Admissible two-stage designs for phase II cancer clinical trials that incorporate the expected sample size under the alternative hypothesis

Two-stage studies may be chosen optimally by minimising a single characteristic like the maximum sample size. However, given that an investigator will initially select a null treatment effect and the clinically relevant difference, it is better to choose a design that also considers the expected sample size for each of these values. The maximum sample size and the two expected sample sizes are here combined to produce an expected loss function to find designs that are admissible. Given the prior odds of success and the importance of the total sample size, minimising the expected loss gives the optimal design for this situation. A novel triangular graph to represent the admissible designs helps guide the decision-making process. The H₀-optimal, H₁-optimal, H₀-minimax and H₁-minimax designs are all particular cases of admissible designs. The commonly used H₀-optimal design is rarely good when allowing stopping for efficacy. Additionally, the δ-minimax design, which minimises the maximum expected sample size, is sometimes admissible under the loss function. However, the results can be varied and each situation will require the evaluation of all the admissible designs. Software to do this is provided.