From: “David MacLean”<david.maclean@I.hate.spam.com>
Subject: EPA Claim Revisited
Date: Monday, October 30, 2000 14:36
The EPA stated “ETS is a human lung carcinogen responsible for approximately 3,000 lung cancer deaths annually in the U.S. nonsmokers.”
The relative risk that they use is 1.19
The report was published in 1992. Most of the work was done in 1991, and the latest figures that they would have had to work from were from 1990.
Checking the figures:
| Smoking status rates (from NHSDA, 1990) | Male | Female |
|---|---|---|
| Current smokers | 28.4% | 22.8% |
| Former smokers | 30.3% | 19.5% |
| Never smokers | 41.3% | 57.7% |
| Calculate numbers | Male | Female |
|---|---|---|
| Population (from U.S. Census, 1990) | 94,755,000 | 102,292,000 |
| Current smokers | 26,910,420 | 23,322,576 |
| Former smokers | 28,710,765 | 19,946,940 |
| Never smokers | 39,133,815 | 59,022,484 |
| Male | Female | |
|---|---|---|
| Lung cancer deaths (Age >= 35, 1990, from CDC) | 91,685 | 52,064 |
| Relative risks for lung cancer (From CDC SAMMEC II) | Male | Female |
|---|---|---|
| Current Smokers | 22.4 | 11.9 |
| Former Smokers | 9.4 | 4.7 |
| Never Smokers | 1.0 | 1.0 |
The fundamental equation for calculating lung cancer deaths from risks is:
| NumDeaths = | BaseRate * NumNeverSmokers +BaseRate * RelativeRisk(Former) * NumFormerSmokers +BaseRate * RelativeRisk(Current) * NumCurrentSmokers |
|---|
We have everything for the above equation except the base rate.
Manipulating the equation algebraically results in:
| BaseRate = | NumDeaths /(NumNeverSmokers +RelativeRisk(Former) * NumFormerSmokers +RelativeRisk(Current) * NumCurrentSmokers) |
|---|
Filling in the figures and calculating results in:
| Relative risks for lung cancer (From CDC SAMMEC II) | Male | Female |
|---|---|---|
| Base Rate | 0.000100553 | 0.000120991 |
We can now calculate the expected number of lung cancer deaths by gender and smoking status:
| Male | Female | |
|---|---|---|
| Current smokers | 60,613 | 33,580 |
| Former smokers | 27,137 | 11,343 |
| Never smokers | 3,935 | 7,141 |
Q. In the EPA’s claim, does “non-smoker” mean “never-smoker” or “never-smoker AND former smoker”?
First, we can calculate the “new” lung cancer death base rate by the equation:
| EPABaseRate = | (Lung Cancer Deaths – 3000) / Total population |
If “non-smoker” means “never-smoker”, then that rate becomes:
| EPABaseRate = | ((3,935+7,141)-3000) / (39,133,815+59,022,484) |
| = | 8,076 / 98,156,299 |
| = | 0.00008227694 |
Since:
| Lung Cancer Deaths = | EPABaseRate * Unexposed Population + EPABaseRate * Relative Risk * (Total Population – Unexposed Population) |
|---|
We can manipulate the equation to give us the Unexposed Population:
| Unexposed population = | (Lung Cancer Deaths – EPABaseRate * Relative Risk * Total Population)/ (EPABaseRate – EPABaseRate * Relative Risk) |
For “non-smoker” meaning “never smoker”, the unexposed population can be calculated to be:
| Unexposed Population = | ((3,935 + 7,141) – 0.000082276794 * 1.19 *98,156,299)/(0.000082276794 – 0.000082276794 * 1.19) |
| = | (11,076 – 9610.44) / -0.000015632 |
| = | -93,753,838 |
Unfortunately for the EPA, a negative figure for the unexposed population is not physically possible. Therefore, “non-smoker” does NOT mean “never-smoker” alone. It can only mean, therefore, “never-smoker” + “former-smoker”.
Doing the same calculations again, using “never-smoker” + “former-smoker” as “non-smoker” results in:
| EPABaseRate = | ((27,137 + 11,343 + 3,935 + 7,141) – 3000) /(28,710,765 + 19,946,940 + 39,133,815 + 59,022,484) |
| = | 46,556 / 146,814,004 |
| = | 0.0003171087 |
| Unexposed population = | ((27,137 + 11,343 + 3,935 + 7,141) – 0.0003171087*1.19 * 146,814,004)/(0.0003171087 – 0.0003171087 * 1.19) |
| = | (49,556 – 55,401.64)/(-0.000060250) |
| = | -5845.64 / -0.000060250 |
| = | 97,023,071 |
Meaning, of course, that 97,023,071 / 146,814,004 = 66.1% of the non-smoking population is unexposed, leaving 33.9% of the non-smoking population (or 49,790,933) exposed to ETS sufficiently to produce “measurable” results.
But now that we have the proportion exposed, we can calculate the base rates for each of those groups (never-smokers and former-smokers) by way of the formula:
| Base Rate = | Lung Cancer Deaths /(Unexposed population +Relative Risk * Exposed population) |
For never-smokers, this works out to be:
| Base Rate = | (3,935 + 7,141) /(66.1% * (39,133,815 + 59,022,484) +1.19 * 33.9% * (39,133,815 + 59,022,484)) |
|---|---|
| = | 11,076 /(0.661 * 98,156,299 * 0.40341 * 98,156,299) |
| = | 11,076 / 98,156,299 * (0.661 + 0.40341) |
| = | 11,076 / (98,156,299 * 1.06441) |
| = | 11,076 / 104,478,546.21859 |
| = | 0.00010601219 |
The expected number of lung cancer deaths for never-smokers, in an “ideal” world (assuming that the model used is correct), where no never-smoker was exposed to ETS, would be:0.00010601219 * 98,156,299 = 10,406
However, in that group, there were 11,076 lung cancer deaths, so we can assume (if the model is correct) that
11,076 – 10,406 = 670
lung cancer deaths of never-smokers due to the exposure to ETS annually.
The number of lung cancer deaths of former-smokers due to SHS would therefore be3000 – 670 = 2,330.
But hold on just one minute, here. The relative risk ratios used by SAMMEC II were derived from studies which accounted for ALL the lung cancer deaths in each of the three groupings – never-smoker, former-smoker and current-smoker. Therefore, those 2,330 “additional” deaths of former smokers have already been counted.
So, what the EPA is really saying is that each year, 2,330 ex-smokers die of lung cancer, then are miraculously resurrected, only to die *again* from lung cancer.
