We may already note that if the disease is rare, then OR=RR. Indeed, for a rare disease, we will have formula_19 and so formula_20 but then formula_21 in other words, for the exposed population, the risk of developing the disease is approximately equal to the odds. Analogous reasoning shows that the risk is approximately equal to the odds for the non-exposed population as well; but then the "ratio" of the risks, which is RR, is approximately equal to the ratio of the odds, which is OR. Or, we could just notice that the rare disease assumption says that formula_22 and formula_23 from which it follows that formula_24 in other words that the denominators in the final expressions for the RR and the OR are approximately the same. The numerators are exactly the same, and so, again, we conclude that OR ≈ RR.