Table 5.

Comparison between the proposed two-stage optimal design with survival endpoint and Simon’s two-stage optimal design with binary endpoint with or without interim accrual, when α=5%, β=20%, and the shape parameter k=0.5 in the Weibull distribution

						Simon’s two-stage optimal designs
		Survival endpoint				No interim accrual				Interim accrual
S0(tc)	S1(tc)	n 1	n	E S S 0	E T S L 0	n 1	n	ESS0(%)	ETSL0(%)	ESS0(%)	ETSL0(%)
0.1	0.2	26	72	45.1	2.2	30	89	50.8 (11%)	3.3 (35%)	67.6 (33%)	3.0 (27%)
0.1	0.25	15	37	24.0	2.2	18	43	24.7 (3%)	3.1 (29%)	34.9 (31%)	2.8 (22%)
0.1	0.3	10	23	15.0	2.2	10	29	15.0 (0%)	3.1 (29%)	21.6 (30%)	2.8 (21%)
0.6	0.7	66	179	109.2	2.7	53	173	91.4 (-20%)	3.3 (18%)	124.0 (12%)	2.9 (9%)
0.6	0.75	27	76	46.1	2.6	27	67	39.4 (-17%)	3.2 (18%)	53.9 (14%)	2.9 (10%)
0.6	0.8	15	41	25.1	2.5	11	43	20.5 (-23%)	3.1 (17%)	28.9 (13%)	2.8 (7%)

% is for the ESS₀ or the ETSL₀ percentage saving of the new proposed two-stage design as compared to Simon’s two-stage design, which is computed as (Simon-New)/Simon. When the percentage saving is positive, the new design requires a smaller ESS₀ or a shorter ETSL₀ as compared to the existing Simon’s design

The patient accrual rate θ is determined by the sample size from Simon’s minimax design with no interim accrual as θ=n_minimax/3