How do we know something causes cancer? Aren’t there essentially infinite variables it would be impossible to control for?
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Yes, but you can remove their Influence by looking at huge sample sizes. The law of the large numbers will make it unlikely you’re wrong UNLESS there is something cancer causing that heavily correlates with the thing you’re investigating.
For example:
In a sample of 10,000 users of cigarettes there was a 50,000% increase in lung cancer compared to non smokers. What kind of thing would be common to all those smokers that could cause such a big outlier if it isn’t the tobacco? Is there a shampoo that could cause lung cancer that only smokers use? Possible but very unlikely.
What you can’t do is a detailed analysis when things correlate too much. For example many weed smokers also smoke tobacco, so it’s very difficult to find out how much cancer smoking weed causes
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