Bayesian Shrinkage and Why Rare Events Need Special Handling

Rare events create a specific statistical problem that Lesson 7.3 touched on and this lesson unpacks more fully: with only a handful of reported cases, a raw disproportionality ratio can swing wildly based on one or two additional reports, making it an unreliable basis for a screening decision on its own. Bayesian shrinkage methods, which underlie both EBGM and IC, exist specifically to manage that unreliability without simply discarding rare-event data altogether.

The underlying idea is intuitive even without the statistics: an estimate based on very little data should be trusted less, and pulled closer to what’s typical across the whole database, than an estimate based on a large volume of consistent data. A drug-event pair with 3 cases and a PRR of 8 gets shrunk substantially toward the database-wide average in its EBGM calculation; a pair with 300 cases and the same PRR of 8 barely gets shrunk at all, because there’s enough independent data to trust the raw ratio on its own merits.

This is exactly why FAERS commonly screens using EB05 — the lower bound of a 90% Bayesian interval around the EBGM — rather than the EBGM point estimate itself. Using the conservative lower bound as the actual alert threshold means a pair only crosses into signal territory when the data supports it robustly, even after accounting for the uncertainty inherent in a small sample. It’s a deliberately cautious design choice, and it’s the direct statistical descendant of the same principle the forest plot in the previous lesson visualised: don’t trust a point estimate without also weighing how much uncertainty surrounds it.

None of this means genuine signals in rare events go undetected — it means they require either a strong enough effect size or enough accumulated cases to clear a deliberately conservative bar, which is exactly the tradeoff a well-designed screening system should make. A method that flagged every high ratio from a 2-case pair without shrinkage would generate an overwhelming number of false alarms; shrinkage is what keeps signal detection at scale from drowning medical reviewers in noise.