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Table 2.

Nomenclature terms of importance in this work for consideration of the risk due to toxicants in tobacco smoke

TermMeaningUnits
i A toxicant of interest (e.g., 1,3-butadiene, benzene, N-nitrosonornicotine, NNK, etc.) —
Ai Per cigarette smoke delivery (aka yield of toxicant iμg/cigarette
z Total smoking dose in pack-years pack-years
$$\mathrm{CDI}^{i}_{1}$$

Average (chronic) rate of daily intake of toxicant i by smoking when the total smoking dose is 1 pack-year and, in this work, when the dose is averaged over 70 y mg/kg d
$$\mathrm{CDI}^{i}_{\mathit{z}}$$

Average (chronic) rate of daily intake of toxicant i by smoking when the total smoking dose is z pack-years and, in this work, when the dose is averaged over 70 y mg/kg-d
CSFi Cancer slope factor for carcinogen i (also known as the cancer potency of i(mg/kg-d)−1
$$\mathrm{ILCR}^{i}_{1}$$

Incremental calculated lifetime cancer risk for carcinogen i for a z = 1 pack-year smoking dose risk for 1 pack-year
$$\mathrm{ILCR}^{i}_{\mathit{z}}$$

Incremental calculated lifetime cancer risk for carcinogen i for a smoking dose of z pack-years risk for z pack-years
$$\overline{\mathrm{ILCR}}^{i}_{1}$$

Average calculated value of the
$$\mathrm{ILCR}^{i}_{1}$$
for a given group of cigarettes of a certain type (e.g., the average for all light cigarettes)
risk for 1 pack-year
subΣ A subtotal for a specific subset of carcinogens —
subΣ-lung A subtotal for a specific subset of human lung carcinogens —
$$\mathrm{ILCR}^{\mathrm{sub{\Sigma}}}_{1}$$

A subtotal of individual calculated
$$\mathrm{ILCR}^{i}_{1}$$
for all carcinogens measured, with the smoking dose z = 1 pack-year
risk for 1 pack-year
$$\overline{\mathrm{ILCR}}_{1}^{\mathrm{sub{\Sigma}}}$$

Average value of calculated
$$\mathrm{ILCR}^{\mathrm{sub}{\Sigma}}_{1}$$
for a given group of cigarette brands of a certain type (e.g., the average for light brands)
risk for 1 pack-year
$$\mathrm{ILCR}^{\mathrm{sub{\Sigma}}{-}\mathrm{lung}}_{1}$$

SubΣ of individual calculated
$$\mathrm{ILCR}^{\mathit{i}}_{1}$$
for all human lung carcinogens that have been measured (analytically), for a z = 1 pack-year smoking dose
risk for 1 pack-year
$$\overline{\mathrm{ILCR}}^{\mathrm{sub{\Sigma}}{-}\mathrm{lung}}_{1}$$

Average value of calculated
$$\mathrm{ILCR}^{\mathrm{sub{\Sigma}{-}lung}_{1}}$$
for a given group of cigarette brands of a certain type (e.g., the average for light brands)
risk for 1 pack-year
$$\overline{\mathrm{ILCR}}^{\mathrm{obs{\Sigma}}{-}\mathrm{lung}}_{\mathit{z}}$$

Actual observed risk from smoking z pack-years risk for z pack-years
M Percent match between
$$\overline{\mathrm{ILCR}}^{\mathrm{sub{\Sigma}{-}lung}_{1}}$$
for conventional cigarettes and Ω1lung
RPREP Amount by which the calculatable per pack-year risk of lung cancer is reduced by switching from conventional cigarettes to a particular PREP
$${\Omega}^{\mathrm{lung}}_{1}$$

Observed total ILCRΣ−lung risk per pack-year for lung-cancer for z = 1 pack-year as averaged over all smokers and all smokers' doses in a particular real population (not a subΣ, but the full observed Σ) risk per pack-year
TermMeaningUnits
i A toxicant of interest (e.g., 1,3-butadiene, benzene, N-nitrosonornicotine, NNK, etc.) —
Ai Per cigarette smoke delivery (aka yield of toxicant iμg/cigarette
z Total smoking dose in pack-years pack-years
$$\mathrm{CDI}^{i}_{1}$$

Average (chronic) rate of daily intake of toxicant i by smoking when the total smoking dose is 1 pack-year and, in this work, when the dose is averaged over 70 y mg/kg d
$$\mathrm{CDI}^{i}_{\mathit{z}}$$

Average (chronic) rate of daily intake of toxicant i by smoking when the total smoking dose is z pack-years and, in this work, when the dose is averaged over 70 y mg/kg-d
CSFi Cancer slope factor for carcinogen i (also known as the cancer potency of i(mg/kg-d)−1
$$\mathrm{ILCR}^{i}_{1}$$

Incremental calculated lifetime cancer risk for carcinogen i for a z = 1 pack-year smoking dose risk for 1 pack-year
$$\mathrm{ILCR}^{i}_{\mathit{z}}$$

Incremental calculated lifetime cancer risk for carcinogen i for a smoking dose of z pack-years risk for z pack-years
$$\overline{\mathrm{ILCR}}^{i}_{1}$$

Average calculated value of the
$$\mathrm{ILCR}^{i}_{1}$$
for a given group of cigarettes of a certain type (e.g., the average for all light cigarettes)
risk for 1 pack-year
subΣ A subtotal for a specific subset of carcinogens —
subΣ-lung A subtotal for a specific subset of human lung carcinogens —
$$\mathrm{ILCR}^{\mathrm{sub{\Sigma}}}_{1}$$

A subtotal of individual calculated
$$\mathrm{ILCR}^{i}_{1}$$
for all carcinogens measured, with the smoking dose z = 1 pack-year
risk for 1 pack-year
$$\overline{\mathrm{ILCR}}_{1}^{\mathrm{sub{\Sigma}}}$$

Average value of calculated
$$\mathrm{ILCR}^{\mathrm{sub}{\Sigma}}_{1}$$
for a given group of cigarette brands of a certain type (e.g., the average for light brands)
risk for 1 pack-year
$$\mathrm{ILCR}^{\mathrm{sub{\Sigma}}{-}\mathrm{lung}}_{1}$$

SubΣ of individual calculated
$$\mathrm{ILCR}^{\mathit{i}}_{1}$$
for all human lung carcinogens that have been measured (analytically), for a z = 1 pack-year smoking dose
risk for 1 pack-year
$$\overline{\mathrm{ILCR}}^{\mathrm{sub{\Sigma}}{-}\mathrm{lung}}_{1}$$

Average value of calculated
$$\mathrm{ILCR}^{\mathrm{sub{\Sigma}{-}lung}_{1}}$$
for a given group of cigarette brands of a certain type (e.g., the average for light brands)
risk for 1 pack-year
$$\overline{\mathrm{ILCR}}^{\mathrm{obs{\Sigma}}{-}\mathrm{lung}}_{\mathit{z}}$$

Actual observed risk from smoking z pack-years risk for z pack-years
M Percent match between
$$\overline{\mathrm{ILCR}}^{\mathrm{sub{\Sigma}{-}lung}_{1}}$$
for conventional cigarettes and Ω1lung
RPREP Amount by which the calculatable per pack-year risk of lung cancer is reduced by switching from conventional cigarettes to a particular PREP
$${\Omega}^{\mathrm{lung}}_{1}$$

Observed total ILCRΣ−lung risk per pack-year for lung-cancer for z = 1 pack-year as averaged over all smokers and all smokers' doses in a particular real population (not a subΣ, but the full observed Σ) risk per pack-year

NOTE: For each ILCR value, a specific CDI is assumed. The units of each ILCR are “fractional risk.” For exposed individual, an ILCR = 0.001 indicates a 1 in 1,000 chance of cancer above the background risk.

*

Because a CSF is a slope of cancer incidence versus CDI, a CSF may alternately be viewed as having units of risk/(mg/kg d).

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