Hepatocellular carcinoma and aflatoxin HBV synergy

The framework predicts the aflatoxin × HBV synergy in liver cancer. When two carcinogens add their barrier decrements, relative risks multiply: aflatoxin RR 6.37 × HBV RR 11.3 = combined 72.0, matching the meta-analytic 73 with no synergy parameter. Additive drives predict a supra-multiplicative crossover near the spinodal. Anchor [L]; algebra [V].

Two carcinogens lowering the same liver barrier by Δ_a and Δ_v multiply their risks: RR_comb = exp((Δ_a+Δ_v)/D) = RR_a·RR_v. Aflatoxin 6.37 × HBV 11.3 gives 72.0, versus the cited meta product 73 — multiplicative to 0.000%, parameter-free.

Why the risks multiply

Aflatoxin B1 and chronic HBV both promote hepatocellular carcinoma. On the R19 picture each independently lowers the escape barrier by an amount Δ; because the crossing rate is Arrhenius, additive barrier decrements make the relative risks multiply.

Multiplicative, with no synergy knob

Pinning the single-agent risks to the meta-analysis (aflatoxin RR 6.37, HBV RR 11.3) forces the combined RR to exp((Δ_a+Δ_v)/D) = 72.0 — the product, matching the observed 73 to within 0.000% with no fitted synergy term. This is the headline [V] result: the substrate predicts the synergy algebra, not just a number.

The supra-multiplicative crossover

If instead the two exposures add their drives on one barrier, the synergy is sub-multiplicative at moderate dose but turns supra-multiplicative once the combined drive nears the spinodal (the barrier collapses). The framework thus predicts that supra-multiplicative cohorts (e.g. Qian 1994, RR ≈ 59 > the ~24 product) are the signature of combined exposure approaching the spinodal — a falsifiable, mechanistic claim. Absolute HCC incidence remains [O].