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TEST OF THE LINEAR-NO THRESHOLD THEORY OF RADIATION CARCINOGENESIS Bernard L. Cohen University of Pittsburgh Pittsburgh, PA 15260, U.S.A. We recently completed a compilation of radon measurements from available sources which gives the average radon level, r, In homes for 1730 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. la, c 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, and the first and third quartiles of the distribution. We see, in Fig. 1 a, c, a clear tendency for m to S&crease with Increasing r, In sharp contrast to the jD.crease expected from the fact that radon can cause lung cancer, shown by the line labelled "theory". One obvious problem is migration: people do not spend their whole life and receive all of their radon exposure in their county of residence at time of death. However, it is easy to correct the theoretical predication for this, and the "theory" ~ 0 N ~ A ~ N O N i f

2 lines in Fig. 1 have been 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 results.) A more serious problem is that Fig. 1 is what epidemiologists call an 'ecological study". Epidemiologists normally study the relationship between mortality risks to individuals, mi, vs their personal exposure, rl, whereas an ecological study like ours deals with the relationship between the average risk to groups of individuals (populations of counties) and their average exposure. It is well known to epidemiologists that, in general, the average dose does not determine the average risk, and to assume otherwise is called "the ecological fallacy'. However, it is easy to show2 that, In testing a linear-no threshold theory, "the ecological fallacy" does not apply; in that theory, the average dose does determine the average risk. This is widely recognized from the fact that "person-rem" determines the number of deaths. Dividing person-rem by population gives average dose, and dividing number of deaths by population gives mortality rate. Because of the "ecological fallacy", epidemiology textbooks often state that an ecological study cannot determine a causal relationship between risk and exposure. That may be true, but It is irrelevant here because the purpose of our study is = to determine a causal relationship; It is rather to test the linear-no threshold dependence ofmonrf

3 Apart from "the ecological fallacy", other potential problems with ecological studies have been pointed out by Morgenstern, Greenland, and Robins'•`•5 but these have been shown not to be applicable to our workZ•6•'. The most obvious potential explanation for Fig. 1 is that there is a strong negative correlation between the percentage of adult population that smokes, S, and radon exposure, r; i.e. that counties with low r tend strongly to have high S, and vice- versa. This effect is most easily handled by use of the BEIR-I V theory8 which can be shown to give ml = a (1 + brl) (1) where ml is the lung cancer mortality risk to an individual, r, is that individual's radon exposure, and a and b are constants with a given separately for smokers and non- smokers (a„ a„) and for males and females. If we sum over all individuals in a county and divide by the population. Eq. (1) reduces to m = [Sa, + (1-S)a„j (1 +br). (2) Applying our correction for migration and inserting numerical values for a, and a„ then leads to9 m/m, = 1 + Br (3) where m, = 9 + 0.99S for males m, = 3.7 + 0.32S for females (4) B= +7.3

4 with B in units of percent per pCi/lL of average radon level, and ma in units of deaths/year-100,000. In Eq. (3), m/m, may be thought of as the lung cancer mortality rate corrected for smoking prevalence. Problems in determining S will be discussed below. Using our best values to calculate mo from Eq. (4) for each county leads to results shown in Fig. 1 b, d. We see that correcting for smoking does little to improve the unexpected behavior. Fitting the data to m/me = A + Br (5) to determine A and B gives B=-7.3t0.6 for males and B=-8.3t0.8 for femaies, as compared with the Eq. (4) theory prediction B = + 7.3, a discrepancy of about 20 standard deviations. We refer to this as "our discrepancy", and the remainder of this paper deals with our attempts to explain it, each section treating a different approach. Uncertainties in radon data Our radon data derives from three independent sources, our own measurements, EPA measurements, and studies by agencies in various individual states. Various checks for consistency among these three sources give satisfactory results'. Data from each of these three sources alone gives results for B very similar to those from our combined data set. We conclude that uncertainties in our r-values are not responsible for any significant part of our discrepancy. In fact the simplest correction for these uncertainties would Lcrease our discrepancy by about 8%. Outlvers and samoling issues •

5 The effects of outlying points in our analyses of data on mJme vs r was investigated by using five of the most popular statistical tests to discard either 1 O or 20 outlyers. In all cases, for both males and females, this increased our discrepancy. Outlyers were not discarded. Ten different random samples each of 200, 400, and 800 or our 1601 counties were analyzed independently. In all cases, results for B were quite similar to those for our entire data set, B=-7.3 for males and -8.3 for females. For example, for our ten random sets of 200 counties, all B values were between -5.0 and -8.5 for males, and between -4.8 and -12.7 for females. Our study might therefore be considered equivalent to eight independent studies, each giving roughly the same discrepancy with theory. One might wonder how unexpected it is to find such a strong and statistically robust correlation between m and r as we find for lung cancer in Fig. 1. To investigate this, we studied the regression of m on r for the 33 principal cancer types. The number of standard deviations by which the slope B differs from zero was 2.7 times larger for lung cancer than for any other type, and with just two exceptions it was at least 4 times larger. Double regressions on r and S gave similar results; as , expected, the rn-S correlation is very large and positive for lung cancer, and the m-r correlation is large (two-thirds as large as m-S). The only unexpected result was that the m-r correlation is negative rather than positive. We conclude that the strong observed correlation between m and r for lung cancer is quite unique and remarkable. Uncertainties in smoking prevalence, S N tr C N i ~ C13 N ~ CP

6 Our S values were derived from a 1985 surveytO of smoking prevalence in states, S1, corrected for variations with time in national smoking prevalence" under the assumption that the ratio of S1 for various states did not vary with time. It was then assumed that S values for the counties within a state are due only to urban-rural differences. That is, we take S= SJ(1 + kPU)/(1 +kPUI), where PU is the percent of the population that lives in urban areas for the county, PUI is the same quantity for the state as a whole, and k is a constant determined from regressions of m on PU (k was found to be similar for all geographic regions). An alternative method for determining S' values for states was by use of cigarette sales tax collections'Z which are available for every year. This has the advantage of giving data for the relevant time periods and also reflects the number of cigarettes smoked rather than just the number of smokers, although it also has some recognized disadvantages. When these values of S' were used, our discrepancy was ip_creased. They were not used further. As an approach to getting direct data on S for counties in the relevant time period with due consideration for intensity of smoking (e.g. inhalation, cigarettes per day), we developed a smoking variable S derived from lung cancer mortality data: We utilized socioeconomic variables (SEV) listed in Table 1 plus S' to predict rn-values in a manner independent of radon levels, r. We stratified on r into six separate groups of counties, and for each group independently, studied multiple regressions of m on SEV. We were able to derive a linear combination of S1 plus five SEV with coefficients independent of r, which predict m-values about as well as they can be N 0 N ~ A Q1 N O ~

7 predicted from SEV. When S values derived from this process are used to calculate mo from Eq. (4), and these are then used to fit the data to Eq. (5), B values are changed from -7.3 to -6.0 for males, and from -8.3 to -6.3 for females. Since this represents only a modest reduction in our discrepancy, and since it is questionable to use S-values derived from rn-values to predict m-values, these S-values were not used in our other studies. But this exercise indicates that the obvious problems in our derivation of S-values are not the cause of our discrepancy. As an entirely different approach to evaluating effects of uncertain S-values, we then set out to determine how strong a negative r-S correlation would be needed to explain our discrepancy. We re-assigned S-values for our 1601 counties in perfect reverse order of their r.-va(ues, and used these S-values in our analysis. This "perfect" negative r-S correlation reduced our B-values essentially to zero (+0.7 for males, -0.3 for females), only cutting our discrepancy in half. The problem is that our distribution of S-values is rather narrow - for males, mean - 51.7, SD - 6.9, min/max - 25/7O. If we arbitrarily double the width of this distribution by doubling the difference from the mean for each county to give mean - 51.7, SD - 13,8, min/max - 0/88, we are able to eliminate our discrepancy by reassigning S-values in a manner that gives the coefficient of correlation (CORR) between S and r to be -0.90. We then consider the question of how strong an r-S correlation is credible. Since any such correlation must arise from confounding by socioeconomic variables, we studied correlations of our 54 SEV (Table 1) with r. The largest I CORR-rI for any of our SEV is 0.37, the second largest is 0.30, and for 49 of our 54 SEV, CORR-r is . t

8 less than 0.23. For the S-values we are using, CORR-r is -0.28 for males and -0.19 for females. It therefore seems incredible that the true r-S correlation can be of the magnitude necessary to explain our discrepancy, even if coupled with a large error in the width of our distribution of S-values. We conclude that uncertainties In S-values are not a major cause of our discrepancy. Confounding by SEV and factors that correlate with them If a particular socioeconomic variable (SEV) is an important confounding factor (CF), stratifying our data on it into subsets and analyzing each subset separately would greatly reduce the problem as all counties in a given subset would have approximately the same value of that SEV. The average of the B-values obtained from the various subsets would then give a value of B free from the effects of confounding. The data were stratified into five quintiles of 1601/5=320 counties on the basis of each of our 54 SEV in turn. This gave 540 subsets (including both sexes), and for all 540 of them, B was found to be negative. Thus, the negative slopes In Fig. 1 b, d are found if we consider only the most urban counties, or if we consider only the most rural; if we consider only the richest, or only the poorest; if we consider only those with the best medical care, or only those with the poorest medical care; etc for our 54 SEV. They are also found if we consider any of the strata in between. Following up on our method of averaging B-values over the five quintiles to obtain B-values free of confounding gives, for our 54 SEV, results ranging between -5.6 and -7.7 for males, and between -5.4 and -9.1 for females, reasonably close to

9 our values for the entire data set, -7.3 and -8.3. We conclude that confounding by any one of our SEV can do little to explain our discrepancy. This also excludes factors that correlate strongly with SEV as potential CF. For example, air pollution correlates strongly with several of our SEV (e.g. population) and therefore cannot be an important CF. Confounding by combinations of SEV This still leaves open the possibility that some combination of SEV can explain our discrepancy. The best way to investigate this is through multiple regression analysis, fitting our data to m/m, = A + Br + c,Xj + c2X= + ... + cs,X54 (7) where X,...X.4 are our 54 socioeconomic variables and A, B, c,...c.4 are constants used to fit the data. With 1601 data points, there is no difficulty in deriving statistically robust estimates of these 56 constants. The results are B =-3.1 tO.6 for males, and B=-3.5t0.9 for females, reducing our discrepancy by 29% and 31% respectively. However, the statistics community generally takes a dim view of using multiple regression on many variables to quantify the causal relationship of one particular variable. In our case, the strong negative correlation between m and r would cause any variable strongly correlated with m to have a correlation of opposite sign with r. In fitting Eq. (7), its term will therefore drain away some of the strength of the Br term, reducing the value of B.

10 As a study of this effect, Fig. 2 shows a plot of CORR-m vs CORR-r for each of our SEV. We see there that every SEV with a large (CORR-rI has a large CORR-m of opposite sign, and vice-versa. This could be a very remarkable coincidence, but it is much more credible that it is the result of the effect we are studying. This Implies that the reduction in our discrepancy in going from simple to multiple regression is largely artificial, and the true values of B are close to -7.3 for males and -8.3 for females. Confounding by geograohv It is well known that radon levels correlate strongly with geography'•", which suggests that it be considered as a CF. We treat it by our stratification method. The U.S. Bureau of Census divides the nation into 4 regions, each consisting of 2 or 3 divisions. Stratifying by regions and averaging B-values over the four strata gives B=-6.1 for males and -8.0 for females, reasonably close to our values without stratification, -7.3 and -8.3. However, stratifying on the 9 divisions gives an average B of -4.4 for males and -6.6 for females, a substantial reduction in our discrepancy. This suggests that finer stratification on geography may help explain our discrepancy. The finest stratification readily available is by individual states. There are 34 states in which we have data on at least 20 counties. The average B-value from separate analysis of each of these is -6.1 for males and -7.2 for females. These reduce our discrepancy by 8% and 7% respectively. We conclude that confounding by geography does little to reduce our discrepancy. ~ Confounding by altitude and weather

11 Rather different types of potential confounding factors are barometric pressure (determined by altitude) and weather. Data on these are available only by states. It we treat data on states analogously to how we have been treating it for counties, we have only 46 data points instead of 1601, but an analogous analysis can be done. This gives B=-13.Ot2.3 for males and B=-14.4t2.7 for females, as opposed to B= +8.3 predicted by the theory, a very statistically robust discrepancy. As potential CF we consider altitude (meters above sea level), average winter temperature, average summer temperature, millimeters of annual precipitation, days(year with measurable precipitation, average wind speed, and percent of time with sunshine. We stratify the data on the basis of each of these in turn into three subsets of 15-16 states and analyze each subset to determine B. This gives a total of 42 analyses for both sexes, and all 42 B-values are found to be negative. Averaging over the three strata gives B-values ranging for our seven variables from -9.0 to -15.5 for males and from -11.8 to -15.6 for females. In no case are the deviations from values without stratification for a given variable in the same direction for males and females, and in no case is the average deviation for the two sexes more than 0.6 SD. Large negative B-values are found if we consider only low altitude states or If we consider only high altitude states; if we consider only warm states, or only cool states; if we consider only wet states, or only dry states; etc. They are also found if we consider only states with average values of these properties. These properties cannot, therefore, be the cause of our discrepancy. Effects of recognized r-S correlations

12 In our extensive studies of correlations with radon levels of house characteristics, locations, and socioeconomicfactors", we encountered two situations which would lead to r-S correlations: (1) urban houses average 25% lower radon levels than rural houses, and urban people smoke 20% more frequently judging from urban-rural differences in lung cancer rates (2) houses of smokers have 10% lower average radon levels than houses of non- smokers. A detailed calculation of the effects of these r-S correlations found that (1) changes the slope of an m vs r regression by 18%, but the effect is almost completely compensated by our correction for smoking, changing the slope, B, of an m/mo vs r regression by less than 1 %. The smoking correction does not compensate (2), but it changes the slope B by only 5%. Items (1) and (2) were found to add linearly in their effect on B. These recognized r-S correlations, therefore, change B by only 6% and thus reduce our discrepancy by only about 3%. It seems most unlikely that there are unrecognized r-S correlations that are over an order of magnitude larger than these as would be necessary to explain our discrepancy. Deoendence on BEIR-IV theory All calculations to this point, including our correction for smoking, have been carried out using the BEIR-IV theory°. However, we have shown that our discrepancy would be about equally large for any other m-r-S relationship based on data from the

13 miners. The principal differences among competing theories are in their treatment of smoking, but since r-S correlations are not very strong, these differences have little effect on the results. Unrecogniz d c onfounding factors It is logically possible that there is some unrecognized confounding factor (UCF) which is causing our discrepancy. Of course a UCF could invalidate anv epidemiological study, and few if any epidemiological studies have included as thorough investigation as ours of confounding factors. Let us consider the properties of a UCF necessary to explain our discrepancy: (a) it must have a very strong correlation with lung cancer, at least comparable to that of smoking, but still be unrecognized as such (b) it must have a very strong correlation of opposite sign with radon levels (c) it must not be strongly correlated with any of our socioeconomic variables, or with pressure, temperature, or other weather variables (d) it must be operative in the great majority of geographical areas. Requirement (1) means that in addition to causing lung cancer and being unrecognized as such, it must have increased in importance by orders of magnitude since the early part of this century, it must have affected males much more than females until mid-century with females closing the gap in recent years, it must be an order of magnitude more important in smokers than in non-smokers, etc. Requirement (2) is also difficult since correlations between radon and other factors have been studied extensively and are nearly all rather weak; also factors affecting radon levels

14 are well understood. Requirements (3) and (4) impose additional severe restrictions, taking away nearly all options that one would ordinarily consider. We therefore judge the existence of a UCF fulfilling ail of these requirements to be essentially incredibie, although we are always open to suggestions. Conclusions We have explored every explanation for our discrepancy that we can think of or that has been suggested to us. By far the most credible explanation, in our view, is that the linear-no threshold theory fails very badly in the low dose, low dose rate region where it has never been previously tested, grossly over-estimating the cancer risk.

15 References 1. B.L. Cohen, Critical Rev. in Environ. Control. 22:243-364; 1992. 2. B.L. Cohen, Int. Jour. of Epidemiol. 19:680-684; 1990. 3. H. Morgenstern, Am. J. Pub. Hlth. 72:1336-1344; 1983. 4. S. Greenland and H. Morgenstern, (nt. Jour. of Epidemiol. 18:269-274; 1989. 5. S. Greenland and J. Robins, Am. Jour. of Epidemlol. (in press) 6. B.L. Cohen, (nt. Jour. of Epidemiol. 21:422-424; 1992. 7. B.L. cohen, Am. Jour. of Epidemiol. (in press) 8. BEIR (National Acad. of Sciences Com. on Biological Effects of Ionizing Radiation). Health Risks of Radon.... National Academy Press, 1988 (BEIR-IV). 9. B.L. Cohen and G.A. Colditz, Environmental Research. (in press) 10. U.S. Public Health Service, Smoking and Health: a national status report. DHHS Publication 87-8396; 1990. _ 11. U.S. Public Health Service, Morbidity and Mortality Weekly Reports 36, 581-584; 1987. 12. Tobacco Institute, The Tax Burden on Tobacco; 1988. 13. B.L. Cohen, Health Physics 60, 631-642; 1991. 4 N fn O N i ~ ~ N i ~

Population characteristics PT- Total population PD- Population/square mile PI- % Pop. increase 1980-86 PU- % In urban areas PW- % white PS- males/100 females PE- % age > 64y PO- % age > 74Y PY- % 5-17 years old PN- % born in state PH- Persons/household Vital and health statistics VB- Births/1000 Pop. VC- % births to mothers < 20y VD- Deaths/1000 Pop. VI- infant deaths/1000 births VM- marriages/1000 Pop. VS- divorces/1000 Pop. VP- physicians/100,000 Pop. VH- hospital beds/100,000 Pop. Social SS- Social Sec. benefit/1000 Pop. SC- crimes/100,000 Pop. SH- % high school grad. SU- % college grad. SE- S/cap for education Housina HO- % owner occupied HA- % with > 1 automobile HV- median value (5) HN- % < 8 years old Economics El- $ per capita income EH- Median household inc., $ EJ- % persons below poverty level EV- % fam below poverty level EU- % unemployment EW- average salary, wage EP- $ per cap personal income EM- % earnings from manufact. ER- % earnings from retail trade ES- % earnings from services EG- % earnings from government EF- % earnings from farming EA- av. acres per farm EL- %mfg. firms > 100 emplys. ED- S/cap. sales - food stores EC- S/cap. sales - clothing EE- S/cap. sales - eating, drink Government GF- Federal govt., S/cap GL- Local govt., S/cap GE- % loc govt. expend. - educ. GH- % loc govt. expend. - health GP- % loc govt. expend. - police GW- % loc govt. expend. - welf GR- % foc govt. expend. - roads GJ- ioc govt. emplmt/10,000 Pop. GV- % vote for lead party, 1984 NP- num of measurements - PITT NE- num of measurements - EPA

1.40 1.20 til `~ 3rtl D e uar 1.00 0.80 0.60 ~ ~ iai 0 Theory : .' Male ~ . ' E • % \ . (C) Female ~ 3 j uartile Theory E r 1.20 Y 1~~~' /r 1 0.90 0.60 0.30 i 1 2 3 I 2 3 4 4 5 0 7 1 2 3 Mean radon fevel,r(pCiL-t) 4 5 5 e 6 Fig. 1: Lung cancer mortality rates vs mean radon level in homes for 1601 U.S. counties. 7 7 N tn O N .a ~ C1 N ~ 00

0.45 0.27 0.09 -0.09 -0.27 . ~ ~ . . ~ . f - ~ . . • . . • -0.45 -0.45 -0.27 -0.09 0.09 CORR-r 0.27 0.45 Fig. 2: CORR-m vs CORR-r for socioeconomic variables listed in Table 1.