Predicting the Effects of Changes: Could Removing Arsenic from Tobacco Smoke Significantly Reduce Smoker Risks of Lung Cancer?

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.

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