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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 I CORR-r I 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 impiies 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 aeograohv It is well known that radon levels correlate strongly with geography'•'3, 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=-fi.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 0 3

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=-13.0 t 2.3 for males and B=-'! 4.4 t 2.7 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 'i 5-1 fi 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. NJ Effects of recognized r-S correlations L.M w ~ w ~ co

12 In our extensive studies of correlations with radon levels of house characteristics, locations, and socioeconomic factors", 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 mlmo vs r regression by less than 196. 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 BEfR-IV theory All calculations to this point, including our correction for smoking, have been carried out using the BEIR-IV theory8. 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. Unrecoanized confoundin factors It is logically possible that there is some unrecognized confounding factor (UCF) which is causing our discrepancy. Of course a UCF could invalidate my 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 0 N Ln 0 ~ ~ ~ ~ ~ , w a ~

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 a!l of these requirements to be essentially incredible, 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. 0

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. Hith. 72:1336-1344; 1983. 4. S. Greenland and H. Morgenstern, Int. Jour. of Epiderniol. 18:269-274; 1989. 5. S. Greenland and J. Robins, Am. Jour. of Epidemiol. (in press) 6. B.L. Cohen, lnt. 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. , 9 1. 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. .

Pooulation characteristics PT- Total population PD- Population/square mile PI- % Pop. increase i 980-86 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/i 000 Pop. VC- % births to mothers < 20y VD- Deaths/'1000 Pop. Vl- infant deaths/'! 000 births VM- marriages/'1000 Pop. VS- divorces/1000 Pop. VP- physicians/100,000 Pop. VH- hospital beds/7 00,000 Pop. Social SS- Social Sec. benefit/7 000 Pop. SC- crimes/'! 00,000 Pop. SH- % high school grad. SU- % coliege grad. SE- $/cap for education Housing HO- % owner occupied HA- % with > 1 automobile HV- median value iS) HN- % < 8 years old . Economics El- S per capita income EH- Median household inc., S 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- $/cap. sales - food stores EC- $/cap. sales - clothing EE- $/cap. sales - eating, drink Government GF- Federal govt., $/cap GL- Local govt., $/cap GE- % 1oc govt. expend. - educ. GH- % loc govt. expend. - health GP- % loc govt. expend. - police GW- % loc govt, expend. - welf GR- % loc govt. expend. - roads GJ- loc govt. empimt/9 0,000 Pop. GV- % vote for lead party, 1984 NP- num of measurements - PITT NE- num of measurements - EPA ; 3

%. 0 E ~ OS ... L 70 60 50 I 0 2 2 3 4 5 3 4 a 7 5 a 7 I 2 3 1 2 3 4 4 5 5 a Mean radon level,r(pCIL-') Fig. '! : Lung cancer mortality rates vs mean radon level in homes for 1601 U.S. counties. 7 7

. ~ . . . • • • . • • • a CO RR-r Fig. 2: CORR-m vs CORR-r for socioeconomic variables listed in Table N ~ ~ 5 ~ ~ ~ . ~ w 0