Table 2.

Number of events (d) and sample sizes (n) were calculated from formulae (3) and (4) for various of hazard ratios (δ) under the Weibull distribution, with nominal type I error of 0.05 and power of 80%, 85%, and 90%. The empirical type I errors $(\widehat{\alpha })$ and powers $(1-\widehat{\beta })$ were estimated based on 100,000 simulation runs.

Power	Design		κ = 0.5			κ = 1			κ = 2
	δ−1	d	n	$\widehat{\alpha }$	$1-\widehat{\beta }$	n	$\widehat{\alpha }$	$1-\widehat{\beta }$	n	$\widehat{\alpha }$	$1-\widehat{\beta }$
90%	1.2	258	415	0.051	0.904	338	0.051	0.901	285	0.049	0.902
	1.3	125	205	0.051	0.903	166	0.052	0.902	139	0.049	0.901
	1.4	76	128	0.052	0.904	103	0.051	0.904	85	0.049	0.900
	1.5	53	90	0.053	0.907	72	0.051	0.904	59	0.050	0.901
	1.6	39	68	0.052	0.905	54	0.052	0.902	44	0.049	0.900
	1.7	31	54	0.052	0.904	43	0.052	0.906	35	0.050	0.903
	1.8	25	45	0.055	0.908	36	0.052	0.908	29	0.049	0.905
	1.9	21	38	0.054	0.902	30	0.052	0.904	24	0.049	0.900
	2.0	18	33	0.054	0.903	26	0.053	0.903	21	0.050	0.903
85%	1.2	217	349	0.051	0.854	284	0.051	0.853	240	0.049	0.852
	1.3	105	172	0.051	0.854	140	0.051	0.856	116	0.049	0.852
	1.4	64	107	0.054	0.856	86	0.051	0.855	71	0.050	0.853
	1.5	44	75	0.053	0.855	60	0.052	0.856	49	0.049	0.853
	1.6	33	57	0.054	0.858	46	0.051	0.860	37	0.050	0.853
	1.7	26	46	0.053	0.861	36	0.052	0.856	29	0.049	0.854
	1.8	21	38	0.053	0.861	30	0.052	0.861	24	0.049	0.855
	1.9	18	32	0.054	0.858	26	0.052	0.865	20	0.050	0.851
	2.0	15	28	0.055	0.859	22	0.053	0.859	17	0.049	0.848
80%	1.2	186	300	0.052	0.806	244	0.051	0.805	206	0.050	0.806
	1.3	90	148	0.052	0.805	120	0.051	0.807	100	0.048	0.805
	1.4	55	92	0.051	0.806	74	0.052	0.807	61	0.049	0.803
	1.5	38	65	0.052	0.808	52	0.052	0.811	43	0.050	0.812
	1.6	28	49	0.055	0.809	39	0.052	0.810	32	0.048	0.808
	1.7	22	39	0.053	0.809	31	0.052	0.810	25	0.049	0.808
	1.8	18	33	0.054	0.818	26	0.053	0.818	21	0.049	0.815
	1.9	16	28	0.055	0.816	22	0.053	0.816	17	0.048	0.801
	2.0	13	24	0.056	0.813	19	0.053	0.814	15	0.048	0.809