Why base rates matter
When a prosecution case alleges a rare mechanism repeated many times, base rates matter. If a mechanism is itself extraordinarily rare, the prior probability of any given case being an instance of that mechanism is low. Proving that case therefore requires correspondingly strong specific evidence. Proving that mechanism in a cluster requires correspondingly stronger cluster-level evidence.
This is not a bar to prosecuting rare offences. It is a principle of how the evidential weight must be structured. If the Crown alleges an unprecedented cluster of a rare mechanism, the specific evidence on each case has to be strong enough to compensate for the unusual base rate.
The base rate of deliberate neonatal air embolism
The peer-reviewed forensic-pathology and neonatology literature contains a small number of reported cases of deliberate neonatal air embolism worldwide, across decades. Most reported cases are isolated single events. A cluster of seven fatal deliberate air-embolism acts plus several attempts on one small neonatal unit over eighteen months has no precedent in the international medical-legal record.
The most-cited British historical case is Beverley Allitt (1991). Allitt was not principally an air-embolism case — her methods were insulin and potassium. No other UK case approaches the cluster density the Letby indictment alleges.
The prior-probability problem
On a straightforward application of Bayesian reasoning:
- Prior probability of deliberate neonatal air embolism at any given neonatal death: extremely low. Most neonatal deaths have identifiable natural causes; deliberate harm by any mechanism is vanishingly rare; deliberate harm by air embolism is rarer still.
- Likelihood of observing the clinical signs given deliberate air embolism: not specific — the Lee 1989 paper’s skin signs are the only published specific marker, and Dr Lee himself says the Letby descriptions do not meet them.
- Likelihood of observing the clinical signs given natural causes: high — non-specific mottling is routine in collapsing preterm infants from any cause (sepsis, NEC, thrombosis, cardiac failure, terminal shock).
On Bayesian terms, the probability of any given case being deliberate air embolism is low. Shifting that probability upward requires specific positive evidence — the Lee-1989-paper-level diagnostic signs, post-mortem imaging showing intravascular gas, or forensic-chain-of-custody-compliant histology. None of these is present in any Letby case.
The cluster-level base rate
Even setting aside the individual-case Bayesian calculation, the cluster-level question remains: how often does a single nurse on a single unit deliberately commit seven fatal air embolism acts plus several attempts in eighteen months? The international forensic-pathology and criminological literature contains no such cluster. The Letby case would be the single worst cluster of this kind on record anywhere.
This makes the prior probability of the Crown’s theory, on the base-rate question alone, approximately zero. It could still be true — extraordinary cases do occur — but establishing it requires correspondingly strong evidence. On the independent expert review, that evidence is not present.
The alternative hypothesis base rate
Now consider the alternative: a Level 2 NICU admitting extremely preterm and multiple-pregnancy infants beyond its design capacity, experiencing a multi-drug- resistant outbreak, with chronic staffing shortages and infrastructure failures, producing a cluster of deaths. The international NICU outcomes literature contains many examples of this pattern. The Morecambe Bay case is the closest UK precedent. Systems-failure clusters of this kind are the expected pattern, not the extraordinary one.
The two base rates compared
Base-rate for the Crown’s hypothesis: approximately zero, internationally unprecedented. Base-rate for the alternative hypothesis (systems-failure cluster on a struggling NICU): routine, documented in every UK and international NICU outcomes database. The Crown’s case therefore has to overcome a large base-rate deficit to be the more probable reading. On the independent expert review, it does not.