Simon’s like design with relaxed futility stopping

This program generates Simon's admissible two-stage designs (Simon, 1989; Jung et al., 2004) for Phase II single arm clinical trials with relaxed probability of stopping for futility (Ivanova and Deal, 2013).
The primary outcome is the probability of treatment response (TR), where treatment response is defined as complete response (CR) or partial response (PR), TR = CR + PR. The null hypothesis is that the TR rate is p_0T and the alternative is that the TR rate is p_AT. However, the trial is stopped for futility only if the number of patients with disease control (DC) is less than or equal to stage 1 futility boundary, where disease control is defined as DC = TR + SD, with SD denoting stable disease. The trial is also stopped for futility if the number of TRs in stage 1 is such that it is impossible to reject H₀ after stage 2, that is, if the number of TRs is less than r₂ - (n - n₁).
The user needs to input lower and upper bounds for the probability of stable disease, p_S^L and p_S^U , 0 ≤ p_S^L ≤ p_S^U ≤ 1 - p_AT. We assume that p_S ~ Uniform(p_S^L, p_S^U).
The optimal design minimizes the expected sample size under H₀, that is, given p_0T and over the distribution of p_0S.
The design guarantees the type I error rate not exceeding α for given p_0T and p_S^U, and required power for given p_AT and p_S^L.
When p_S^L=p_S^U=0 the design is equivalent to the Simon's two-stage design.