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"Low Level Revision 1 1.2.6 1.2.6.2
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In consideration of the additive linear
model, r = ro + kD, Frigerio states: "There must be roughly equal distribution of radiogenic malignant mortalities among the 56 Mn types. At k = 3.2 and D = 5.1, this would lead to an excess national mortality of about 33,600/yr, i.e., about 10% of current experience. Spread over 56 Mn types, this corresponds to r ~ 0.3 per Mn type, i,e,, an expectation of about 54 radiogenic deaths per million population per Mn type for the 18-year period of observation. In order to run the gamut of proposed expectations, we first identified populations presenting at rates below 0.3 and 0.03, discriminated by sex, race, Mn type, and state of residence. The hope was that we would thus bracket some rate which the linear additive model would be easily tenable." "Although in cancer epidemiology, one would not usually consider expectations less than 5 or so, (Brownlee 1960) much less express them as decimals, this has been the practice in radiation carcinogenesis studies. (ICRP 1969; BEIR 72) Thus, we have allowed this practice at r = 0.3 or 0.03. At r = 0.003 we have used only a plus sign (+) to indicate that the value for t is mathematically real but less than 1. "With so many Mn sites violatingthe requirements of the model, even as judged simply by the normal "t" test, we had to admit that it was extraordinarily improbable, at least at these levels. So, we continued dropping our search value for r until, at 0.006, all of the observations went to zero except for those three stalwarts, ICD 151, 153 and 171. Since we thought we might have something here, we did our estimations on the basis of r = 0.003, the mid-value of the interval, rather than 0.006, its upper bound. "In this range level, the normal t test becomes awkward (Brownlee, 1960; Kendall, 1958). Thus, we resorted to the much more powerful, albeit lengthy and expensive, Monte Carlo method. (Shreider, 1966) Briefly the population of the U. S. was subjected to a random "rain" of radiocarcinogenci deaths at r = 0.003 for 100 18-year periods, and the results of each period analyzed as above. ...Ergo, not only is the null hypothesis (r = 0.003) improbable, but the Monte Carlo results suggest that a level of roughly 0.003/20 would be needed to reach even a 63% confidence level. This corresponds to about 16 deaths/yr per 200,000,000 population, or about 0.005% of current U. S. mortality. "In any case the model certainly seemed untenable at any level much greater than r = 0.003/20 = 1.5x10-4, at least as its authors originally presented it. In theory, we thought it might be saved ...confining higher expectations to 10 of the 56 types, even though these 10 corresponded poorly to those for which human radio-carcinogenesis had been shown. (BEIR 72) In practice, though, even this turned out to be improbable when we examined this unholy decade..." "As an aside, we might note that this sort of epidemiological approach possesses some peculiar advantages over less direct studies of radiation effects. For one thing it addresses itself directly to the population of interest, in this case that of the U. S. rather than to small. select populations of the war-torn (e.g., Hiroshima and Nagasaki), of the ill (e.g. , those irradiated for spondylitis, tuberculosis, thyroiditis, malignancies, thymic disorders, etc.), of the young (e.g., irradiation for tinea), or of the occupationally stressed (e.g., uranium miners). It may be noted, for example that even the smallest population groups in Table 1 are as large and usually much larger than these select irradiated groups. "Then, too, the time span of observation is large. Although we have deal only with an 18-year span here, the data can quite properly be regarded as an 18-year sampling of a continuing procession of cohorts which span the full biblical three score years and ten. And, of course, the radiation is being delivered over this entire time span, at the very rates of interest, an compounded, so to speak, for effects in utero, on the young, on the general population, and on the aged. "While each malignancy type at r = 0.003 is within its respective statistical expectation, the consistent string of zero observed deaths, over populations that range from tens of thousands to nearly ten million, is a bit unsettling." "Despite this heterogeneity, some socioeconomic bias exists in the U. S. data. Many of the 10 apocalyptic horsemen.., who refused to show significant groups below r = 0.3, appear less formidable when viewed in the light of worldwide malignancy mortalities. .. (T)he fact that cancer is a reportable disease in the Scandanavian countries (Ringertz 1971) with their remarkably complete registries, estiminates 163 entirely and produces some very low rates for 174 and for some of the ICD types included in 65... (T)he very low rates observed help to dispel the enticing, if mildly parochial, notion that the remaining 7 types somehow constitute "common" malignancies, while the 46 eliminatedble are rare. While these 7 do account for perhaps a third of total U. S. malignant mortality, (Burbank 1971) they hardly constitute important malignancies in other lands. Indeed, the only one of these to coincide with the BEIR list ( BEIR 72) of important radiogenic malignancies, ICD 151 [stomach], is dropping so linearly and rapidly in the U. S. that it bids fair to reach zero within the coming two decades. (Burbank 1971; Cowdry 1968) "If these are indeed valid, a goodly fraction of the total radiogenic insult must have been received by age 10 and a significant number of radiogenic mortalities should have appeared by age 30. However, this does not seem to be the case, ...Here we have isolated those national rates for which we had age-specific data, and for which R = O up to age 30 or beyond. Again, if these ten horsemen were truly riding to the beat of a radiogenic drum, they were certainly riding more slowly than predicted by the linear additive models so far proposed. "All in all, then, it appears that even the abandonment of polycarcinogenesis
would do little for the additive model, especially in the long run, and this model will
probably have to be abandoned in toto." |
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Figerio 1973
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