Table 2:

The characteristics for optimal two-stage design with restricted follow-up x = 1, 2 under Weibull (WB), log-normal (LN), gamma (GM) and log-logistic (LG) distributions with nominal type I error 5%, power of 80%, accrual rate r = 10. Overall empirical type I error and power for the two-stage designs were estimated from 10,000 simulated trials.

Dist.	Shape	S 0	δ	x	t 1	c 1	c	n 1	n	$\widehat{\alpha }$	$1-\widehat{\beta }$
WB	0.5	.3	.65	1	3.71	0.169	1.631	38	63	.039	.796
		.3	.65	2	3.25	0.109	1.632	33	53	.038	.803
	1	.3	.65	1	3.76	0.141	1.629	38	63	.039	.796
		.3	.65	2	3.01	−0.042	1.635	31	46	.038	.813
	2	.3	.65	1	3.74	0.068	1.629	38	63	.039	.797
		.3	.65	2	2.88	−0.180	1.639	29	41	.037	.821
LN	0.5	.3	.65	1	3.84	0.110	1.628	39	63	.040	.801
		.3	.65	2	2.93	−0.160	1.638	30	42	.038	.818
	1	.3	.65	1	3.78	0.143	1.629	38	63	.040	.800
		.3	.65	2	3.12	0.046	1.632	32	48	.038	.810
	2	.3	.65	1	3.74	0.178	1.631	38	63	.040	.799
		.3	.65	2	3.25	0.098	1.631	33	54	.038	.804
GM	0.5	.3	.65	1	3.71	0.151	1.631	38	63	.040	.801
		.3	.65	2	3.13	0.055	1.633	32	50	.038	.808
	1	.3	.65	1	3.76	0.141	1.629	38	63	.040	.800
		.3	.65	2	3.01	−0.042	1.635	31	46	.037	.813
	2	.3	.65	1	3.72	0.084	1.629	38	63	.040	.801
		.3	.65	2	2.96	−0.109	1.637	30	43	.038	.815
LG	0.5	.3	.65	1	3.71	0.196	1.631	38	63	.040	.800
		.3	.65	2	3.33	0.102	1.632	34	57	.039	.803
	1	.3	.65	1	3.75	0.165	1.630	38	63	.040	.800
		.3	.65	2	3.29	0.084	1.633	33	52	.038	.805
	2	.3	.65	1	3.86	0.168	1.628	39	63	.040	.800
		.3	.65	2	3.12	0.045	1.632	32	47	.037	.810

S₀ is the survival probability at x₀ under the null hypothesis; δ is the hazard ratio; x is the restricted follow-up period; t₁ is the calendar time for the first-stage interim analysis; c₁ and c are the boundaries for the first-stage and final analysis; n₁ and n are the sample sizes for the first-stage and final analysis; Abbreviations: Dist.: distribution.