AaBbCcDdE AaBbCcDdEr AaBbCendEm A v Normal List Paragraph Coption Styles Dictate Editor Pane EMSE 6020 Decision Making Under Uncertainty Fall 2022, Midterm Name: 20 October 2021 Equation 2 -In 1 506 / a Where SMR = standardized mortality ratio The parameter, B, would have been estimated from an epidemiologist's study of workers experiencing occupational exposures to benzene. White, Infante, and Chu (1982) relied on two studies-one by NIOSH and one by Dow. They state "we have greater confidence in the risk estimates based on the NIOSH study and our discussion will focus on these risk estimates." Therefore, to calculate B, they recommend using the NIOSH estimate of the standardized mortality ratio, SMR, and also the weighted estimates of the benzene exposures experienced by workers in their study. Using the following inputs: SMR = 2100 Lower benzene dose estimate (ding) - 415 ppm-yr. Upper benzene dose estimate (drew) =1500 ppm-yx Po - 0.00707 for all types of leukemia White, Infante, and Chu computed the following range of B: Blower = 0.00370 and Buzes= 0.000102. You can use this model to estimate the excess cancer risk for a working lifetime exposure to benzene. For example, you could assume that "lifetime exposure" is only 10 years' worth of benzene exposure at the 10 prim standard (in 1982). This corresponds to d = 10 ppm * 10 yrs = 100 ppm-yr in Equation 1. You would then use Po and either Brower or Bugg to compute the excess risk associated with 10 ppm-yr exposure to benzene. 4) Use sensitivity analysis to explore the sensitivity of additional lifetime leukemia risk, Pa (in Equation 1), 7 Pe, B, and exposure level. Assume that Bowe and Bapps given above correspond to the best- and worst-case scenario for that variable. Further, assume that the best-case scenario for lifetime exposure is 10 ppan-y and that the worst-case scenario is 500 ppm-yr. Finally, assume that the worst-case Po is 0.100 and the best-case Po is 0.0010. a) Construct a table of your inputs and output for the worst-, base-, and best-case. b) Use one-way sensitivity analysis for the three variables indicated and prepare a tornado graph or spider plot (or three one-way graphs) to summarize your analysis. c) Discuss how your sensitivity analysis could be used to either. () prioritize additional refinement of the benzene model; or, it) support occupational benzene exposure mitigation decisions, Focus E MacBook Pro EX B I U % & * CA O > CO OAaBbCcDdE AaBbCCDdE AD BbCCDdBe Normal List Paragraph Caption Styles Dictate Editor Pane Case Study QUESTION 5: [40pts] In White, Infante, and Chu (1982) "A quantitative estimate of leukemia mortality associated with occupational exposure to benzene," Risk Analysis 2(3):195-204, the authors describe a model for estimating the risk of developing leukemia from occupational exposure. Their objective in publishing their analysis was to "stimulate interest and discussion on the methodology and assumptions which can be used when the underlying scientific evidence is less than ideal for the development of a quantitative risk assessment, in a scientific rather than a regulatory context." Background Questions 1) Based on Lecture 1, describe the ways the distinctions between the scientific and regulatory context that might influence the development of the risk estimate? 2) Would the occupational exposure to benzene be dominated by epistemic or aleatory uncertainty? a) Please explain your choice. b) Based on your choice, identify one specific uncertainty in that category and describe its impact on the characterization of the risk associated with the occupational exposure to benzene. 3) In class, we extensively studied the use of probability elicitation methods to characterize uncertainty through the elicitation of probability distributions. Yet, in White, Infante, and Chu (1982), we see that the risk model they constructed required the extensive use of extrapolation from other data sources and construction of complex assumptions. In no more than 3 paragraphs, describe how subjective probability elicitation could be related to risk model construction. Sensitivity Analysis White, Infante, and Chu (1982) selected a "one-hit model" for a quantitative risk assessment for benzene exposure. The one-hit model is based on an assumption that a single dose of a carcinogen can affect some biological phenomenon in the organism which subsequently will lead to the development of cancer. The one-hit model for the lifetime excess risk of developing leukemia from a given level of benzene is: Equation 1 Pa= [1 - exp(-B x d)] (1 -Po) Where: Pa = excess cancer risk at exposure to dose (d) of benzene Po = "background" cancer risk in the absence of exposure to benzene d - benzene exposure level and- Focus E - MacBook Pro EX B I U Lo % A 6 7 O