How do you determine causation? (based on this example)
We know correlation is not causation.
Consider following example.
Let's say we observe that on average people who smoke, die earlier that those who don't.
This is correlation right?
But how do you design a study that would exclude that above correlation
exists because of following factor: people have a need to smoke because they have condition A,
condition A is what makes them die early.
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I think this question is too vague for a definite answer, but areas to consider would include:
confounding vs effect modifier: where do smoking and condition A lie in relation to the outcome of mortality?
matched pairs study: if it is ethical, you could get a simple random sample consisting of people with condition A that do not smoke and pair each individual in that sample with another individual in a simple random sample consisting of people with condition A that do smoke.
case-control study: this study design is useful for if condition A is a rare disease (note: not rare exposure; in that case you would use a cohort study). You would then adjust for confounding variables based on your study population.
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