Table 3.

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 power based on 100,000 Monte Carlo samples for data generated with p₁ = 40% and p₂ = 35%

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	–	0.000	–	0.047	–	0.022	–	0.010	–	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	0.004	0.004	0.088	0.036	0.052	0.027	0.028	0.017	0.000	0.000
0.3
Efficacy	–	0.003	–	0.003	–	0.003	–	0.003	–	0.003
Futility	–	0.023	–	0.056	–	0.041	–	0.029	–	0.001
0.4
Efficacy	0.012	0.009	0.012	0.009	0.012	0.009	0.012	0.009	0.012	0.009
Futility	0.075	0.054	0.096	0.044	0.081	0.051	0.083	0.041	0.012	0.011
0.5
Efficacy	–	0.017	–	0.017	–	0.017	–	0.017	–	0.017
Futility	–	0.078	–	0.042	–	0.053	–	0.052	–	0.045
0.6
Efficacy	0.045	0.027	0.045	0.027	0.045	0.027	0.045	0.027	0.045	0.027
Futility	0.158	0.057	0.099	0.044	0.125	0.049	0.100	0.068	0.132	0.089
0.7
Efficacy	–	0.034	–	0.034	–	0.034	–	0.034	–	0.034
Futility	–	0.080	–	0.043	–	0.073	–	0.051	–	0.122
0.8
Efficacy	0.071	0.038	0.070	0.038	0.071	0.038	0.071	0.038	0.071	0.038
Futility	0.132	0.051	0.084	0.038	0.090	0.048	0.115	0.070	0.254	0.136
0.9
Efficacy	–	0.041	–	0.039	–	0.040	–	0.041	–	0.041
Futility	–	0.061	–	0.035	–	0.041	–	0.065	–	0.167
1.0
Efficacy	0.085	0.046	0.082	0.044	0.084	0.045	0.085	0.046	0.086	0.046
Futility	0.418	0.376	0.424	0.403	0.440	0.380	0.460	0.381	0.387	0.211
Power	0.213	0.215	0.209	0.211	0.212	0.213	0.213	0.215	0.214	0.215