Joint likelihood for correlated observations O-9, O-10, O-11, O-12, O-13 (shared basis: D-14). 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-31..E-35: all five Kadoorie endpoint associations rest on the same
# China Kadoorie cohort/FFQ (basis D-14), so they are ONE witness (rule 1), not five. The whole pattern: a
# graded, monotonic INVERSE dose-response across every CVD endpoint in a large Chinese cohort — total CVD 0.89,
# CVD mortality 0.82, IHD/MCE 0.86-0.88, ischaemic stroke 0.90, and strongest of all haemorrhagic stroke 0.74,
# all with tight CIs and P-trend <0.001, no visible high-intake uptick (ceiling category is "daily"). Members
# in HC-1.hypotheses order [H-6 protective, H-21 null, H-27 harm, H-44 U-shape, H-49 residual]. Anchored on
# H-6 = 1 (rule 7): a Chinese/Asian graded inverse is exactly what causal Asian protection predicts.
lik_kad_H6 = 1.0 # anchor: H-6 (causal protection in Chinese adults) predicts precisely a graded Asian inverse
# across endpoints — the tightest fit. A-3 (corrected) only bars exporting the aggregate to the
# West; it does NOT lower the fit of this China-internal pattern under H-6, so no dock here.
lik_kad_H21 = 0.45 # 0.45x: under a true null the inverse must be healthy-user/SES confounding (in China higher egg
# intake tracks higher SES/better health) — routine in nutritional epi and it readily makes HR
# ~0.85-0.9 graded signals, so quite plausible; docked below H-6 because a clean 5-endpoint
# dose-response with the extra-strong haemorrhagic-stroke arm (0.74) is a touch more coherent
# than pure confounding usually delivers.
lik_kad_H27 = 0.18 # 0.18x: monotonic egg-cholesterol HARM predicts the OPPOSITE sign; producing a strong graded
# inverse needs confounding not just to mask but to overturn a real harmful effect — a lot to
# ask. Worst fit of the five. H-27's US scope does not rescue it: a universal atherogenic
# mechanism should still not read as protective here.
lik_kad_H44 = 0.4 # 0.4x: the descending arm (never/rarely -> daily falling) matches the LEFT side of a U, and the
# missing high-intake uptick is hidden by the qualitative FFQ ceiling ("daily", no >1/day or
# >=10/week category), so H-44 is not refuted — but it does not specifically predict the
# haemorrhagic-stroke-dominant gradient, so below H-6.
lik_kad_H49 = 0.55 # 0.55x: a region-dependent-sign world (Asia inverse) predicts a Chinese inverse about as well
# as H-6 but is more diffuse (covers many shapes/regions), so slightly under the anchor;
# middling per rule 3, not extreme.
t_kad = 0.6 # cap = trust_score(S-80) = 0.60, the min over {O-9..O-13} (all one source). Left at the cap:
# the non-validated single-baseline qualitative FFQ, no >1/day category, and healthy-user
# confounding are already priced into 0.60; the confounding is a truth question (it lives in the
# H-21/H-6 ratio), not a data-reliability one, so it is not double-docked into t.
evidence("HC-1", ["O-9", "O-10", "O-11", "O-12", "O-13"],
[lik_kad_H6, lik_kad_H21, lik_kad_H27, lik_kad_H44, lik_kad_H49], t=t_kad)