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On being rare

The good news is that rare adverse events don't happen very often. The bad news is that rare events don't happen very often, and that the rare adverse events that we want to know about are bad, significant, and usually irreversible.

It is the rarity of rare events that makes them hard to identify, and it is harder still to measure their frequency with any accuracy. This issue of Bandolier looks at a number of examples of rare adverse events to explore the point. Examples come from cohort studies, from case-control studies, and from a long-term follow up of a randomised trial.

All share the same problem, that the number of events of interest is small, even in large studies. The number of cases of interest varied from eight to 24 in total, despite huge cohorts, or large numbers of cases in case-control studies. We find ourselves worrying about whether there are sufficient numbers to avoid chance findings.

How much we worry depends to some extent on how statistically significant an effect is. Large relative risks or odds ratios might be real despite small numbers. Small relative risks are more of a worry, especially when we find that biases can and do occur inobservational studies. Where relative risks or odds ratios are close to 1, unknown biases are likely make a difference, but not when they are far from 1.

Bandolier has no formula that can be applied universally to studies of rare events to tell whether a particular result is true or not. But it does have a rule of thumb it is working to perfect:

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