others -- but that does not satisfy
our two corollaries to Lubin’s proof.

There are few, if
any, other bases on which case-control studies match cases and controls, but in
my study I gave similar treatments to a host of other potential confounding
factors -- educational attainment, urban vs rural differences, ethnicity,
occupation, housing, medical care, family structures, etc, etc. I have found
nothing that can help substantially to explain our discrepancy.

Aside from
cross-level bias, more generalized and less specific discussions of limitations
of ecological studies have appeared in the literature and have been used to
criticize our study. But there are many very important differences between our work and other ecological studies. One
such difference is in the quantity of data involved. Most ecological studies
involve 10-20 (or less) groups of people, whereas ours involves 100 times that
number (1729 counties). Not only does
that give a tremendous improvement in statistical accuracy, but it allows much
more elaborate and sophisticated analyses to be done, including consideration
of large numbers of potential confounding factors and use of stratification
techniques.

A more important
difference is that our work avoids the “ecological fallacy”; I know of no other
ecological study that contains that feature. That alone makes our paper very
different from the others, and should earn it the right to be considered free
from the prejudice attached to consideration of other ecological studies.

Ecological
studies are normally viewed as being fast, simple to carry out, and
inexpensive, but none of these adjectives applies to our project. It was the
focus of my research effort for many years. Our radon measurements extended
over six years and involved hundreds of assistants with millions of dollars in
salaries, and the completely separate EPA and State-sponsored measurements we
used were comparably elaborate. Our data analysis efforts involved dozens of
assistants and several years of their efforts and mine. Without the power of
modern computers and software packages, which have not been available until
quite recently, such analyses would have been completely impractical. I know of
no other ecological study to which any of the considerations of this paragraph
would apply.

Since any deep
understanding of how radon causes lung cancer must be based on its effects on
individuals, it is essential to study the problem in terms of risks to
individuals, which seems contrary to the ecological approach. However our
treatment __is__ based on risks to individuals (cf derivation of Equation
(1) above). That theory is then developed by rigorous mathematics to obtain the
prediction, Eqn. (1), we use to compare with observations. This is a
time-honored procedure in science; for example, Newton’s famous formula,

F = m *a
*

is rarely tested by direct measurements of acceleration,*a *, but rather, the formula is developed
mathematically to determine distance travelled vs time which is much easier to
measure, as a test of the theory.

__Other published proposals for explaining our discrepancy__

__ __The BEIR-VI Report pointed out that no consideration had been
given to variations in intensity of smoking, and proposed a model in which this
is expressed as the ratio, k, of one pack per day to two pack per day smokers.
To evaluate this proposal, one must recognize that there is surely no direct
causal relationship between k and radon levels, r, so any correlation between
the two must arise from socioeconomic variables, SEV. How large a correlation
between k and r, Corr(k,r), is not completely implausible? For the 500 SEV we
have studied, the largest |Corr(SEV,r)| is 0.45.

Some indication
of intensity of smoking in various states is included in cigarette sales (cs)
data, available from tax collection records for each year. From these data,
Corr(cs,r) varied between -0.14 and -0.29 between 1960 and 1975. From this and
the maximum |Corr(SEV,r)| , it seems reasonable to conclude that |Corr(k,r)|
larger than 0.5 would be highly implausible. The effect of Corr(k,r) = -0.5 is
to change the slope B in Fig. 1b from -7.3 to -5.0, and even Corr(k,r) = -0.8
gives B =-2.3, still a long way from the LNT prediction B =+7.3 . Of course
there is no reason to believe that Corr(k,r) is negative, and a positive
Corr(k,r) would change B in the opposite direction.

Field et al pointed out that radon gas levels in homes
is not the same as exposures to radon progeny which determine the dose, because
the latter are affected by time spent in homes, exposures in other places, the
ratio of radon progeny to radon gas, etc. and these may be correlated with
radon levels. To investigate this, we define a modifying factor, f, by

r(effective) = r (1 + f)

and use r(effective) rather than r in determining B. The results
depend on two features of f, the width of the distribution of f-values and
Corr(f,r). As a rather extreme example, assuming a perfect correlation,
Corr(f,r)=1.0

and w=0.7, changes B only from -7.3 to -3.7. Of course there is no
reason to believe that the effects would be anywhere near that large, or that
they do not change B in the opposite direction.

Letters-to-the-Editor
have proposed that our discrepancy might be explained by confounding by
population, or by population density -- an expression of the urban-rural
differences. However stratification of our data into 10 deciles, or even finer
stratifications on the basis of these variables, showed practically no evidence
of a change in B-values. In these fine stratifications, the counties in most
strata have essentially the same populations or population densities, but still
the analysis for these counties with the same population, or with the same
population density, gives a large negative value of B.

__Negative slopes and
conflict with data from case-control studies__

__ __It is frequently suggested that the negative slopes in our data
for m vs r (I.e. m decreases with increasing r) are incredible and are in
conflict with the results of the case-control studies. It should be recognized
at the outset that case-control studies investigate the causal relationship
between radon exposure and lung cancer, whereas our work has the much more
limited objective of testing the linear-no threshold theory; if that theory
fails as we have concluded, “the ecological fallacy” becomes relevant and our
results cannot be directly interpreted as representing the risks to
individuals. We have therefore never claimed that Fig. 1 gives risks to
individuals, or that low level exposure to radon is protective against lung
cancer. Our only conclusion is that LNT fails very badly, grossly
over-estimating the cancer risk of low level radiation.

However, if one
insists on interpreting our data as representing the dose-response relationship
to individuals, it should be recognized that the negative slopes in our data
are entirely based on radon exposures
in the range r=0-3.5 pCi/L (0- 130 Bq/m^{3}), whereas the
case-control studies give essentially no statistically meaningful information
on the slope in this region. Detailed analysis shows that there is no
discrepancy between our data and the case-control studies in that region.

__ __

__The smoking-radon interaction__

__ __Our Eq. (1), derived to relate lung cancer rate, m, to r and S is

m = [ S a_{s }+ (1-S) a_{n
}] (1 + B r )

where a and B are constants. This has given many the impression
that we have assumed some special and simple (linear) relationship between
smoking and radon exposure in causing lung cancer. Despite the appearance of
the above equation, that is not the case, as we now demonstrate.

BEIR-IV considers
smokers and non-smokers as separate “species”, each with its own lung cancer
risks. The relationship between radon and smoking in causing lung cancer in an
individual can be infinitely complex. In utilizing the BEIR-IV model to
mathematically derive the mortality rate for a county, the fraction of the
county population that smokes, S, logically arises and the result is the above
formula. Note that S is __not__ the intensity of smoking by an individual,
but it is simply the fraction of the population that smokes cigarettes, the fraction of the population that is in
that “species”.

If counties kept
separate statistics on cause of death for smokers and non-smokers, S would not
be involved. We could do two completely separate and independent studies for
smokers and non-smokers. It is only because counties do not keep separate
statistics that we must combine these two studies, and this introduces the
relative sizes of the two groups which is represented by S.

__CONCLUSION__

__ __

Since no other
plausible explanation has been found after years of effort by myself and
others, I conclude that the most plausible explanation for our discrepancy is
that the linear-no threshold theory fails, grossly over-estimating the cancer
risk in the low dose, low dose rate region. There are no other data capable of
testing the theory in that region.

An easy answer to
the credibility of this conclusion would be for someone to suggest a potential
not implausible explanation based on some selected variables. I (or he) will
then calculate what values of those variables are required to explain our
discrepancy. We can then make a judgement on the plausibility of that
explanation. To show that this procedure is not unreasonable, I offer to provide
a not-implausible explanation for any finding of any other published ecological
study. This alone demonstrates that our work is very different from any other
ecological study, and therefore deserves separate consideration.

__Caption for Figure__

Fig. 1: This is the same as Fig. 1 of Reference 1 which is posted
on this web site

__References__

1. Cohen,B.L.Test of the linear-no threshold theory of radiation

carcinogenesis for inhaled radon decay products”, Health Physics
68: 157-174; 1995.

2. Cohen, B.L. Relationship between exposure to radon and various
types of cancer. Health Phys. 65:529-531; 1993

3. Greenland,S.; Robins,J. Ecologic studies: biases,
misconceptions, and counter examples. Am. J. Epidemiol. 139:747-760; 1994

4. Cohen,B.L. Problems in the radon vs lung cancer test of the
linear-no threshold theory and a procedure for resolving them. Health Phys.
72:623-628;1997