Drug-Combination Synergy Analysis

Decide whether a two-drug combination does more than expected (synergy), exactly as expected (additivity), or less (antagonism) — and pick the right reference model for the data you have.

"Synergy" only means something relative to a null model of additivity, and the models define additivity differently — so the first decision is which model, driven by what data you measured.

Step 0 — Pick the model by the data you have

You measured…	Use model	Tool	Input
Single effects of A, B, and A+B at one dose pair	Bliss	DrugSynergy_calculate_bliss	effect_a, effect_b, effect_combination (each a fraction 0–1)
Effects of A, B, A+B across several dose points	HSA	DrugSynergy_calculate_hsa	effects_a, effects_b, effects_combo (arrays)
Single-agent dose-response curves + one combination point	Loewe	DrugSynergy_calculate_loewe	doses_a_single/effects_a_single, doses_b_single/effects_b_single, dose_a_combo, dose_b_combo, effect_combo
Single-agent dose-response + combo point, want Chou-Talalay CI	Combination Index	DrugSynergy_calculate_ci	same as Loewe + assumption
A full dose × dose viability matrix	ZIP	DrugSynergy_calculate_zip	doses_a, doses_b, viability_matrix (% , 0–100)

Effects must be on a consistent inhibition scale. Bliss/HSA/Loewe expect fractional inhibition 0–1 (0 = no effect, 1 = complete kill). If your data is % viability, convert: inhibition = 1 − viability/100. ZIP takes the viability matrix in % directly. Mixing scales is the most common error.

Step 1 — What each model's "additivity" means

Model	Null (additive) expectation	Best when
Bliss independence	drugs act independently: E_exp = E_a + E_b − E_a·E_b	different mechanisms; quick single-point screen
HSA (highest single agent)	combo should beat the better single agent: E_exp = max(E_a, E_b)	conservative "does it beat monotherapy?" question
Loewe additivity	a drug combined with itself = additive (dose equivalence)	same/similar mechanism; needs dose-response
ZIP	combines Bliss + Loewe; potency shift of one drug's curve by the other	dose-matrix screens (the SynergyFinder default)
Chou-Talalay CI	CI<1 synergy, =1 additive, >1 antagonism (median-effect)	classic isobologram-style analysis with dose-response

There is no single "correct" model — state which one you used. Bliss and Loewe genuinely disagree for some combinations (that's expected, not an error); reporting two models (e.g. Bliss + HSA, or Loewe + ZIP) is good practice.

Step 2 — Run it

# Bliss (single dose pair, fractional inhibition)
tu run DrugSynergy_calculate_bliss '{"operation":"calculate_bliss",
  "effect_a":0.4,"effect_b":0.3,"effect_combination":0.7}'
# -> expected 0.58, bliss_synergy_score 0.12, "Strong synergy"

scripts/synergy_reference.py computes the Bliss, HSA, and Loewe-style expected combination effects side-by-side from one dose pair, so you can see at a glance whether the models agree before running the full tools.

Step 3 — Interpret the score

For Bliss/HSA/Loewe/ZIP, the synergy score is (observed − expected) (often ×100):

Score (fractional, ×100 scale)	Call
> +10	synergy
−10 to +10	additive (no meaningful interaction)
< −10	antagonism

For Combination Index (Chou-Talalay): CI < 1 = synergy, CI = 1 additive, CI > 1 antagonism (note the opposite direction — lower is more synergistic).

• A positive Bliss/HSA score means the combination exceeds the additive expectation at that point.
• Synergy is often dose-dependent — a combination can be synergistic at one ratio and antagonistic at another; for a matrix, report the synergistic region, not one number.

Step 4 — Gotchas (state these)

• Scale mismatch (% viability vs fractional inhibition) — convert first (Step 0).
• Effects near 0 or 1 (ceiling). If both single agents already kill ~everything, the combo can't show synergy (no headroom) — Bliss/HSA saturate; interpret with care.
• ZIP/Loewe/CI need real dose-response with ≥3 non-zero, measurable-effect dose points per drug, or the Hill fit fails (the tools say so).
• Model disagreement is normal — don't shop for the model that gives "synergy"; pre-specify the model and report it.
• A synergy score is not efficacy — a strongly synergistic combination can still be weak overall; report the absolute combination effect too.

Honest limitations

• These are reference-model synergy scores, not statistical tests — for confidence, replicate and report variability across the dose matrix.
• Synergy in vitro does not guarantee clinical benefit (PK/PD, toxicity, scheduling all matter).

Related skills

• tooluniverse-dose-response — fit the single-agent IC50/EC50 curves that Loewe/CI/ZIP need.
• tooluniverse-cell-line-profiling — look up pre-computed combination synergy (SYNERGxDB).
• tooluniverse-drug-repurposing / tooluniverse-network-pharmacology — rationale for combinations.