Joint likelihood for correlated observations O-20, O-21 (shared basis: D-7). Step 8 writes the single ## Likelihood block here; the member edges point back via group.
Likelihood
# CG-6 (HC-2) - ONE joint estimate over E-22 + E-23. Both observations come from S-11 / the PURE
# programme resting on D-7 (rule 1), so they are one witness, not two. The pattern judged whole is:
# a 21-country, 146k-participant, 14.7k-event cohort finds NO association on lipids, all-cause
# mortality or major CVD, AND its one deviating secondary signal (higher intake -> lower MI) fails
# to replicate in ONTARGET/TRANSCEND and is disowned by the authors. Read jointly this is a single
# clean null, NOT "a null plus a protective finding": the non-replication is part of the null.
# Members in HC-2.hypotheses order: [H-2, H-3, H-4, H-9, H-10, H-12].
# Anchored on H-10 = 1 (rule 7); others are ratios to it.
lik_pure_H10 = 1.0 # ANCHOR. PURE is exactly H-10's stated scope - diverse global populations across
# low/middle/high income - and reports nulls on precisely H-10's three endpoint
# families (lipids, CVD, mortality). This is the single most direct test of the
# broad-scope null that exists in this evidence set; the joint pattern (null +
# a spurious sub-signal that does not replicate) is what a true global null
# generates. Nothing else in the cluster predicts this pattern as tightly.
lik_pure_H4 = 0.55 # 0.55x. H-4 also says ~null, and its reverse-causation rider positively predicts
# the second half (apparent inverse signals turning out artefactual, which is
# exactly the ONTARGET/TRANSCEND non-replication). Docked because H-4's claim is
# scoped to ischemic heart disease and says nothing about all-cause mortality or
# lipids - two thirds of the observed null are outside what H-4 commits to, so it
# would have been unsurprised by a positive mortality signal here. Does not cover
# non-Western populations explicitly.
lik_pure_H9 = 0.40 # 0.40x. H-9 asserts a null only in generally healthy Western adults up to ~1/day.
# PURE is majority non-Western and mostly low-intake, so most of the observed
# pattern falls OUTSIDE H-9's scope: H-9 is compatible with it but does not
# predict it - a non-Western signal in either direction would leave H-9 intact.
# Lowest of the three null members for that reason (per the flagged scope-overlap
# issue: the spread across nulls is driven by whose scope PURE actually tests).
lik_pure_H2 = 0.12 # 0.12x. H-2 (moderate ~1/day protective on CVD) predicts a visible protective
# association on major CVD in a 14.7k-event cohort spanning 21 countries. It got
# none, and the one protective-looking signal (MI) failed external replication -
# the worst joint fit in the cluster. Not lower because PURE's egg intake is low
# in most regions, so the ~1/day contrast H-2 speaks to is thinly sampled.
lik_pure_H3 = 0.15 # 0.15x. H-3 (high intake raises all-cause mortality, esp. diabetics) predicts a
# positive mortality association; PURE's primary all-cause-mortality analysis is
# flat. Marginally above H-2 only because PURE has little high-intake exposure at
# all, so its power against the specifically HIGH-intake arm of H-3 is weak, and
# the diabetic subgroup is not what the primary analysis reports.
lik_pure_H12 = 0.45 # 0.45x. Residual / direction-varies (rule 3). Unconstrained members accommodate
# most patterns, and H-12 can absorb this one - a J-shape averaging to null across
# 21 heterogeneous countries is entirely possible. Docked below the null members
# because a genuinely direction-varying effect would be the likeliest of all to
# show heterogeneity SOMEWHERE across 21 countries and income levels, and PURE's
# regional analyses surfaced none that survived. Kept well clear of zero: an
# unmodelled or intake-dependent mechanism producing a flat global average is not
# something this observation rules out.
t_pure = 0.60 # cap = trust_score of S-11 = 0.8 (both observations share that source). Docked
# to 0.60 for weaknesses between raw data and the stated observation, per D-7's
# known_biases: diet from a single baseline FFQ varying by country and language
# (large non-differential misclassification, which biases toward the null - and a
# null is precisely what is observed here, so this is not a neutral flaw); low egg
# intake in most PURE regions leaving little high-intake contrast; residual
# confounding by region and income level. Not docked further because the endpoint
# ascertainment (14,700 adjudicated composite events) is the strong part.
evidence("HC-2", ["O-20", "O-21"],
[lik_pure_H2, lik_pure_H3, lik_pure_H4, lik_pure_H9, lik_pure_H10, lik_pure_H12],
t=t_pure)