What the analysis says
The cluster asks whether early controlled introduction of heated egg causally prevents egg allergy in high-risk eczema infants: H-10 - Early stepwise egg introduction causally prevents egg allergy in high-risk infants yes (induced oral tolerance) versus the constructed null H-46 - Early egg introduction does not causally prevent allergy (safe but non-causal). The single witness, CG-31 - HC-11 joint over O-20+O-21 (the PETIT RCT, trust 0.8) — confirmed egg allergy 8% vs 38%, RR 0.221, p=0.0001, with blinding and randomization leaving H-46 only a differential-dropout escape that O-21’s similar acute-event counts (15% vs 18%) bound — moved the prior [0.608, 0.392] to posterior [0.851, 0.149].
What the model may not capture
The verdict rests on one interim-stopped trial (n=121) in one narrow population, and H-46’s external-validity pole — non-generalizability beyond the eczema-controlled protocol — is by construction unable to lower the within-trial likelihood, so genuine doubt about transfer sits outside what the 0.851 can express.
What would help
Independent replication of PETIT in a broader infant population — exists, unread (later early-introduction egg trials, some null) to unclear.
Confusions and contradictions
None irreducible; the one live oddity — higher hospital admissions in the egg arm (10% vs 0%) — is consistent with real exposure under H-10 rather than a contradiction.