. Author manuscript; available in PMC: 2017 Oct 4.

Published in final edited form as: Clin Trials. 2008;5(2):93–106. doi: 10.1177/1740774508089279

Table 4.

Operating characteristics of additional examples using Simon’s two-stage designs and the PP design with type I and type II error rates of 0.10

	Simon’s Minimax/Optimal Two Stage Design⁺						Predictive Probability Design

P₀/p₁	r1/n1	r/N_max	PET(p₀)	E(N\| p₀)	α	β	θ_L	θ_T	r/N_max	PET(p₀)	E(N\| p₀)	α	β
0.1/0.3	1/16	4/25	0.52	20.37	0.095	0.097	0.001	[0.782,0.911]^*	4/25	0.79	19.99	0.096	0.095
	1/12	5/35	0.66	19.84	0.098	0.099	0.001	[0.855,0.942]	5/29	0.86	21.98	0.062	0.099
							0.001	[0.838,0.933]	5/30	0.85	23.25	0.072	0.081
							0.001	[0.821,0.924]	5/31	0.83	23.94	0.082	0.068
							0.001	[0.804,0.913]	5/32	0.81	25.42	0.093	0.054
							0.003	[0.786,0.902]	5/33	0.81	23.50	0.100	0.056
							[0.037,0.046]	[0.767,0.890]	5/34	0.84	19.96	0.099	0.069
							0.001	[0.879,0.949]	6/35	0.89	26.01	0.054	0.070
							0.001	[0.866,0.942]	6/36	0.87	26.75	0.061	0.059
							0.001	[0.852,0.934]	6/37	0.86	28.16	0.070	0.048
							0.001	[0.838,0.926]	6/38	0.85	29.14	0.078	0.040
0.2/0.4	3/19	10/36	0.46	28.26	0.086	0.098	0.001	[0.852,0.922]	10/36	0.86	27.67	0.088	0.094
	3/17	10/37	0.55	26.02	0.095	0.097	0.011	[0.830,0.908]	10/37	0.85	25.13	0.100	0.084
							0.001	[0.876,0.935]	11/39	0.88	29.24	0.073	0.092
							0.001	[0.857,0.923]	11/40	0.86	30.23	0.086	0.075
							0.003	[0.837,0.910]	11/41	0.85	30.27	0.100	0.062
							0.043	[0.816,0.895]	11/42	0.86	23.56	0.099	0.083
0.3/0.5	7/28	15/39	0.37	34.99	0.094	0.100	0.001	[0.859,0.918]	16/42	0.86	32.47	0.096	0.083
	7/22	17/46	0.67	29.89	0.097	0.095	0.001	[0.881,0.932]	17/44	0.88	33.50	0.081	0.088
							0.001	[0.858,0.916]	17/45	0.86	34.84	0.098	0.069
							0.048	[0.834,0.899]	17/46	0.87	25.11	0.099	0.092
							0.001	[0.880,0.929]	18/47	0.88	35.70	0.083	0.073
							0.001	[0.858,0.914]	18/48	0.86	37.33	0.100	0.056
0.4/0.6	11/28	20/41	0.55	33.84	0.095	0.099	0.001	[0.868,0.923]	20/41	0.87	31.07	0.096	0.098
	7/18	22/46	0.56	30.22	0.095	0.100	0.001	[0.875,0.927]	21/43	0.88	32.12	0.091	0.093
							0.001	[0.882,0.930]	22/45	0.89	33.65	0.086	0.087
							[0.024,0.025]	[0.854,0.911]	22/46	0.87	27.33	0.100	0.084
							0.001	[0.889,0.934]	23/47	0.89	35.00	0.082	0.082
							[0.010,0.011]	[0.862,0.915]	23/48	0.87	31.58	0.099	0.068
0.5/0.7	11/23	23/39	0.50	31.00	0.098	0.099	0.001	[0.869,0.925]	23/39	0.87	29.15	0.100	0.095
	11/21	26/45	0.67	28.96	0.096	0.098	[0.019,0.020]	[0.863,0.920]	24/41	0.88	25.39	0.100	0.091
							0.001	[0.892,0.939]	25/42	0.90	30.82	0.082	0.097
							0.037	[0.858,0.915]	25/43	0.88	24.39	0.100	0.091
							0.001	[0.887,0.934]	26/44	0.89	32.48	0.087	0.082
							0.060	[0.852,0.910]	26/45	0.88	24.31	0.099	0.087
0.6/0.8	18/27	24/35	0.82	28.47	0.097	0.100	0.001	[0.885,0.939]	25/36	0.89	25.51	0.090	0.089
	6/11	26/38	0.47	25.38	0.097	0.096	[0.042,0.046]	[0.864,0.924]	26/38	0.88	21.65	0.099	0.081
							0.001	[0.889,0.940]	27/39	0.89	27.73	0.088	0.075
							0.001	[0.909,0.952]	28/40	0.91	27.43	0.071	0.088
							0.026	[0.869,0.926]	28/41	0.88	24.65	0.100	0.062
0.7/0.9	11/16	20/25	0.55	20.05	0.091	0.902	[0.001,0.011]	[0.884,0.953]	20/25	0.89	16.42	0.091	0.098
	6/9	22/28	0.54	17.79	0.099	0.090	[0.103,0.133]	[0.860,0.937]	22/28	0.88	15.73	0.100	0.077
							0.001	[0.883,0.949]	23/29	0.89	19.55	0.093	0.064
							0.001	[0.903,0.959]	24/30	0.91	19.64	0.077	0.073

⁺

The first row represents Simon’s minimax two-stage design and the second row represents Simon’s optimal two-stage design.

The numbers within the bracket indicate a closed interval with both endpoints included.