Table 4.

Comparison of the exit probabilities between the proposed time-varying CP method with the four different β-spending functions and the fixed CP method at each interim analysis and the overall size based on 100,000 Monte-Carlo samples for data generated with p1 =p2 = 40%

Information time (t)	f1(t)		f2(t)		f3(t)		f4(t)		Fixed CP method with γ = 0.1
	k = 4	k = 9	k = 4	k = 9	k = 4	k = 9	k = 4	k = 9	k = 4	k = 9
0.1
Efficacy	–	0.000	–	0.000	–	0.000	–	0.000	–	0.000
Futility	–	0.001	–	0.079	–	0.040	–	0.018	–	0.000
0.2
Efficacy	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Futility	0.012	0.011	0.171	0.070	0.111	0.055	0.067	0.038	0.000	0.000
0.3
Efficacy	–	0.001	–	0.001	–	0.001	–	0.001	–	0.001
Futility	–	0.064	–	0.113	–	0.091	–	0.072	–	0.005
0.4
Efficacy	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002
Futility	0.184	0.126	0.184	0.078	0.168	0.105	0.171	0.094	0.044	0.038
0.5
Efficacy	–	0.004	–	0.004	–	0.004	–	0.004	–	0.004
Futility	–	0.141	–	0.080	–	0.097	–	0.097	–	0.118
0.6
Efficacy	0.010	0.007	0.010	0.007	0.010	0.007	0.010	0.007	0.010	0.007
Futility	0.285	0.104	0.171	0.077	0.222	0.086	0.200	0.126	0.305	0.192
0.7
Efficacy	–	0.009	–	0.009	–	0.009	–	0.009	–	0.009
Futility	–	0.119	–	0.069	–	0.108	–	0.084	–	0.187
0.8
Efficacy	0.017	0.010	0.016	0.010	0.017	0.010	0.017	0.010	0.017	0.010
Futility	0.183	0.073	0.125	0.060	0.136	0.068	0.180	0.100	0.352	0.170
0.9
Efficacy	–	0.010	–	0.010	–	0.010	–	0.010	–	0.010
Futility	–	0.080	–	0.050	–	0.053	–	0.085	–	0.129
1.0
Efficacy	0.021	0.013	0.021	0.012	0.021	0.012	0.021	0.013	0.022	0.013
Futility	0.287	0.227	0.300	0.269	0.313	0.242	0.332	0.232	0.248	0.106
Size	0.050	0.056	0.049	0.055	0.050	0.055	0.050	0.056	0.051	0.056