Probability can be deceptive. The concept sounds easy to understand and we glibly use the ideas in everyday life but there are many subtleties involved. Given how important probabilistic ideas are in life, some have suggested that it be introduced into school mathematics curricula much earlier than it currently is and discussed in more depth.
One subtlety can be highlighted by this example. Suppose that you read about a new study that finds that by taking some measures, you can reduce the risk of stroke by 50%. Should you adopt those measures?
To make a decision you need to weigh the benefit against the costs, which in this case may be that the measures involve taking medications that have rather serious side effects, or that the regimen involved is arduous, or that it is very expensive. But even taking those into account is not enough to decide because you need to know another key piece of information and that is the absolute risk numbers.
The relative risk is what is usually reported and quoted in the media. It is obtained by comparing the results of the test group with the control group. So if the test group has five positive cases and the control group has ten, then the relative risk reduction is 50%. But this ignores the importance of sample size that determines the absolute risk. If the sample size had been 10,000, the absolute risk would have dropped from 0.1% to 0.05%.
Paula Byrne, one of the authors of a recent study on the benefits of taking statins to lower cholesterol, says that focusing only on relative risk does not give enough information to make an informed decision.
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