Joint likelihood for correlated observations O-62, O-63, O-64, O-65, O-67 (shared basis: S-60). Step 8 writes the single ## Likelihood block here; the member edges point back via group.
Likelihood
# CG-27 (HC-9) — ONE joint estimate over E-28+E-29+E-30+E-44+E-45: all five observations are arms of the
# same Wilcox 2021 RCT (shared basis S-60), so priced jointly (rule 1). The whole pattern: 4 eggs/day x4wk
# leaves fasting TMAO flat (O-62) while choline was absorbed (O-65); free choline raises fasting TMAO ~6-fold
# (O-63) but phosphatidylcholine — egg-yolk's chemical form without the whole-egg matrix — does not (O-64);
# and egg white fails to suppress the choline-driven rise (O-67). A form-dissection signature. Members in
# HC-9.hypotheses order [H-28 form-governs, H-29 fasting-null, H-30 renal-only, H-42 real-postprandial-rise,
# H-43 benign, H-56 residual]. Anchored on H-28 = 1.0 (rule 7).
lik_wilcox_H28 = 1.0 # anchor / best fit: "chemical form, not total choline, governs TMA generation" is the
# ONLY member predicting the full contrast — free choline positive, egg + PC null,
# matrix (egg white) irrelevant. A-22 (approved) chains the four arm facts to isolate
# form as the operative variable; this pattern is its exact fingerprint.
lik_wilcox_H29 = 0.85 # egg fasting null (O-62) is precisely H-29's claim, so strongly consistent; priced just
# below the anchor because H-29 speaks only to the egg readout and does not itself
# predict the free-choline/PC form contrast (consistent with it, not entailing it).
lik_wilcox_H30 = 0.55 # 0.55x: the normal-renal null is what a renal-only-rise expects for this intact-
# clearance sample, and A-23 (approved) holds the null cannot extrapolate to impaired
# renal — so not discriminated against; but a 6-fold free-choline rise in the same
# normal-renal people shows clearance alone does not keep TMAO flat, and H-30 does not
# explain the form contrast, so below the fasting-null poles.
lik_wilcox_H42 = 0.35 # 0.35x: a chronic 4-egg/day dose leaving FASTING TMAO flat is evidence against "eggs
# raise TMAO production" as the best summary; not lower because Wilcox measures only
# fasting, leaving H-42's postprandial rise (the Miller pattern) an available escape.
lik_wilcox_H43 = 0.65 # 0.65x: a fasting null is consistent with a rise that is purely postprandial/benign
# (H-43 locates the rise off the fasting axis), but H-43 does not predict the
# free-choline/PC form contrast, so below the fasting-null and form poles.
lik_wilcox_H56 = 0.4 # 0.4x residual, kept real and middling (rule 3): a 4-week fasting null argues against
# its concrete reading (a chronic steady-state elevation in normal-renal people), and
# E-45 disfavours a matrix-inhibitor alternative, but an unlisted route is unconstrained.
t_wilcox = 0.72 # cap = min trust_score over {O-62,O-63,O-64,O-65,O-67}, all via S-60 = 0.72; kept at
# cap — the modest egg-arm n=18 is already priced into S-60's trust_score, and the
# far-from-threshold positive control (p<0.0001) shows the egg null is genuine, not underpowering.
evidence("HC-9", ["O-62", "O-63", "O-64", "O-65", "O-67"], [lik_wilcox_H28, lik_wilcox_H29, lik_wilcox_H30, lik_wilcox_H42, lik_wilcox_H43, lik_wilcox_H56], t=t_wilcox)