Table 6.

Results using the Braun and Gumbel copulas for data simulation under Scenario 5

Data	ψ k	Model			Dose
			Futility	1	2	3	4
Braun	0.5	Braun	0.87	0.001	0.005	0.023	0.101
				4.086	4.59	4.62	11.946
		Gumbel	0.872	0	0.006	0.022	0.1
				4.05	4.44	4.896	11.316
		Indep	0.872	0.002	0.009	0.016	0.101
				4.176	4.656	4.803	11.319
	0.7	Braun	0.928	0	0.004	0.009	0.059
				4.065	4.209	4.56	10.095
		Gumbel	0.887	0.002	0.014	0.014	0.083
				3.936	4.485	4.869	11.748
		Indep	0.895	0.002	0.01	0.016	0.077
				4.254	4.467	4.596	11.256
	0.9	Braun	0.945	0.001	0.004	0.009	0.041
				4.053	4.29	4.566	9.531
		Gumbel	0.904	0.003	0.006	0.016	0.071
				4.248	4.701	5.148	11.091
		Indep	0.905	0	0.006	0.016	0.073
				4.227	4.608	5.196	11.22
Gumbel	0	Braun	0.895	0.001	0.011	0.01	0.083
				4.035	4.41	4.674	11.196
		Gumbel	0.878	0.003	0.008	0.015	0.096
				3.999	4.293	4.692	11.391
		Indep	0.897	0.001	0.007	0.014	0.081
				4.197	4.494	4.659	11.886
	0.4	Braun	0.898	0.002	0.01	0.013	0.077
				3.966	4.254	4.368	11.061
		Gumbel	0.901	0.001	0.004	0.021	0.073
				4.179	4.452	4.89	11.112
		Indep	0.892	0.004	0.006	0.018	0.08
				4.065	4.365	4.644	11.559
	0.8	Braun	0.913	0.003	0.005	0.013	0.066
				4.002	4.536	4.623	10.794
		Gumbel	0.925	0.002	0.005	0.013	0.055
				4.152	4.488	4.632	11.028
		Indep	0.897	0.003	0.006	0.012	0.082
				4.179	4.611	4.452	11.286

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.