Evaluating the performance of copula models in phase I-II clinical trials under model misspecification

Table 2 Results using the Braun and Gumbel copulas for data simulation under Scenario 1

Data	ψ _k	Model			Dose
			Futility	1	2	3	4
Braun	0.5	Braun	0.039	0.045	0.212	0.475	0.229
				5.91	12.792	17.13	8.298
		Gumbel	0.038	0.039	0.225	0.482	0.216
				6.075	12.738	16.596	8.775
		Indep	0.037	0.046	0.223	0.504	0.19
				6	13.146	16.923	8.115
	0.7	Braun	0.037	0.034	0.197	0.514	0.218
				5.667	12.966	17.496	7.86
		Gumbel	0.023	0.032	0.235	0.524	0.186
				5.613	13.32	17.562	7.941
		Indep	0.033	0.035	0.219	0.528	0.185
				5.796	13.356	17.334	7.77
	0.9	Braun	0.024	0.018	0.208	0.514	0.236
				5.19	12.888	17.58	8.814
		Gumbel	0.011	0.037	0.225	0.538	0.189
				5.901	13.428	17.895	7.542
		Indep	0.006	0.041	0.226	0.526	0.201
				5.994	13.605	17.349	7.95
Gumbel	0	Braun	0.042	0.033	0.217	0.503	0.205
				6.054	12.786	17.007	8.373
		Gumbel	0.042	0.041	0.21	0.499	0.208
				6.033	12.651	17.094	8.28
		Indep	0.034	0.054	0.208	0.478	0.226
				6.591	12.447	16.671	8.622
	0.4	Braun	0.036	0.034	0.216	0.506	0.208
				5.871	12.828	17.157	8.322
		Gumbel	0.029	0.039	0.222	0.461	0.249
				5.775	13.287	16.029	9.081
		Indep	0.018	0.044	0.213	0.501	0.224
				5.946	12.81	17.205	8.67
	0.8	Braun	0.036	0.028	0.237	0.475	0.224
				5.886	13.875	16.119	8.307
		Gumbel	0.016	0.036	0.231	0.506	0.211
				5.877	13.182	17.34	8.22
		Indep	0.032	0.032	0.216	0.524	0.196
				5.388	13.242	17.616	8.079

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.

ISSN: 1471-2288