Joint likelihood for correlated observations O-1, O-2 (shared basis: S-12). Step 8 writes the single ## Likelihood block here; the member edges point back via group.
Likelihood
# CG-1 (HC-1) - ONE joint estimate over E-1 + E-2: O-1 and O-2 are two readouts of the same lipid
# panel in the same 17-subject Sacks 1984 crossover (shared data basis S-12), so they are priced as
# one pattern (rule 1), not as two witnesses. The pattern judged whole: at a very LOW baseline
# cholesterol intake (97 -> 418 mg/d), one egg/day for 3 weeks raised LDL-C 12% and ApoB 9%, while
# HDL-C, ApoA-I, ApoA-II, VLDL-C and TG did not move. Two features carry the discrimination: the
# SIZE of the LDL/ApoB rise, and its CONFINEMENT to the atherogenic fraction.
# A-1 (approved) is what lets the rise be read as caused by the egg at all; its own caveat is that
# a low-baseline vegetarian sample may show a larger fractional response than omnivores - which is
# precisely the thing H-8 predicts, so A-1 lifts H-8 rather than H-1.
# Anchored on H-1 = 1; the rest are ratios to it (rule 7).
lik_sacks_H1 = 1.0 # anchor: H-1 (large, CVD-relevant ApoB rise) predicts this pattern almost
# exactly - a double-digit LDL/ApoB rise from a single egg, isolated to the
# atherogenic particles. Nothing here is surprising under H-1.
lik_sacks_H8 = 0.85 # 0.85x as expected as under H-1. H-8 (real but saturating) predicts a small
# effect AT HIGH habitual intake; this experiment sits at 97 mg/d, the steep
# part of the curve, where H-8 predicts a LARGE fractional rise too. So the
# magnitude barely separates H-1 from H-8 in this study - the small markdown
# is only that 12% is at the upper end even of a steep-segment prediction.
# H-8 is equally silent-and-compatible on O-2's fraction confinement.
lik_sacks_H5 = 0.15 # 0.15x. H-5 (egg-matrix cholesterol poorly absorbed) predicts a much smaller
# plasma response than this at ANY baseline - a +12% LDL from ~320 mg/d extra
# is roughly what good absorption plus partial hepatic compensation gives.
# Not near zero: N=17 leaves room for the point estimate to overshoot a truly
# small effect, and lacto-vegetarian gut adaptation could raise absorption
# atypically. H-5 is near-silent on O-2, so O-2 adds little against it.
lik_sacks_H11 = 0.3 # 0.3x. Residual is unconstrained and could accommodate a 12% LDL rise, but
# O-2 bites here specifically: the main non-listed characterizations in play
# are "no material atherogenic-lipid effect" and "the effect runs through HDL
# functionality / particle size / TG rather than LDL-ApoB mass", and both are
# disfavoured by a clean isolated LDL-ApoB move with HDL, ApoA and TG flat.
# Kept well above zero (rule 3) - some unlisted mechanism could still produce
# an ApoB-only rise, and I do not know that none could.
t_sacks = 0.68 # cap = trust_score of S-12 = 0.78 (both observations, same source). Docked
# modestly below the cap for what sits between the raw panel and the stated
# observation: N=17 makes both the 12%/9% point estimates and, more sharply,
# the "unchanged" null in O-2 low-powered - underpowered nulls on HDL/ApoA/TG
# can read as confinement when a real smaller effect exists; and 1984 apoB
# immunoassays are less standardized than modern ones.
evidence("HC-1", ["O-1", "O-2"], [lik_sacks_H1, lik_sacks_H5, lik_sacks_H8, lik_sacks_H11], t=t_sacks)