Commonly used statistical models to evaluate drug
combination efficacy are the Bliss independence and
Loewe additivity models. Greco et al.4 have discussed
these two reference models in detail. Conceptually, the
Loewe additivity model focuses on dose reduction and the
Bliss independence model focuses on treatment effect
enhancement. The two reference models handle the same
question from two different perspectives. The Bliss independence
model has been criticized for its potential to
incorrectly claim synergy when two identical drugs are
combined (i.e., the “sham” experiment). But in reality, ethical
and economic constraints preclude “sham” testing of a
combination of two identical drugs to evaluate synergy in a
clinical setting. Furthermore, we find that Bliss independence
is legitimately derived from the complete additivity
of probability theory5 and serves well as a reasonable reference
model.
Suppose two drugs, A and B, both inhibit tumor growth:
drug A at dose a inhibits Ya percent of tumor growth and
drug B at dose b inhibits Yb percent of tumor growth. If two
drugs work independently, the combined percentage inhibition
Yab,P can be predicted using the complete additivity of
probability theory as