Table 4.

Results using the Braun and Gumbel copulas for data simulation under Scenario 3

Data	ψ k	Model			Dose
			Futility	1	2	3	4
Braun	0	Braun	0.195	0.001	0.004	0.045	0.755
				3.426	3.636	5.358	27.504
		Gumbel	0.174	0.001	0.005	0.042	0.778
				3.459	3.744	5.418	27.855
		Indep	0.149	0.001	0.003	0.035	0.812
				3.384	3.69	4.938	29.169
	0.4	Braun	0.162	0.001	0.005	0.025	0.807
				3.297	3.762	4.884	28.719
		Gumbel	0.139	0	0.003	0.042	0.816
				3.417	3.693	5.487	29.025
		Indep	0.13	0	0.003	0.049	0.818
				3.423	3.705	5.547	28.857
	0.8	Braun	0.143	0	0.002	0.033	0.822
				3.351	3.552	5.502	29.19
		Gumbel	0.101	0	0.002	0.037	0.86
				3.387	3.636	5.568	29.775
		Indep	0.093	0	0.002	0.04	0.865
				3.381	3.804	5.628	29.592
Gumbel	0	Braun	0.189	0.001	0.004	0.047	0.759
				3.327	3.585	5.31	27.942
		Gumbel	0.173	0	0.004	0.044	0.779
				3.336	3.675	5.313	28.224
		Indep	0.16	0.001	0	0.034	0.805
				3.435	3.789	5.172	28.434
	0.4	Braun	0.16	0	0.001	0.048	0.791
				3.45	3.63	5.61	28.101
		Gumbel	0.163	0	0.004	0.049	0.784
				3.363	3.666	5.49	28.164
		Indep	0.156	0	0.001	0.034	0.809
				3.405	3.591	4.977	28.875
	0.8	Braun	0.171	0.001	0.001	0.029	0.798
				3.342	3.645	5.25	28.116
		Gumbel	0.156	0.001	0.004	0.029	0.81
				3.384	3.702	5.262	28.776
		Indep	0.144	0	0.002	0.042	0.812
				3.342	3.804	5.484	28.824

The first row is the selection probability for dose z; and the second is the average number of patients treated at dose z. Y_T and Y_S are simulated with association, ψ_k; k=1,2 when appropriate. The operating characteristics for the target dose are in bold.