The toxicity of an agent or the therapeutic effect of a drug may be as
sessed by a dose-response study. We present a method for computing the
exact power of exact and large sample statistical tests employed for
binary response data from such a study. This method, based on recursiv
e polynomial multiplications, enables fast computation of exact power
for studies with up to a moderately large sample size. We demonstrate
the efficiency of our method using three examples. The method is suita
ble for the design and power analysis of dose-response studies in whic
h the usual asymptotic approximations are suspect.