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On tobacco products one can often see the statistic that nine out of ten lung cancers are caused by smoking but is this number accurate?

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I am sceptical about this stat for two reasons.

Firstly, if you compare cigarette consumption rates over time for the USA and Norway and compare them with male lung cancer rates you can construct the following chart. You can obtain cigarette consumption data for the US here and for Norway here and the cancer data for both countries from here.

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In the USA it looks like 9 out of 10 lung cancers could very well be caused by smoking but in Norway it looks very doubtful because there is an awful lot of lung cancer for comparatively few cigarettes smoked. In the US the cause (cigarettes) comes before the effect (lung cancer) but in Norway the cause (cigarettes), seems to come after the effect (lung cancer). Which does not back up the hypothesis that smoking causes 9 out of ten lung cancers very well in the case of Norway.

In addition to the curiosity of Norway there is another problem because in a country such as the USA millions of people have been encouraged to quit smoking over decades and lung cancer rates have gone down. But in former soviet union countries millions of people have not been encouraged to quit smoking and as a result per capita cigarette consumption has been stable in these countries to this day.

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So quite by accident, we have a massive experiment (billions of subject years) to see if encouraging millions of people over many decades to quit smoking makes any difference to lung cancer rates. It is arguably, I would guess, the biggest experiment into smoking and lung cancer ever. Here are male lung cancer for three countries the USA (population 325.7 million ), Russian Federation (population 144 million) and Ukraine (population 45 million).

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Clearly, male lung cancer has declined in these countries in the same way as in the US but without a preceding decline in smoking.

Secondly, in the US, according to the following National Health Survey , 17.9% of lung cancer occurs in never smokers, table reproduced below and original can be found here.

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In my mind, the figure of 17.9% of lung cancer that occurs in never smokers makes the nine out of lung cancers caused by smoking as untenable.

I would guess that to calculate this number all you really need to know is what percentage of the adult population are never smokers but I have found this number surprisingly elusive for the US. The closest I can find is in this study that states that in the US never smokers make up 22.2% of the population, current smoker 39.4%, former smoker 38.5%.

But this can not be right and I think the authors have swapped current smokers with never smokers and that the number of never smokers is really 39.4% and the number of current smokers is really 22.2%. This is quite unsatisfactory but I have found it easy to find numbers for current smokers but difficult to find numbers for never smokers.

So having given a few relevant epidemiological statistics (and hopefully interesting to readers) as to why the number of lung cancers caused by smoking may not be quite as high as nine out of ten my question is as follows:

Given the statistics that 17.9% of lung cancers occur in never smokers and never smokers make up 39.4% of a population how much lung cancer is really caused by smoking?

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    $\begingroup$ Cool question; nice to see someone put up a long argument like this; but a few questions. Your infographic comes from the UK, and you use US and Norway data, and additionally only male smoking numbers. $\endgroup$ – Azor Ahai -- he him Jun 8 '18 at 20:15
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    $\begingroup$ Aside from the many good answers that go into the specifics of the statistics used in epidemiology... another point is that your statistics are already outdated. The number of lung cancers among people that are (ex-)smokers has been increasing (especially among women) while the number of lung cancers among non-smokers is decreasing slightly. $\endgroup$ – Sextus Empiricus Jun 8 '18 at 23:21
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    $\begingroup$ In your comparison Russia-US you should look at the rate of lung cancer, not just mortality from lung cancer. It may very well be that the death rate has other influences than just the number of people that are smoking (for instance the state of health care and how well the doctors in a country can prevent mortality for people with cancer). $\endgroup$ – Sextus Empiricus Jun 9 '18 at 13:56
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    $\begingroup$ I have voted to close this question as too broad because in it's current form, as the question has been changed into a discussion after receiving sufficient clear and acceptable answers, it is unclear what the actual statistical question is. $\endgroup$ – Sextus Empiricus Jun 10 '18 at 17:08
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    $\begingroup$ I'm voting to close this question as off-topic because the addition of new (& not entirely relevant) lines of evidence about the risk of lung cancer from smoking after good answers addressing the statistical issues had already been provided implies that this isn't a statistical question, but a substantive one about the relationship between smoking & lung cancer. $\endgroup$ – gung - Reinstate Monica Jun 10 '18 at 18:14
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For the US data:

You are confusing two important but different concepts in epidemiology: prevalence and incidence. A Wikipedia page describes the difference.

The anti-smoking warning that you show says that 9 of every 10 lung cancers that occur are caused by smoking. That's the incidence of smoking-related lung cancers among all lung cancers that occur. Incidence has to do with how frequently in time cases of each type initially occur.

The Table 2 that you present, however, is for "age-adjusted prevalence" of smoking status among people who presently have each of the listed diseases. Prevalence has to do with the fraction of each type of case that is found at a given time. Of people currently having lung cancer, 17.9% have never smoked.

So why can't you say that "17.9% of lung cancer ... occurs in never smokers"? Because that's the prevalence of never smokers among those who are currently lung cancer survivors, not the fraction of all lung cancer cases that occur in never smokers.

There's a big difference between prevalence and incidence here because smokers tend to die of lung cancer (and of other cancers, or from other causes) more quickly than never smokers. So at any given time, never smokers will thus be a higher fraction of all lung cancer survivors (prevalence) than their fraction in the total numbers of original cases (incidence).

For the Norway data:

What you present for Norway isn't directly comparable to the US data in terms of the relation between the risk of lung cancer and tobacco use, as you only show the use of manufactured cigarettes. The reference for cigarette consumption in Norway that you cite shows high use of self-rolled cigarettes and of pipe smoking (Figure 1 in that reference), with manufactured cigarettes representing less than 30% of Norwegian tobacco use until about 1980. These other forms of tobacco use aren't included in your graph for Norway, but would nevertheless be related to risk of lung cancer. In contrast, 75-80% of US tobacco use between 1955 and 2005, from your cited reference, was manufactured cigarettes. So you have to be careful with selective comparisons of tobacco consumption data, as manufactured cigarettes are not the entire story.

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    $\begingroup$ It is also important to consider how the age adjustment is done. This could also change the numbers a bit if the older people, who have lots of cancer and smoke(d) a lot, are counted less strong due to some adjustment (it is not clear what the reference population is to which it has been adjusted but in case that it is some previous population or world population than there are less older people being counted). Age adjustment is not appropriate when a total number/fraction is desired. $\endgroup$ – Sextus Empiricus Jun 8 '18 at 23:17
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    $\begingroup$ @JBentley "A non-smoker's lung cancer can't be caused by smoking" - this is not correct. There's plenty of evidence for an association between second-hand smoke and lung cancer. $\endgroup$ – Geoffrey Brent Jun 9 '18 at 4:31
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    $\begingroup$ @JBentley see this review, with 1000+ references to the literature, for the biochemical and cell biological mechanisms by which smoking causes lung cancer. There is much experimental, not just epidemiological, evidence for causality here. The specific types of mutations ("signatures") in lung tumors from smokers (mutations that lead to cancer) are the same as those caused by treating cells with carcinogens found in smoke; see this recent paper. $\endgroup$ – EdM Jun 9 '18 at 5:37
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    $\begingroup$ @JBentley ...and that smoke is produced by people smoking. If the statement had been "90% of lung cancers are attributable to the patient's own history of smoking" that would be a different matter, but that's not what was said. $\endgroup$ – Geoffrey Brent Jun 9 '18 at 11:00
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    $\begingroup$ @JBentley For context, here is another cigarette warning label from the same campaign: i2-prod.mirror.co.uk/incoming/article5334198.ece/ALTERNATES/… Seems pretty clear that the campaign IS trying to warn smokers of risks to those around them, as well as the more direct risks. Not sure how that is misleading. $\endgroup$ – Geoffrey Brent Jun 10 '18 at 2:41
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What you're asking about is called the "Population Attributable Fraction"—the number of cases in the entire population that can be attributed to the exposure (in this case, smoking). The formula for this is:
$$ PAF = \frac{P_{{\rm pop}}\times (RR-1)}{P_{{\rm pop}}\times (RR-1)+1} $$

Here, $P_{{\rm pop}}$ is the proportion of exposed subjects in the population, and RR is the relative risk of developing the disease if you're exposed.

In the U.S., $P_{{\rm pop}}$ for smokers is $\approx 16\%$.

The RR for smoking is highly variable depending on what cancer you're talking about specifically, but using this document from the CDC, it appears the answer is $\approx 25$. So, $$ PAF = \frac{0.16\times (24)}{(0.16\times 24)+1} = \frac{3.84}{4.84} = 0.793 $$ So that estimate you've linked to, which is effectively $0.90$ as their PAF, is a little aggressive. Though as @EdM notes, with a higher prevalence due to the time between smoking and developing lung cancer, you can get to a PAF of $0.90$ relatively easily.

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    $\begingroup$ Note that there's about a 30-year lag between smoking and developing clinically detectable lung cancer, implicit in the plots versus time for US smoking and cancer. 30 years ago, adult smoking prevalence (P_pop) in the US was closer to 40%, which under your other assumptions would give a PAF of 0.9. $\endgroup$ – EdM Jun 8 '18 at 19:44
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    $\begingroup$ @EdM Added that at the end of the answer. Good catch. I mostly work in infectious diseases, which have a much lower latent period. $\endgroup$ – Fomite Jun 8 '18 at 19:46
  • $\begingroup$ @EdM Thanks for your responses, I am very grateful. The 30-year time lag is one of the things I was interested in because as far as I can see even if you add in total cigarettes for Norway there is no time lag to speak of. I can believe that cigarettes cause an epidemic of lung cancer 30 years later (as in the US) and I can believe that they could do so in the year of purchase as in Norway but I can not believe both are true! $\endgroup$ – Fredrik Eich Jun 9 '18 at 21:54
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    $\begingroup$ @FredrikEich As noted in one of the other answers here (I think in a comment), the Norway data may dramatically underestimate smoking, especially in the past periods. There may functionally be a lagged peak there that we can't see based on the consumption of non-manufacturered cigarette smoking. $\endgroup$ – Fomite Jun 9 '18 at 21:58
  • $\begingroup$ @Fomite I did actually add a chart for total cigarettes as per answer by EdM as I thought it was a very good point! $\endgroup$ – Fredrik Eich Jun 11 '18 at 21:22

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