Looking at the final expression for the OR: the fraction in the numerator, formula_25 we can estimate by collecting all the known cases of the disease (presumably there must be some, or else we likely wouldn't be doing the study in the first place), and seeing how many of the diseased people had the exposure, and how many did not. And the fraction in the denominator, formula_26 is the odds that a healthy individual in the population was exposed to the childhood injury. Now note that this latter odds can indeed be estimated by random sampling of the population—provided, as we said, that the prevalence of the exposure to the childhood injury is not too small, so that a random sample of a manageable size would be likely to contain a fair number of individuals who have had the exposure. So here the disease is very rare, but the factor thought to contribute to it is not quite so rare; such situations are quite common in practice.