association obtained from a case-control study, can be used to estimate the odds ratio of the outcome, given exposure, which is usually the question of interest.
To see how this works, suppose that we now conduct a case-control study in the population in order to estimate the association between gun ownership and suicide. We might do this by selecting all 100 suicides that occurred during the study year, and by drawing a random sample of 100 control subjects who did not commit suicide during the study year. The results of the case-control study might be as follows:
Even though the control group in the case-control study now contains only 100 subjects, we have selected these subjects so that they are representative of the frequency of exposure to firearms in the population of nonsuicides from which the control sample was drawn. So the odds ratio for our case-control study is:
Prospective studies can measure the frequency of the outcome among persons with different levels of exposure; retrospective case-control studies measure the frequency of exposure among persons with different levels of the outcome. But the symmetry of the odds ratio allows us to estimate the risk of the outcome, given exposure, from information about the odds of exposure, given the outcome.
In fact, by themselves, neither the odds ratio nor the risk ratio can assist policy makers who need to compare the number of occurrences that could be altered through intervention with the costs of the intervention. Policy makers would prefer to know the attributable risk, which can be defined as the difference between the incidence of the outcome among the exposed and the incidence of the outcome among the unexposed: