Table 5.

Results using the Braun and Gumbel copulas for data simulation under Scenario 4

Data	ψ k	Model			Dose
			Futility	1	2	3	4
Braun	0.5	Braun	0.023	0.003	0.057	0.665	0.252
				3.42	6.39	23.19	11.268
		Gumbel	0.015	0.001	0.055	0.683	0.246
				3.402	7.041	23.358	10.809
		Indep	0.017	0.003	0.078	0.621	0.281
				3.351	7.071	22.74	11.304
	0.7	Braun	0.02	0.001	0.057	0.684	0.238
				3.333	6.849	24.066	10.146
		Gumbel	0.019	0.003	0.069	0.671	0.238
				3.39	7.107	23.286	10.68
		Indep	0.01	0.001	0.085	0.655	0.249
				3.39	7.593	22.854	10.875
	0.9	Braun	0.017	0.001	0.062	0.658	0.262
				3.303	6.996	23.376	10.839
		Gumbel	0.002	0	0.078	0.698	0.222
				3.315	7.476	23.46	10.695
		Indep	0.007	0.001	0.081	0.647	0.264
				3.543	7.743	22.329	11.172
Gumbel	0	Braun	0.027	0.002	0.064	0.664	0.243
				3.282	6.885	23.109	11.034
		Gumbel	0.027	0.001	0.065	0.657	0.25
				3.351	6.711	22.95	11.136
		Indep	0.025	0.002	0.084	0.633	0.256
				3.375	7.374	22.767	10.788
	0.4	Braun	0.025	0.002	0.066	0.631	0.276
				3.504	7.338	22.515	11.013
		Gumbel	0.021	0.002	0.074	0.655	0.248
				3.45	7.296	22.599	11.013
		Indep	0.013	0.001	0.069	0.649	0.268
				3.315	7.032	22.542	11.787
	0.8	Braun	0.012	0.002	0.063	0.65	0.273
				3.318	7.152	22.647	11.502
		Gumbel	0.019	0.001	0.075	0.669	0.236
				3.297	7.038	23.154	10.923
		Indep	0.013	0.004	0.075	0.673	0.235
				3.33	7.389	23.172	10.755

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.