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Table 1 Characteristics of theoretical models describing mixtures

From: Theory of synergistic effects: Hill-type response surfaces as ‘null-interaction’ models for mixtures

   Assumptions Properties
Approach Eq. u max Slopes γ Pure a.i. limit Sham compliance
Bliss / Colby 13 Unequal γ a γ b Ok No
Loewe / CA 14 Equal γ a =γ b Ok Yes
GCA 18 Unequal γ=1 Ok Yes
Chou exc 19 Equal γ a =γ b Ok Yes
Chou nonex 20 Equal γ a =γ b Ok No
Greco 17 Equal γ a γ b a (Ok)b (Yes)b
Minto / Fidler 21 Variable Variable (Ok)c (Yes)c
Hill 5, 7 Variable Variable Ok Yes
  1. aanalytical expression for the effect only for identical slopes
  2. bfor α=0
  3. cif the polynomial expansions are truncated after the linear terms