Table 4.

Operating characteristics of two-stage futility designs with the final sample size $N=100$

		Stage 1 Sample Size ${\mathit{N}}_{\mathbf{1}}\mathbf{=}\mathbf{30}$			Stage 1 Sample Size ${\mathit{N}}_{\mathbf{1}}\mathbf{=}\mathbf{50}$			Stage 1 Sample Size ${\mathit{N}}_{\mathbf{1}}\mathbf{=}\mathbf{70}$
Futility Threshold	Effectiveness Success Rate	Probability of Rejecting Null Hypothesis	Expected Sample Size ($\mathit{E}\mathbf{(}\mathit{N}\mathbf{)}$)	Probability of Early Termination ($\mathit{PET}$)	Probability of Rejecting Null Hypothesis	Expected Sample Size ($\mathit{E}\mathbf{(}\mathit{N}\mathbf{)}$)	Probability of Early Termination ($\mathit{PET}$)	Probability of Rejecting Null Hypothesis	Expected Sample Size ($\mathit{E}\mathbf{(}\mathit{N}\mathbf{)}$)	Probability of Early Termination ($\mathit{PET}$)
0.05	0.5	0.017	70.11	0.427	0.017	66.80	0.664	0.018	76.12	0.796
	0.55	0.116	84.18	0.226	0.117	80.75	0.385	0.12	85.06	0.498
	0.6	0.441	93.98	0.086	0.439	92.85	0.143	0.446	93.97	0.201
	0.65	0.818	98.32	0.024	0.817	97.95	0.041	0.829	98.74	0.042
	0.7	0.975	99.58	0.006	0.973	99.50	0.01	0.976	99.88	0.004
0.10	0.5	0.016	59.68	0.576	0.016	63.05	0.739	0.016	74.11	0.863
	0.55	0.114	76.48	0.336	0.115	76.45	0.471	0.117	82.00	0.600
	0.6	0.428	89.01	0.157	0.427	89.65	0.207	0.44	92.08	0.264
	0.65	0.799	95.31	0.067	0.810	96.95	0.061	0.826	97.93	0.069
	0.7	0.966	98.74	0.018	0.969	99.15	0.017	0.971	99.55	0.015
0.15	0.5	0.016	57.93	0.601	0.016	61.20	0.776	0.015	73.15	0.895
	0.55	0.110	73.61	0.377	0.114	74.40	0.512	0.115	80.56	0.648
	0.6	0.419	87.12	0.184	0.423	88.20	0.236	0.429	90.67	0.311
	0.65	0.795	94.47	0.079	0.806	96.60	0.068	0.817	97.27	0.091
	0.7	0.964	98.6	0.020	0.968	99.05	0.019	0.969	99.31	0.023

Note: Probabilities of rejecting null hypothesis of single-stage design with the final sample size of $N=100$ are 0.0185, 0.1344, 0.461, 0.8332, and 0.9793 when the effectiveness success rates are 0.5, 0.55, 0.60, 0.65, and 0.7, respectively