This link says
In epidemiological terms, the odds ratio is used as a point estimate of the relative risk in retrospective studies.
I understand that odds ratio is calculated in case control studies, while relative risk is calculated in cohort studies. Calculating incidences and risks in case control studies doesn't make sense because we ourselves are choosing the ratio of cases and controls which is never how it happens in nature. But it is usually taught that, odds ratio gives an estimate of this.
Why is this so?
Best Answer
It is not true in all situations. The odds ratio only gives an estimate of the relative risk if the outcome is a low probability outcome. (Same insight as Poisson approximation to the binomial distribution).
Imagine a case-control study for lung cancer, then we check the number of smokers in both groups. Technically, the only thing we can test is given that an individual has lung cancer, what is the probability that they smoke. We can do the same for the non cancer group, and obtain a ratio of the both probabilities. This would be the relative risk. But we do not really care about this quantity. We actually want, given that an individual smokes, what is the probability that they have lung cancer divided by the same probability for non-smokers.
The nice thing about the odds ratio is that it is bi-directional. So: the odds of smoking given lung cancer divided by the odds of smoking given control is actually equivalent to the odds of lung cancer given smoking divided by the odds of lung cancer without smoking. This bi-directionality of the odds ratio allows us to obtain the comparison we want from case-control studies.
Now, if we know the outcome to have a low rate in both groups $-$ the proportion of individuals with lung cancer is small among smokers and non-smokers $-$ then the odds ratio approximates the relative risk. This is the one time we can use the odds ratio to approximate the relative risk in case-control studies. I'm assuming that in case-control studies, the cases are rare events. So certain persons may skip this caveat and state what the OP stated.
The best resource I've found for questions like the one here is Agresti's book on Categorical Data Analysis.