i ee a Risk = da(2Risky + apdFishy + gc(dEsky | (2) The terms in parenthesis are the partial derivatives of risk with respect to a, b or c. b and c. We assumed the partial derivatives were constant’ over the ranges of a, For our purposes Eq. 2 reduces to A Risk , da , 4b , Ac Risk b a c (3) We do not know the actual uncertainty Ma, Ab or Ac, however, we know the standard deviation, 0, which is characteristic of the probable uncertainty. Bevington (Be69) develops the use of standard deviation to estimate the uncer- _— . tainty with the result that for our application ORisk a’ da? ~% Sb +o ay) Here we have assumed the fluctuations in a, b and c are uncorrelated. Eq. 4 to Eq. 1 yields go. Risk -,2 Risk * go* a a gt% b go 2 (4) Applying . c 2 12. 2 b ¢ (5) The standard deviation in the number of effects, 0,, was assumed to be equal to the square root of the number of excess nodules, a= 30. that is, 9, 7 5.5 and Thus the relative standard deviation equals 0.18 (i.e. d,/a = 0.18). This is in fair agreement with the fact that out of 48 persons undergoing surgery for nodules only 44 had nodules. undetected. In the reverse sense nodules could have gone The standard deviation in the number of years at. risk, O,, was taken as equal to the standard deviation associated with the mean years at risk, which we reported in Table 25. Thus, 0, equals 5.5 years and 0,/c equals 0.30. The standard deviation in absorbed dose to the thyroid, Oy, was estimated from the standard deviations associated with 1) the urine result,.2) the L3ly ine take estimate, 3) the absorbed dose from 131 and 4) the ratio of !311 dose to total thyroid dose. Each of these was assigned a relative standard deviation equal to 0.7. i ue a — C2 The assigned value of 0.7 for each of the relative standard devigfions of 1 through 4 above was based on the following. The observed value for “Sr urine activity was nearly 0.7 (Le84). This uncertainty in urine activity excreted is largely from two sources, the measurement technique and the day-to-day metabolism changes in adults. It was assumed that the relative standard deviation associated with 2%sr activity in urine applied to 131y activity in urine as well. The uncertainty associated with transforming a urine result into an intake estimate comes from uncertainty in the true excretion function for iodine in adults and from not knowing the true time of intake. Assigning a relative atandard deviation of 0.7 was thought to be conservative. The uncertainty ay - 66 =