The remainder of the book applies principles from earlier chapters to several challenging quantitative risk assessment (QRA) problems for complex, uncertain, and nonlinear systems. This chapter returns to the problem of predicting how removing a specific constituent (arsenic) from a complex mixture (cigarette smoke) would affect lung cancer risks. This goes beyond the bounding and portfolio QRAs in Chapters 8 and 10 by applying the systems dynamics model in Chapter 11 to obtain explicit quantitative results. Rather than only estimating bounds for the probable changes in consequences, this chapter predicts specific quantitative reductions in risk, contingent on specified assumptions about causal mechanisms. Quantitative sensitivity analysis shows how predicted risk reductions (under stated assumptions) and preventable fractions of risk change as key assumptions are changed.
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Appendices
Appendix A: Listing for TSCE Model of Smoking and Lung Cancer
Intermediate_cells(t) = Intermediate_cells(t – dt) + (initiation + promotion – conversion) * dt
INIT Intermediate_cells = 0
INFLOWS:
initiation = mu1 s*Normal_cells
promotion = Intermediate_cells*es
OUTFLOWS:
conversion = mu2 s*Intermediate_cells
Malignant_cells_TSCE(t) = Malignant_cells_TSCE(t – dt) + (conversion) * dt
INIT Malignant_cells_TSCE = 0
INFLOWS:
conversion = mu2 s*Intermediate_cells
Normal_cells(t) = Normal_cells(t – dt) + (development – initiation) * dt
INIT Normal_cells = 0
INFLOWS:
development = if (TIME < 20) then (1E7/20) else 0
OUTFLOWS:
initiation = mu1 s*Normal_cells
e0 = 6.5E-2 {Schollberg, 2006, joint fit for males and females}
e1 = m1 {Schollberg, 2006, joint fit for males and females}
e2 = 1.19 {Schollberg, 2006, joint fit for males and females}
es = e0*(1 + fse1e2)
fse1e2 = e2*(1 – exp(–(e1/e2)*s))
fsm1m2 = m2*(1 – exp(–(m1/m2)*s))
m1 = 0.15 {Schollberg, 2006, joint fit for males and females}
m2 = 1.83 {Schollberg, 2006, joint fit for males and females}
Malignant_cells_TSCE_x_100 = Malignant_cells_TSCE*100
mu0 = 1.87E-7 {Schollberg, 2006, joint fit for males and females}
mu01 = mu0
mu02 = mu0
mu1 s = mu01
mu2 s = mu02*(1 + fsm1m2)
Appendix B: Listing for MSCE Lung Cancer Model with Field Carcinogenesis
F(t) = F(t – dt) + (fPF_new + net_births – fFM_new) * dt
INIT F = 0
INFLOWS:
fPF_new = P*muPF
net_births = muF*F
OUTFLOWS:
fFM_new = F*muFM
M(t) = M(t – dt) + (fFM_new) * dt
INIT M = 0
INFLOWS:
fFM_new = F*muFM
N(t) = N(t – dt) + (development_2 – fNP_new) * dt
INIT N = 0
INFLOWS:
development_2 = if (TIME < 20) then (100/20) else 0
OUTFLOWS:
fNP_new = N*muNP
P(t) = P(t – dt) + (fNP_new – fPF_new) * dt
INIT P = 0
INFLOWS:
fNP_new = N*muNP
OUTFLOWS:
fPF_new = P*muPF
bF = 0.08
bFM = 0.00008
bNP = 0.05
bPF = 0.00006
effective_internal_dose_s = (1 – exp(–0.1*s))/0.1
muF = (bF + qF*effective_internal_dose_s)
muFM = (bFM + qFM*effective_internal_dose_s)
muNP = if (TIME < 11) then 0 else (bNP + qNP*effective_internal_dose_s)
muPF = (bPF + qPF*effective_internal_dose_s)
qF = 0.0072
qFM = 0.0000176
qNP = 0.001
qPF = 0.000012
s = if ((TIME >= start_age) and (TIME < stop_age)) then x else 0
start_age = 20
stop_age = 60
x = 60
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Cox, L.A. (2009). Predicting the Effects of Changes: Could Removing Arsenic from Tobacco Smoke Significantly Reduce Smoker Risks of Lung Cancer?. In: Risk Analysis of Complex and Uncertain Systems. International Series in Operations Research & Management Science, vol 129. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-89014-2_12
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DOI: https://doi.org/10.1007/978-0-387-89014-2_12
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