Table 1: Notations used in the present paper

Notation Parameter
p (Unknown) true response probability of the treatment
p0, p1 Probabilities that are deemed unpromising (p0) and promising (p1)
δ Effect size (δ=p1-p0 )
α, β Type I and II error probability
n, n1 Total sample size and sample size after the first stage of a two-stage design
r, r1 Rejection number at the end of a trial and after the first stage of a two-stage design
B( ; n, p) Binomial distribution function with parameters n and p
p0;min, p0;max Lower and upper bound of the acceptable range of p0
αmax, βmax Upper bounds for acceptable values of α and β
τ Step size for the discretized ranges of acceptable values of p0 , α and β
EN Expected sample size of a two-stage design
ε Small value of misspecification of the true p0
nε, rε Sample size and rejection number of a design where p0 is misspecified by ε
αε(p0) Probability of rejecting H0: p ≤ p0 + ε, given p=p0
βε(p0) Probability of not rejecting H0: p ≤ p0 + ε, given p=p1