Designs for clinical trials with time-to-event outcomes based on stopping guidelines for lack of benefit

Table 4 Simulation results (50,000 replicates) for 3 three-stage trial designs with accrual rates (r _i) of (a) 250 and (b) 500 patients per year.

Design	Stage	α _i	ω _i	δ _i	e _i	t _i	N _i	α _i\|i-1		ω _i\|i-1
(a) r _i = 250
1	1	0.50	0.95	1.000	73	1.53	191	0.500	0.495	0.950	0.957
	2	0.25	0.95	0.923	140	0.74	283	0.441	0.452	0.969	0.971
	3	0.025	0.90	0.843	264	2.10	545	0.074	0.084	0.918	0.923
2	1	0.2	0.95	0.910	159	2.45	306	0.200	0.204	0.950	0.955
	2	0.1	0.95	0.885	217	0.55	375	0.427	0.432	0.976	0.978
	3	0.025	0.90	0.844	264	1.36	545	0.144	0.158	0.924	0.930
3	1	0.1	0.95	0.885	217	3.00	375	0.100	0.104	0.950	0.953
	2	0.05	0.95	0.869	272	0.49	436	0.423	0.431	0.980	0.981
	3	0.025	0.90	0.844	264	0.87	545	0.221	0.243	0.926	0.932
(b) r _i = 500
1	1	0.50	0.95	1.000	74	1.03	259	0.500	0.503	0.950	0.957
	2	0.25	0.95	0.923	141	0.46	374	0.441	0.447	0.969	0.971
	3	0.025	0.90	0.844	266	1.40	722	0.074	0.084	0.918	0.925
2	1	0.2	0.95	0.910	161	1.62	404	0.200	0.203	0.950	0.954
	2	0.1	0.95	0.885	220	0.33	487	0.427	0.439	0.976	0.979
	3	0.025	0.90	0.844	266	0.94	722	0.144	0.150	0.924	0.927
3	1	0.1	0.95	0.885	220	1.95	487	0.100	0.103	0.950	0.954
	2	0.05	0.95	0.869	275	0.29	559	0.423	0.433	0.980	0.982
	3	0.025	0.90	0.844	266	0.65	722	0.221	0.224	0.926	0.929

Median survival times are 1 year for the I-outcome and 2 years for the D-outcome. Hazard ratio is 1.0 under H ₀ and 0.75 under H ₁.
Key: i, stage; α _i, nominal significance level at stage i; ω _i, nominal power at stage i; δ _i, cut-off for HR--experimental arm passes to stage i + 1 (or, if i = s, is declared significant) if < δ_i; r _i, rate of patient accrual per year during stage i; e _i, cumulative number of control arm events required at end of stage i; t _i, duration (in years) of stage i; N _i, cumulative number of patients accrued to control arm by end of stage i; α _i|i-1, 'stagewise' significance level, i.e. significance level at stage i given that experimental arm has passed stage i - 1; ω _i|i-1, 'stagewise' power, i.e. power at stage i given that experimental arm has passed stage i - 1.

ISSN: 1745-6215