In a cohort type study one selects samples of subjects based on their exposure status (exposed or not) and then measures and compares the incidence (probability) of a particular outcome in each exposure group.
We can then estimate of the strength of association by computing the risk ratio, i.e., the ratio of the probabilities in the exposed and unexposed groups.
In the hypothetically cohort study summarized on the right, the probability of the outcome in the exposed group 7/1007 = 0.00695134, and the probability of the outcome in the unexposed group is 6/5640 = 0.00106383. Therefore, the risk ratio is 0.00695134/0.00196383 = 6.5343, suggesting that the risk is 6.5343 times greater in the exposed group.
In addition to computing the probability of the outcome in each exposure group, one can also compute the odds of the outcome in each exposure group. The odds of an event is the ratio of (# of events occurring) / (# of events not occurring) during a given number of trials. In the example, the odds of the event occurring in the exposed group are 7/1000 = 0.007, and the odds of the event occurring in the non-exposed group are 6/5634 = 0.00106496. The strength of association with the exposure can also be estimated from the odds ratio, which is 0.007/0.001064963 = 6.5730.
In this case, the odds ratio is a very good approximation of the risk ratio, because the event is rare, and the odds of the event occurring in a given group are similar to the probability of the event occurring. However, this becomes increasingly less true when the outcome is more frequent.
Use the table below to observe how the odds and probabilities change as you make the outcome more common.