Pe is the probability of developing disease, among those exposed to the risk factor. The odds of disease in those exposed to the risk factor. The odds of disease in those not exposed to the risk factor. This is because the disease is rare so that 1-p is close to 1. For rare diseases the odds ratio can be used as a measure of the relative risk.
Cohort studies are expensive because for rare diseases a large sample is required.
The need for long follow-up means that a quick answer to the research question is not obtained. Case control study design can be more efficient for investigating rare diseases and provides a quicker answer. The results of case control studies are more likely to be influenced by bias. Identify cases of disease. Ideally all the cases in the population should be recruited because there may be a selection biases which influence attendance at hospitals.