>"the lung cancer mortality rate has risen substantially between 1914 and 1968 among persons who never smoked cigarettes. For white males the relative increase for ages 35--84 years has been about 15-fold; the relative increase for ages 65--84 years has been about 30-fold." https://www.ncbi.nlm.nih.gov/pubmed/285289
Lung cancer in never smokers (2009) https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3170525/ shows the field in confusion. Radon, indoor air pollution, second-hand smoking are named as possible sources, but it's still not satisfactory.
But do you see why I didn't care if a correlation existed? There are a bunch of ways to explain such a correlation. That line of reasoning was based on the affirming the consequent fallacy[1]:
If
H: Nuclear tests are a significant factor in lung cancer rate O: We should still see a correlation between lung cancer incidence and nuclear test frequency [in non-smokers]
In terms of Bayes' Rule, I only care if p( O|H[0] ) dominates all the other possibilities (H[1:n]) in the denominator. The mere existence of a positive correlation isn't specific enough for me to care:
p( H[0]|O ) = p( H[0] )*p( O|H[0] )/sum( p( H[0:n] )*p( O|H[0:n] ) )
-Not sure what you mean by this, it is quite possible to deduce precise predictions from an epidemiological model. See, eg, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2007940/
>"it depends on whether observation is "specific enough" for you [is] unlikely to arise from other hypotheses, which in turn depends on your prior"
-This has to do with the likelihoods, p( O|H[i] ), not the priors: p( H[i] ).
>"[the prior] is informed by laboratory results in addition to field results"
- Yes
Re: laboratory results, it is noteworthy smoking and non-smoking lung cancer have different molecular signature. Lung cancer probably should be considered two separate diseases, and this probably overstates smoking connection because some lung cancer by smokers is of non-smoking kind and not caused by smoking. This can be better understood by including such signatures in epidemiological study.
Nevertheless, people commit that fallacy all the time in epidemiology. They say stuff like "if smoking caused cancer, then people who smoked would get cancer more often". Then if there is a (statistically significant) positive correlation between cancer and smoking, they conclude smoking causes cancer.
That is quite obviously affirming the consequent. I explain the (completely different and correct) probabilistic way to think about this situation using Bayes' rule in my post.
It has nothing to do with arbitrary cut-offs for telling us whether a correlation exists or not. Instead it requires comparing the relative performance of the various explanations (at least the top few candidates since extremely unlikely ones can be dropped from the sum in the denominator).
Saying smoking is a risk factor of cancer is very different from smoking causes cancer. As you said, you must consider alternative explanations. On the other hand, people can disagree about what alternative explanations are "extremely unlikely" and "can be dropped", that's what I meant by prior. For example, nuclear test causes cancer, is probably extremely unlikely.
Smoking being a risk factor of cancer is an evidence of smoking causing cancer. Being evidence of causal relation is completely different from being sufficient to prove causal relation.
Pick a paper, I bet they do.
Definitely, but if O had been false we might have learned something. More interestingly though:
> another thing to consider is fallout incorporated into tobacco and then smoked
That's an interesting thought, I'd never considered that.
My expectation for beta and gamma emitters is that they would be unlikely to cause cancer specifically in the lungs, because lungs aren't very dense and would have a pretty low interaction cross section for such penetrating radiation. For comparison, I-131 -- a beta emitter common in fallout -- is a significant risk for thyroid cancer only because iodine is biologically concentrated in the thyroid.
However, if there were significant fallout of alpha emitters, which were deposited in tobacco, this could conceivably deliver a significant localized dose to the lungs. Alpha emitters are more or less only dangerous internally, but smoke particulates that become lodged in the lungs could do the job. There appears to be a fair amount of literature on this -- Naturally occurring Po-210 is apparently still considered a danger today [1], and has been known to the cigarette companies since the 60s [2]. Some apparently comes from decay of natural U (via a few intermediaries) in phosphate fertilizer.
A figure in one paper I was able to find [3] suggests up to 100 pCi/kg Pu-239 and Pu-240 (both alpha) in leaves and grass in Finland circa 1963, declining to less than 5 pCi by 1967. The modern Po-210 alpha activity in tobacco appears to be much higher than either of these values (perhaps several hundred pCi/kg in dry tobacco, if not more), but I couldn't find good data on variation over time. For Pb-210 (beta) there is more data, but seems to be a lot of scatter and not so much of a clear trend through time [4].
[1] https://scienceblog.cancerresearchuk.org/2008/08/29/radioact... [2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2509609/ [3] https://www.osti.gov/biblio/5271041 [4] https://doi.org/10.1016/j.jenvrad.2011.01.005