Projected fete cancer nsks @C E Lano er av from seven through 120 of Byg(a), 1€, 2[Le x Byi(@)] In thecase of thyroid cancer, that sum 1s 1 177% (the value for the US SEERpopulation) trmes the ratio of the ASW rate per 100,000 for native Hawanans to that for the US SEER population 1177% X110X757'=1 726% Supposmg an exposure at age 12 y and, therefore, survival until that age, the appropriate US life table for calculatmg lifetime excess risk 1s obtamed from Fig 6 by setting to one the probabilites of survival to ages 1 through 12 y and dividing each of the Fig 6 hfe table probabilities of survival to ages 13, 14, etc , by the Fig 6 probability of survival to age 12 y Then, using the revised fe table survival probabilties for subsequent ages, L(13), L(14), etc , the hfetme excess rate associ- ated with exposure at age 12 y 1s calculated as the sum over a = 13 through 110, ass [L(@) X Byala) X ERRyq(12, @)] Monte Carlo methods use pseudo-random numbers to generate realizations from eachof the assumed uncertamty distributions descnibmg particular uncertam components The randomly sampled values are mtroduced m the excess risk equations, and realizations of the excess numberof cancers are produced The collection of values for the excess numberof cancers, obtamed by repeating the process for many iterations, 1s analyzed to estrmate the mean, median, and uncertainty interval for the excess number of cancers The uncertamty distributions of several mput parameters used in the present analysis (eg, DDREF) are based partly on expert judgment regarding the appropriateness of the available data about that parameterfor the radiation exposures in the Marshall Islands, rather than strictly on statistical analysis of those data, and therefore the term “uncertamty mterval” 1s used mstead of “confidence interval” which mvolves only staustical uncertamty Given a sufficient number of iterations, Monte Carlo methods are accurate and, com- d4) Here, the notation ERRyq(12, 2) 1s required because of the tme-dependent, uncertam latent period discussed above under “Latent period ” In fact, the notation above 1s somewhat overly simplified because radiation dose varied by calendar year m each location, the above formulation should be understood as corresponding to a given calendar year as well In contrast to the BEIR VII dose-response models for leukema, stomach cancer, colon cancer, and the group of solid cancers other than thyroid and nonmelanoma skm cancer, ERR for thyroid cancer does not depend upon attamed age (Table 3) It does, however, depend uponlatent period, mcreasing from zero withm the first 2 y after exposure to tts full value 8 y after exposure A reasonable rough calculation, used here for illustration purposes, of hifetrme risk (excess absolute sk, or EAR) associated with a 004 Gy thyroid dose at age 12 y 1s obtamed by muloplymg ERR,q(12, 20), whichis distributed as lognormal with GM = 0 0805 and GSD = 3 40 (mean = 0170), by the ferme baseline risk at age 16 y, which 1s 1172% The product 1s lognormal with GM = 000094, GSD = 340, and mean = 00020 Computational approach Each factor used m the calculation of the excess number of cancers has an associated uncertamty, mclud- img radiation doses, parameter values of dose-response models, DDREF values and other adjustments of dose- related nsk The uncertainty of each component was described using probabihty distribution functions (e g , in Table 3), and Monte Carlo methods were used to prop- agate these uncertamties 209 pared to first-order analytical methods hike those used by the BEIR VII committee, have defimte practical advan- tages for handlmg any magmtude of uncertainty, distnbutions of any shape, and for dealmg with large numbers of correlated, uncertain parameters For this report, 200 estimates of radiation doses from external sources and 200 from mternal sources were generated for each of 25 population groups of Marshallese [including a Rongelap control group, see BNL (1958) for a discussion of control subjects], 24 atolls and islands where exposure took place, 23 calendar years of exposure, 100 possible exposure ages (treating anyone exposed at ages 100 y or older as havmg been exposed at age 99 y), and 5 target organs or groups of organs The details of the populations, atolls and islands, and exposure years are given m Simon et al 2010a,it should be noted that cancer risks are only estrmated for the Marshallese population, and, therefore, exclude the US military weather observers who were exposed at Rongertk External and mternal doses were assumed to be perfectly correlated within each combinationof place and year of exposure and were assumed to be uncorrelated between years and between atolls Similarly, 200 realizations were generated for the risk per umt dose for each possible combmation of sex, exposure age and subsequent attamed age, and cancer type The Monte Carlo estrmated doses and risks per umt dose were combed together with the number of mdividuals in each exposure age group, each sex, and eachatoll to obtain two hundred estimates of the predicted numberof cancers, from which means, medians, and 90% uncer- tamty mmtervals were generated for each cancer type and selected population The estrmated numbers of cancers were then summedto obtam totals for desired groups of