H-10 - Early stepwise egg introduction causally prevents egg allergy in high-risk infants
The causal, generalizable claim the trial’s measured effect supports: introducing (rather than delaying) heated egg induces oral tolerance and prevents allergy in the high-risk eczema population.
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H-46 - Early egg introduction does not causally prevent allergy
Constructed complement: the logically-required null pole no curated paper states, making the allergy-prevention question a two-answer space. It is the member favoured if the PETIT effect were an artefact of selection or differential dropout rather than induced oral tolerance.
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Carving
The sub-question is whether early controlled egg introduction causally prevents egg allergy in high-risk eczema infants. Two exhaustive answers: a true tolerogenic prevention effect (H-10) or no causal prevention - safe and tolerated, but the reduced incidence is not itself the causal effect (H-46, constructed). One or the other holds, so exhaustive_by_construction is set and no residual is needed. Analysis-failure mode: if the trial’s large risk reduction (confirmed egg allergy 8% versus 38%) were driven by differential dropout of already-reacting infants or by the concurrent eczema-control co-intervention rather than by induced oral tolerance, the analysis would favour H-10 when H-46 is correct - the failure favours the constructed null. H-46 is minted as the complement no curated paper states.
Prior
# HC-11 prior -- does early controlled egg introduction CAUSALLY prevent egg allergy in high-risk (eczema) infants?
# Members in HC-11.hypotheses order:
# [H-10 early stepwise heated-egg introduction CAUSALLY prevents egg allergy (induced oral tolerance),
# H-46 early introduction is safe/tolerated but does NOT causally prevent allergy (the reduced incidence is
# non-causal: differential dropout of already-reacting infants, the concurrent eczema co-intervention,
# or protocol-bound non-generalizability)].
# exhaustive_by_construction: true, exactly 2 members, NO residual (rule 4 does not apply).
# No no-observation arguments exist for this cluster (no_observation_arguments.py --cluster HC-11 -> none).
# Evidence split: NO inbound edge is marked used_for_prior. Both edges are the PETIT trial itself -- the
# confirmed-allergy 8% vs 38% result (O-20, E-5) and the acute-reaction/admission pattern that bounds the dropout
# artefact (O-21, E-7), together CG-31 -- and both DISCRIMINATE H-10 vs H-46, so they are left for step 8. The
# prior rests on the OUTSIDE VIEW from the broader early-allergen-introduction literature (independent of PETIT,
# which postdates the meta-analysis cited below), before the PETIT result is read.
# H-10 -- causal tolerance induction. Reference class: the post-LEAP early-introduction paradigm. LEAP (peanut)
# showed an ~81% relative reduction in peanut allergy with early introduction (Du Toit et al., NEJM 2015), and a
# meta-analysis of early EGG introduction found a protective effect on egg allergy at moderate certainty.
egg_meta_rr = 0.56 # RR 0.56 (95% CI 0.36-0.87) for egg allergy with egg introduction at 4-6 mo, moderate certainty; per Ierodiakonou et al., JAMA 2016 (pre-PETIT, independent of O-20)
# An RR<1 whose CI excludes 1 is moderate-certainty evidence the effect is real, but "moderate certainty" plus a
# mixed egg-trial base (several null/complicated egg-introduction RCTs, and real reaction-at-introduction risk)
# leaves genuine doubt whether the meta-analytic effect is causal tolerance induction vs artefact/non-generalizable.
p_causal_given_metaeffect = 0.62 # credence the protective egg-introduction signal reflects genuine causal tolerance induction in high-risk infants (H-10)
w_causal = p_causal_given_metaeffect # H-10
# H-46 -- safe but non-causal. Argued on its OWN terms (not as 1 - w_causal) so a skeptic can override it
# independently: base rate that a moderate-certainty prevention signal for a high-risk-only protocol proves
# artefactual (differential dropout of already-reacting infants) or fails to generalize beyond the
# eczema-controlled regimen. Kept non-trivial by the mixed egg-introduction replications.
p_noncausal = 0.40 # own estimate of the artefactual / non-generalizable pole (H-46)
w_noncausal = p_noncausal # H-46
prior("HC-11", [w_causal, w_noncausal])