Optimality criteria for futility stopping boundaries for group sequential designs with a continuous endpoint

Table 1 Performance characteristics for the group sequential design with “optimal” futility boundaries based on different admissible condition parameters for N=182 and N=140. The last lines in the two sample size settings show the performance characteristics for the arbitrary choice of α₀=0.5

Sample	Admissible condition		“Optimal” futility	Actual	Probability of wrongly	Probability of correctly
size	parameters		boundary	power	stopping for futility	stopping for futility
n	Pow_loss	π_wrong	α_0,opt	under Δ=0.5	\(P_{\Delta _{\text {true}}=0.5}\left (p_{1}>\alpha _{0}\right)\)	\(P_{\Delta _{\text {true}}=0.25}\left (p_{1}>\alpha _{0}\right)\)	\(P_{\Delta _{\text {true}}=0.0}\left (p_{1}>\alpha _{0}\right)\)
188	0.01	0.01	0.46	0.90	0.01	0.13	0.54
	0.05	0.01	0.46	0.90	0.01	0.13	0.54
	0.01	0.05	0.29	0.89	0.03	0.26	0.71
	0.05	0.05	0.22	0.89	0.05	0.33	0.78
	0.01	0.10	0.29	0.89	0.03	0.26	0.71
	0.05	0.10	0.13	0.85	0.10	0.47	0.87
	0.0013	0.008	0.50	0.90	0.01	0.11	0.50
140	0.01	0.01	0.59	0.80	0.01	0.10	0.41
	0.05	0.01	0.59	0.80	0.01	0.10	0.41
	0.01	0.05	0.33	0.79	0.05	0.27	0.67
	0.05	0.05	0.33	0.79	0.05	0.27	0.67
	0.01	0.10	0.32	0.79	0.05	0.28	0.68
	0.05	0.10	0.21	0.77	0.10	0.41	0.79
	0.0013	0.018	0.50	0.80	0.02	0.15	0.50

ISSN: 1471-2288