The Puskin Observation on Smoking as a Confounder in Ecologic Correlations of Cancer Mortality Rates with Average County Radon Levels
Bernard L. Cohen
University of Pittsburgh
In studies of U.S. counties, we have reported that regression of lung cancer rates, m, with or without correction for smoking prevalence, S, on average radon levels in homes, r, gives a strong negative dependence (less cancer for more radon), a very large discrepancy with the strong positive dependence predicted by linear-no threshold theory. In a recent paper, Puskin reported results of simple regressions on r, and of multiple regressions on r and S, for rates of lung cancer and other smoking related cancers. He observed that the dependence on r is strong and negative in simple regressions, and not much less negative in multiple regressions, for all cases. He contends that a negative dependence on radon exposure for the other smoking related cancers is impossible, and concludes that his observation can only be caused by large errors in our S-values, missing a strong negative S-r correlation. He claims that this invalidates our results for lung cancer. In this paper, we examine Puskin’s proposed explanation quantitatively and find that even a perfect negative S-r correlation does not resolve the problem, regardless of the width or shape of the distribution of S-values assumed; a completely implausible near-perfect negative S-r correlation is required even to make an appreciable difference in the results. We then review the three independent sources of our S-values, and show that they each give essentially the same results both in our studies and in Puskin’s work, and in analogous studies of cancer rates in states (rather than in counties) where S-values have less uncertainty. Alternative explanations for the Puskin observation, which do not conflict with our previous conclusions, are then offered.
Key words: radon; cancer; cigarettes; health effects
In a series of University of Pittsburgh papers starting in 1995 (Cohen 1995, hereafter referred to as PITT), an analysis of age-adjusted mortality rates from lung cancer, m, vs average radon levels in homes, r, for 1600 U.S. counties was used to test the linear-no threshold theory (LNT) of radiation carcinogenesis. The data were fitted to the LNT prediction derived mathematically from the BEIR-IV Report (NAS 1988)
m = [9 + 99 S] (A + B r) males
m = [3.7 + 32 S] (A + B r) females
where S is the fraction (between 0 and 1.0) of the adult population that smoke cigarettes, m is in units of deaths per year per 100,000 population, r is in units of 37 Bq/m3 (pCi/L), and A and B are constants determined by fitting the data (with A very close to 1.00). It was found that the slopes of the r-dependence, B, are strongly negative, in contrast to the expectation from LNT that they should be positive, reflecting the concept that increased radon exposure causes increased lung cancer. In particular, fitting the data to Eqn. (1) gives B = -7.3±0.6 for males and B = -8.3±0.8 for females, as compared to the BEIR-IV prediction, based on LNT, B=+7.3 (all in units of % per 37 Bq/m3, or % per pCi/L). This very large discrepancy, over 20 standard deviations, was interpreted as indicating failure of LNT in the low dose region where it has not been otherwise tested.
In a recent paper (Puskin 2003 -- hereafter referred to as “Puskin”), Puskin utilized the S-values from PITT to fit the data for the four principal smoking-related cancers – lung, oral, larynx, and esophagus -- to
m = a + b r (2)
and also to
m = a¢ + b1 r + b2 S (3)
His principal results are listed in Table 1; where the columns headed by (100b/a) and (100b1/ a¢+b2Sav) are the percentage increase in cancer rates per 37 Bq/m3 (1.0 pCi/L) increase in radon level, assuming the validity of Equations (2) and (3) respectively. Puskin points out that the values in the former column are all negative, and those in the latter column are not much less negative, indicating that including smoking prevalence in the analysis does little to change the apparent negative dependence of cancer risk on radon exposure. We will refer to this very interesting result as the “Puskin observation”.
The Puskin observation is consistent with the findings in PITT for lung cancer, but Puskin contends that they are impossible to explain for the other smoking related cancers because those cancers cannot be affected by radon exposure. He therefore concludes that the only explanation for the Puskin observation is erroneous S-values. Since these S-values are taken from PITT, he interprets this to mean that the PITT results are invalid. More specifically, he concludes that the PITT S-values err in that they miss a strong negative correlation between S and r which would explain the Puskin observation and explain the discrepancy between the PITT results and the predictions of LNT. We call this the “Puskin hypothesis”. The purpose of this paper is first to test this Puskin hypothesis, then to re-examine the validity of the PITT S-values in the light of Puskin’s work, and finally to offer alternative explanations for the Puskin observation.
The Puskin hypothesis can be tested directly by changing the S-values as required to give the very strong S-r correlation it suggests. One extreme way to do this is to put the S-values for our 1600 counties into a pool, and reassign them to counties in perfect reverse order of their r-values – the county with the largest r is assigned the smallest S, the county with the next largest r is assigned the next smallest S, and so forth through our 1600 county data file, ending with the county with the smallest r being assigned the largest S. We call this set of S-values “S-perfect”; for it, the correlation by ranking (Spearman’s ρ), CoRR(S,r) is -1.00.
The results of the Puskin type analysis, fitting the data to Eqn. (3), are listed in the column headed “S-perfect” in Table 1. There is no indication there that the dependence of cancer rate on radon exposure is more positive for lung cancer than for the other smoking related cancers. But, since uncertainties in the PITT S-values is the issue under investigation here, it is important to consider other possible problems with this analysis for CoRR(S,r) = -1.00.
In PITT it was recognized that, with an analysis based on Eqn (1), uncertainty in the width of the distribution of S-values can affect results.. However, with the Puskin type analysis, based on Eqn (2) and (3) and maintaining the perfect negative S-r correlation, CoRR(S,r) = -1.00, the slope of the dependence of cancer rate on radon exposure,
(100b1 / a¢ + b2 Sav), is independent of the width of the distribution of S-values. For example, if this width is doubled, the values in the column of Table 1 headed “S-perfect” remain unchanged. This unexpected result is apparently due to properties of the multivariate regression process not understood by this author. To further check on this point, sets of S-values (with the same average S) based on a normal distribution, and on a uniform distribution between set limits, were generated and the widths of these distributions were varied by a factor of ten, but the same values of the quantity (100b1 / a¢ + b2 Sav) were obtained for all of the different widths.
On the other hand, values of (100b1 / a¢ + b2 Sav) do vary somewhat with the shape of the distribution of S-values. These variations are shown in Table 2 for cases where S-perfect is derived from the pool of S-values from PITT, from a normal distribution, from a uniform distribution between set limits, and for a very extreme distribution with S=0 for all counties with above-the-average radon level, and S=1.0 for all counties with below-the-average radon level.
We see from Table 2 that in all cases, (100b1 / a¢ + b2 Sav) is negative for lung cancer, maintaining the huge discrepancy with the prediction of LNT. For the two most credible distributions of S-values, PITT and Normal, it is negative for lung cancer but positive for the other smoking related cancers, implying that radon causes the latter but does not cause lung cancer – this is the oposite of what Puskin proposes would be found by a strong negative S-r correlation. We thus conclude that the Puskin hypothesis fails to fulfill its intended purpose of explaining the Puskin observation. The extremely strong negative S-r correlation does not cause radon exposure to increase lung cancer risk more than it increases the risks of other smoking related cancers. Purporting to fulfill that purpose was the point of the Puskin paper.
This conclusion applies regardless of the width or shape assumed for the distribution of S-values. The Puskin hypothesis does nothing to change the conclusions of PITT. As was demonstrated in PITT, it can eliminate the negative dependence of lung cancer rates on radon levels but it cannot explain the discrepancy with the LNT prediction of a strong positive slope.
Before closing our discussion of S-perfect as derived from various sources, it is relevant to mention their correlations with lung cancer rates. This is 0.46 when S-perfect is derived from PITT, from normal, or from uniform distributions of any width, and 0.39 when derived from our “extreme” distribution. These are substantially less than the correlation with lung cancer rates for the original PITT S-values, 0.60, which supports the validity of the latter as opposed to the Puskin hypothesis.
Needless to say, the assumption of a perfect negative S-r correlation is highly unrealistic. We next consider more realistic correlations. One approach to doing this is to use for S-values
S = q x S-perfect + (1-q) x S-random
where S-random are randomly chosen selections from the pool of S-values, and q is a number between 0 and 1.0 that can be varied to obtain various direct correlations, Corr(S,r), and correlations by ranking, CoRR(S,r), with radon levels. This was done for males with a normal distribution and the results are shown in Table 3. We see there that more strongly negative correlations, as proposed by Puskin, have essentially no effect on the results until they reaches extremely implausible values. (Plausibility of such correlations is discussed below in Sec. D). Spot checks indicated that this conclusion is valid regardless of the width of the distribution of S-values or the source of the pool of S-values.
Our final conclusion, then, is that Puskin’s very interesting observation, reproduced in Table 1, of similar variation with radon levels for lung cancer and other smoking related cancers cannot be explained even to the slightest extent by erroneous S-values in PITT. It therefore provides no evidence that the PITT S-values are erroneous.
Since questioning the PITT S-values was the purpose of Puskin, it is relevant here to re-examine their validity. Section G of PITT describes three methods used to estimate smoking prevalence, S, for U.S. counties:
Method I. Bureau of Census Survey
A 1985 survey by the U.S. Bureau of Census (U.S. PHS 1990) gives S-values for each state at that time. These are corrected to the earlier more relevant time period with data on the temporal variation of national smoking prevalence (U.S. PHS 1987) assuming the same proportional changes in each state. Evidence supporting this procedure was cited for males, but it was less clear for females. S values for counties within each state were obtained by applying a correction for urban vs rural differences.
Method I has three problems, the uncertainty in the urban vs rural correction, the uncertainty in the correction to the earlier time period, and lack of consideration for intensity of smoking (although this was treated in a separate paper (Cohen 2000a). All of these problems are eliminated in Method II.
Method II. Lung cancer rates
Since the dominant cause of lung cancer is smoking, the relative smoking prevalence in counties can be estimated from lung cancer rates in counties with similar radon levels, using measured characteristics of counties as an intermediary. The procedure for doing this is explained in Section G of PITT.
Method III. State cigarette sales tax collections
Smoking prevalence for males in a state is assumed to be proportional to the cigarettes per capita purchased in the state, as determined by tax collections from cigarette sales (Tobacco Institute 1988). This is done for the years (a)1975, (b)1970, and (c)1960 – in earlier years, available data are more sketchy. Variations among counties in a state were estimated as in Method I.
Evaluations of these three methods are given in Table 4. The column headed Corr(m,S) is the coefficient of correlation of S with lung cancer rates for the entire 1600 county data file. These correlations are quite strong and not much different for Methods I and II, but they are considerably poorer for Method III. Another test is to fit the data on lung cancer rate, m, vs S to
m = P + Q S (4)
to determine the fitting constants P and Q. . Since male lung cancer is predominantly due to smoking, we expect the second term to be much larger than the first. Their values with S set equal to the national average S-value, Sav, are shown in Columns (3) and (4) of Table 4. We see that this expectation is well fulfilled for Methods I and II; the term due to smoking is much larger than the other term, P, and P is negative which means that the smoking term even over-predicts the total number of lung cancers, leaving no lung cancers to be caused by other things. Method III does not do very well on this test so it is safe to conclude that Method III is inferior to Methods I and II. Others have reported that use of cigarette tax collections are an unreliable indicator of smoking prevalence, especially where differences in this tax between neighboring states leads to a sizable price difference; for example, Massachusetts residents commonly purchase cigarettes in New Hampshire because of the lower tax in the latter.
The application for S-values in PITT is using it in Eqn. (1) in order to determine the value of B. B is the slope of the dependence of lung cancer rates on radon exposure, which is the key quantity in PITT. The values of B thus determined are listed in the last column of Table 4. We see there that all of our methods give rather similar values of B, and all are similarly grossly discrepant with the prediction of linear-no threshold theory, B = +7.3. Trying to understand that discrepancy is the point of all of our studies, and the fact that our three different methods for determining S-values does not help in that process suggests that uncertainties in our S-values are not a problem in our analyses.
It is interesting to consider how the different determinations of S-values affects the Puskin observation. This is shown in Table 5 which lists the percentage of each smoking-related cancer that is due to radon exposure according to Equations (2) and (3). We see there that for all cases, these percentages are negative, they are quite similar for the three methods of determining S, and the Puskin observation is clear for each method.
At this point, it seemed judicious to settle on one of our three methods. Clearly the choice was between Methods I and II. Considering the fact that completely independent methods and data were used, the correlation between the S-values from these two is very strong, 0.85 for males and 0.76 for females. The widths of the distributions of S-values (standard deviations) are very similar, 13.3% of the mean for males from both methods, and for females,16.7% and 19.2% of the mean from Methods I and II respectively. Method I was selected because it is more like methods commonly used and therefore easier to understand and less open to suspicion.
There are data in the Puskin paper that support the validity of the PITT S-values.
The R2 from fitting the data to Eqn. (2) and (3), not given in Puskin, are listed in Table 1. It is evident that including PITT S-values in the analysis substantially improves this index of goodness of fit. For example, for male lung cancer, R2 is increased from 20% to 44%.
Assuming the validity of Eqn.(2) and (3), a is the cancer rate in the absence of radon and a¢ is the rate in the absence of either smoking or radon. The ratio a/a¢ , listed in the last column of Table 1, is then roughly the ratio of cancer rates for smokers/non-smokers in the absence of radon. We see that for male lung cancer, the cancer rate is 5.9 times higher for smokers than for non-smokers. For all of the smoking related cancers, in males and females, there is a strong tendency for a/a¢ to be substantially greater than unity.
D. Plausibility of the Puskin Hypothesis of a Strong Negative S-r Correlation
Aside from the fact that the Puskin–type analysis shows that the Puskin hypothesis fails to explain the Puskin observation, it is of interest to further examine the Puskin hypothesis involving a strong negative correlation between smoking prevalence, S, and radon exposures, r, for U.S. counties. This S-r correlation is given in PITT as follows for the different methods of determining S: Method I, -0.28 for males and –0.19 for females; Method II, -0.40 for males and –0.34 for females, Methods IIIa,b,c (applicable only to males), -0.16, -0.16, -0.11 respectively. It is negative in all cases. As perspective on its magnitude, the strongest (in absolute value) correlation with r for the 54 socioeconomic variables studied in PITT is 0.37, the next strongest is 0.30, and for 49 of the 54 it is less than 0.23. Thus the S-r negative correlations used in PITT are indeed quite strong, but as may be seen in Tables 2 and 3, they are not nearly strong enough to affect the large discrepancies with theory reported by PITT.
E. Defense of PITT S-values: Data for States
The most vulnerable issue in determining our S-values by Method I is the urban vs rural correction for counties within each state (although this is not a problem in our Method II which gives very similar results). This urban vs rural correction can be avoided by doing our analysis for states rather than for counties, since S-values for states are directly measured by the Bureau of Census survey. The only correction is for the time period, which is made under the assumption that relative values of S are not changed.
The correlation between these S-values and lung cancer rates is quite strong, 0.75 for males and 0.60 for females (Cohen 2000b). The fit of these data for males to Eqn. (5) gives P= -2.3±9.2 and Q = 132±17 with R2=56%; since values of S are typically 0.5, this suggests that nearly all male lung cancer is due to smoking. For females, P = 5.6±3.4 and Q = 53±10; since typical S-values for females are 0.32, this indicates that most, and perhaps the great majority of female lung cancer is due to smoking. The consistency of these facts with other information gives confidence in our S-values for states
The results of a Puskin type analysis for states are given in Table 6, which is analogous to Table 1 for counties. We see there a strong confirmation of the Puskin observation, that including smoking in the regression does not substantially reduce the negative dependence on radon exposure for lung cancer or for the other smoking-related cancers. The advantage of Table 6 over Table 1 is that there is less uncertainty in the values of S, so it is more difficult to accept Puskin’s contention that the Puskin observation is due to erroneous S-values. The disadvantage of Table 6 over Table 1 is that, due to the much smaller number of data points, the uncertainties in the results are much larger percentage-wise, but they are still small enough to leave no question about the conclusion stated above.
As was the case with Table 1, there is internal support for the S-values used to derive Table 6. The values of R2 are increased by including smoking in the regression in all cases, and become very large for the key example of lung cancer where it is increased from 28% to 66% for males, and from 33% to 60% for females As in the case of Table 1, the ratio a/a¢ is large, indicating that including our S-values in the regression explains a much larger fraction of the cancers; for example, it explains five times as many male lung cancers as not including them
If the data for states are used in Eqn. (1), the result is B = -11.8±2.9 for males and B = -13.7±2.5 for females, a similar but even more dramatic discrepancy with LNT than that reported in PITT for data on counties. The more certain S-values give a larger discrepancy with linear-no threshold theory.
F. Alternative Explanations for the Puskin Observation
Since we have found that the very interesting Puskin observation cannot be explained by erroneous smoking data as Puskin proposes, it is important to find an alternative explanation. One obvious explanation involves hormesis, recognizing that parts of the body exposed to carcinogens from tobacco smoke are also exposed to radiation from radon progeny. The hormesis explanation for the PITT finding that lung cancer rates decrease with increasing radon levels (proposed by others but not put forward by this author), is that low level radiation is protective against lung cancer. It seems likely that this would apply to other smoking related cancers. Puskin dismisses this explanation with a single sentence (applied to oral cancer): “Since the dose from radon decay products to stem cells in the mouth is expected to be minimal, it is impossible to attribute the fall-off in oral cancer [with increasing radon exposure] to radon exposure”. Since oral cancer occurs 17 times less frequently than lung cancer, it is not sufficient to contend that exposure to the mouth is minimal; it must be shown that the ratio of exposures to the lung (especially the bronchi) and mouth is much different for radon than for carcinogens in cigarette smoke. Puskin provides no evidence on that point. Both the mouth and the bronchial regions are protected by mucus which reduces direct contact and provides a removal process. It would require a very elaborate analysis to determine the ratio of exposures to the stem cells from radon and cigarette smoke in the lung and in the mouth, and show that they differ by a factor much larger than 17.
In considering only exposure to stem cells which are presumably involved in cancer initiation events, Puskin ignores biological defense mechanisms which protect against cancer and are known to be stimulated by radiation (UNSCEAR 1994, Sugahara et al 1992, Cohen 2002). Low level radiation is well known to increase the production of DNA repair enzymes (Shadley and Dai 1992, Cai and Liu 1990, Le et al 1998, Kelsey et al 1991, Azzam et al 1996), to stimulate the immune system (Liu 1992, Makinodan 1992), to improve scavenging of corrosive oxidants which initiate the great majority of cancers (Yamaoka 1991), to increase apoptosis of cancerous cells (Kondo 1994), and to affect cell cycle timing in ways that allow more time for this damage repair, all of which are protective against cancer development. In fact there is strong evidence that the cancer risk from low level radiation is determined much more by these biological defense mechanisms than by initiating events (Feinendegen and Pollycove 2001).
G. Miscellaneous comments
It should be recognized that the Puskin procedure of fitting data to Eqn. (3) is far less valid than the PITT procedure of fitting data to Eqn. (1), at least for lung cancer. Eqn. 3 assumes that effects of radon and smoking are additive, whereas the available information derived from studies of miners indicates that it is much closer to multiplicative. It is from these studies of miners that the BEIR IV Report develops the relationship between lung cancer, radon exposure, and smoking used in PITT to derive Eqn. (1).
Puskin points out that, in a very early paper (Cohen 1993), we did analyses using Eqn. (3) and reported that b1 was positive for some smoking related cancers, nasopharynx in males and females, and larynx in females. This is exhibited in Table 2 of Puskin (where b1 is designated B) which seems to indicate a serious discrepancy with his Table 1. However, the reason for this discrepancy is that our 1993 paper was based on mortality data for 1970-1979 (because they were the latest age-adjusted mortality data available at that time) and those data exclude counties for which there were zero deaths during that time period. The results in our 1993 paper were rechecked and found to be correct based on those data.
Puskin states "Cohen attempted to adjust for the effects of smoking
confounding by introducing a separate independent variable, S, for smoking
prevalence". Actually, S derives directly from BEIR-IV which is used as the
LNT version tested in PITT. BEIR-IV treats smokers and non-smokers as two
different "species", with different risks from radon. In summing over the
population of a county in which the fraction that smoke is S and the
fraction that do not smoke is (1-S), the mortality rate depends on S. All
this is done mathematically in PITT. This is not "an attempt to adjust for smoking" but it is rather a straightforward mathematical application of the BEIR-IV version of LNT.
In its Introduction section, Puskin states that the PITT results may be affected by “a negative association between radon and smoking within counties”. This problem was addressed previously (Cohen 1998, 2000a). For example, in the first of these a quantity x was defined as the ratio of average radon levels, r, for smokers to non-smokers in each county. A wide range of assumptions was made about the national average value of x, and about possible correlations between x and r for U.S. counties, stretching and far exceeding the bounds of plausibility. It was found that this exercise had little effect on the results of PITT.
In the “Introduction” section of Puskin, my work is characterized as an
approach to determine the lung cancer risk from radon. I have never
claimed to be doing that, and have stated explicitly in several papers,
including the Introduction to PITT, that this cannot be done with
an ecological study because of “the ecological fallacy”. The logical
structure of my work, testing LNT, is the following: Either (1) LNT is valid in which case the ecological fallacy does not apply and there should be the strong positive relationship between lung cancer and radon exposure predicted by LNT, or (2) LNT is not valid in which case the data cannot be used to determine risks. Since option (1) fails drastically, I conclude that (2) is the correct option, and LNT is not valid.
The author is greatly indebted to J.S. Puskin for informing me about his very interesting observation and for useful suggestions and discussions
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Table 1: Results corresponding to Table 1 of Puskin, with additional information.. Simple regression is from fitting the data to Eqn (3) and multiple regression is from fitting the data to Eqn (4). 100 b/a and 100 b1 / (a¢ + b2 SAv) are the percent increase in cancer rates per unit increase in radon level. R2 is a measure of the goodness of the fit. The column headed S = S-perfect gives values for 100 b1 / (a¢ + b2 SAv) obtained from assigning S-values to counties so as to have a perfect negative correlation by ranking with radon levels.
Simple Regression. ______Multiple Regression a/a¢
Cancer-Male 100 b/a R2 100 b1 / (a¢ + b2 SAv) R2 S-perfect ___
Lung -8.7±0.4 20% -6.0±0.4 44% -0.3±1.8 5.9
Oral -10.2±0.7 9% -8.6±0.8 12% +2.5±3.8 2.0
Larynx -8.5±0.8 5% -6.7±0.9 8% +3.3±4.3 2.2
Esophagus -4.1±0.7 1.6% -3.8±0.8 1.7% +2.1±3.3 0.9
Lung -9.3±0.5 15% -7.7±0.5 29% -2.2±1.6 2.4
Oral -11.3±0.9 6% -10.7±0.9 7% -5.7±3.2 1.3
Larynx -14.2±1.3 4% -12.4±1.4 7% -11.3±4.5 3.1
Esophagus -7.9±1.1 2.5% -6.7±1.1 4% +3.1±3.9 1.9
Table 2: Values of 100 b1 / (a¢ + b2 SAv) for S = S-perfect, with S values derived from the pool of S-values given by PITT, by a normal distribution of any reasonable width, by a uniform distribution between any reasonably set limits, and by an extreme distribution with S=0 for r above-the-average radon level and S=1.0 for r below-theaverage radon level
Cancer-Male PITT Normal Uniform Extreme
Lung -0.3 -1.3 -2.1 -7.0
Oral +2.5 +1.6 -1.3 -8.2
Larynx +3.3 +2.2 -1.7 -6.8
Esophagus +2.1 +1.6 -3.8 -4.6
Table 3: Values of 100 b1 / (a¢ + b2 SAv) for various smoking-related cancer types with a normal distribution of S-values having various Corr(S,r), direct correlations, and CoRR(S,r), correlations by ranking, with radon levels. Results are independent of the width of the normal distribution.
Corr(S,r) CoRR(S,r) lung oral larynx esophagus
-0.02 0 -8.7 -10.2 -8.5 -4.1
-0.25 -0.23 -8.7 -10.3 -8.6 -4.2
-0.39 -0.38 -8.7 -10.3 -8.6 -4.2
-0.54 -0.54 -8.6 -10.3 -8.6 -4.2
-0.68 -0.69 -8.4 -10.1 -8.4 -4.1
-0.80 -0.82 -7.9 -9.5 -7.9 -3.8
-0.91 -0.94 -6.1 -7.0 -5.6 -2.6
-0.96 -1.00 -1.3 +1.6 +2.2 +1.6
Table 4: Properties of S-values from the different sources. Corr(m,S) is the correlation between S and lung cancer rates for the various counties. The next two columns are the results of fitting the data to Eqn. (4). The last column is the results for B obtained from fitting data to Eqn. (1)
Source of S-values Corr(m,S) 100 Q Sav P B (Eqn.1)
Males – Method I 0.59 60 ± 4 -9.7 ± 2.1 -7.3 ± 0.5
- Method II 0.64 66 ± 1.8 -10.2 ± 1.9 -6.0 ± 0.5
- Method IIIa 0.28 16 ± 1.4 41 ± 1.4 -8.3 ± 0.7
- Method IIIb 0.28 23 ± 2 35 ± 2 -9.0 ± 0.6
- Method IIIc 0.10 8 ± 2 49 ± 2 -10.1 ± 0.7
Females – Method I 0.44 13.4± 0.6 3.9 ± 0.7 -8.3 ± 0.8
- Method II 0.51 11.3 ± 0.5 6.1 ± 0.5 -6.3 ± 0.8
Table 5: The Puskin observation as represented in Table 1, with different methods for deriving S-values
100b/a 100b1 / (a¢ + b2 Sav)
Cancer-Male Method I Method II Method IIIa
Lung -8.7 -6.0 -4.7 -8.1
Oral -10.2 -8.6 -6.1 -9.4
Larynx -8.5 -6.7 -4.0 -7.6
Esophagus -4.1 -3.8 -2.5 -3.4
Lung -9.3 -7.7 -5.7
Oral -11.3 -10.7 -9.4
Larynx -14.2 -12.4 -10.0
Esophagus -7.9 -6.7 -4.4
Table 6: Results from analysis for states, analogous to Table 1 for counties
Simple Regression. Multiple Regression a/a¢
Cancer-Male 100 b/a R2 100 b1 / (a¢ + b2 SAv) R2 ___
Lung -12.0±2.8 28% -8.3±2.7 66% 5.0
Oral -17.6±3.8 33% -16.9±6.4 34% 1.3
Larynx -13.5±3.6 24% -11.7±5.0 31% 1.7
Esophagus -8.3±3.6 10% -7.4±3.5 11% 0.9
Lung -13.4±2.8 33% -12.0±2.9 60% 2.3
Oral -17.0±3.3 38% -16.7±4.8 46% 1.2
Larynx -17.6±4.7 24% -16.3±6.4 38% 2.5
Esophagus -14.5±3.9 24% -13.3±4.8 37% 2.0