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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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