Two new formulae for evaluating effectiveness of drug combinations and revision of Bürgi's and Jin's modified Bürgi's formula
Abstract
We have made a theoretical analysis of Bürgi's and Jin’s modified formulae and proposed 2 new formulae:
1. q'=(EA+B-EB)EA to judge the resultant effectiveness of 2 drugs given together, EA=EB.
2. q''=E'C/EC to judge the resultant effectiveness of 2 drugs given successively. EC was the control effect of drug A and E'C was the control effect of drug A and E'C the effect of A after the administration of drug B.
In the perfusion experiments with rabbit, aorta, rat fundus and guinea pig vas deferens, PGE2+Ach and A+DA showed synergistic actions but A+NA showed only an “additive” action. Since the doses were gradually increased, the resultant effectiveness of PGE2+Ach or A+DA showed a course of synergism-assition-antagonism and that of A+NA gave a course of “addition”-antagonism, as judged by q' or/and q'' values.
It is suggested that, with increasing doses of a drug, the increment of its hetero-antagonistic potency can explain the occurrence of the above-mentioned developmental courses. The transition from synergism or addition to complete antagonism depends upon the hetero-antagonistic potency between the two drugs. The addition in the 1st course is a real one, but that in the 2nd course merely an approximate one.
Keywords:
1. q'=(EA+B-EB)EA to judge the resultant effectiveness of 2 drugs given together, EA=EB.
2. q''=E'C/EC to judge the resultant effectiveness of 2 drugs given successively. EC was the control effect of drug A and E'C was the control effect of drug A and E'C the effect of A after the administration of drug B.
In the perfusion experiments with rabbit, aorta, rat fundus and guinea pig vas deferens, PGE2+Ach and A+DA showed synergistic actions but A+NA showed only an “additive” action. Since the doses were gradually increased, the resultant effectiveness of PGE2+Ach or A+DA showed a course of synergism-assition-antagonism and that of A+NA gave a course of “addition”-antagonism, as judged by q' or/and q'' values.
It is suggested that, with increasing doses of a drug, the increment of its hetero-antagonistic potency can explain the occurrence of the above-mentioned developmental courses. The transition from synergism or addition to complete antagonism depends upon the hetero-antagonistic potency between the two drugs. The addition in the 1st course is a real one, but that in the 2nd course merely an approximate one.