If Nothing Goes Wrong, Is Everything All Right? Interpreting Zero Numerators.¶
Hanley, J. A. (1983). If Nothing Goes Wrong, Is Everything All Right? Interpreting Zero Numerators. JAMA, 249(13), 1743-1745.
Cited by¶
2 citations across 2 artifacts.
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Primes¶
- Absence Of Evidence Vs Evidence Of Absence
- In drug and vaccine safety, a rare event observed zero times in N patients only constrains the true rate to roughly below 3/N, and that constraint depends on N, on exposure duration, and on the ascertainment apparatus, so "no signal" is not by itself evidence of safety.
This sourceDerives the rule of three: zero events in N observations bounds the true rate at roughly 3/N, the bound on which the worked drug-safety figures rest.
- In drug and vaccine safety, a rare event observed zero times in N patients only constrains the true rate to roughly below 3/N, and that constraint depends on N, on exposure duration, and on the ascertainment apparatus, so "no signal" is not by itself evidence of safety.
- Empirical No-Failure Anchor
- With zero events observed in n independent units, the one-sided ninety-five-percent upper bound on the underlying rate is approximately three divided by n, so ten clean units remain consistent with a failure rate near thirty percent while a hundred clean units narrow it to roughly three; the anchor level is identical in both cases and the claim differs by an order of magnitude.
This sourceDerives the rule of three, under which zero events in n units leaves rates up to roughly three over n consistent with the observation, and tabulates 0 of 10 as excluding only rates above about 26 percent.
- With zero events observed in n independent units, the one-sided ninety-five-percent upper bound on the underlying rate is approximately three divided by n, so ten clean units remain consistent with a failure rate near thirty percent while a hundred clean units narrow it to roughly three; the anchor level is identical in both cases and the claim differs by an order of magnitude.
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