Table 2.

Operating characteristics of optimized single- and adaptive two-stage designs optimized under the weak and strong biomarker prior for the parameters of Case 1 and a population prevalence of $\lambda =0.5$.

	Societal view				Sponsor view
Treatment effect δ	(0, 0)	(0.3, 0)	(0.3, 0.15)	(0.3, 0.3)	(0, 0)	(0.3, 0)	(0.3, 0.15)	(0.3, 0.3)
Weak biomarker prior
Adaptive designs
P(futility stop)	0.58	0.04	0.02	0.01	0.43	0.05	0.03	0.02
P(full enrichment)	0.12	0.28	0.08	0.01	0.1	0.16	0.06	0.02
P(partial enrichment)	0.3	0.68	0.9	0.97	0.47	0.79	0.9	0.96
Average sample number in S	164	212	199	179	162	174	174	172
Average sample number in $S\prime$	82	98	112	113	57	69	70	66
Power to reject HF	0.011	0.226	0.627	0.907	0.010	0.173	0.453	0.744
Power to reject only HS	0.010	0.626	0.268	0.051	0.010	0.574	0.342	0.129
Single stage designs
Power to reject HF	0.011	0.225	0.614	0.901	0.010	0.160	0.378	0.641
Power to reject only HS	0.010	0.575	0.245	0.043	0.011	0.552	0.374	0.184
Strong biomarker prior
Adaptive designs
P(futility stop)	0.64	0.03	0.02	0.02	0.5	0.04	0.03	0.02
P(full enrichment)	0.25	0.76	0.59	0.39	0.16	0.28	0.14	0.04
P(partial enrichment)	0.11	0.21	0.38	0.59	0.34	0.68	0.83	0.93
Average sample number in S	188	237	231	221	164	187	187	184
Average sample number in $S\prime$	30	32	37	43	37	46	49	52
Power to reject HF	0.008	0.098	0.265	0.507	0.009	0.155	0.384	0.661
Power to reject only HS	0.011	0.797	0.639	0.422	0.011	0.637	0.440	0.216
Single stage designs
Power to reject HF	0	0	0	0	0.010	0.160	0.379	0.643
Power to reject only HS	0.025	0.874	0.874	0.874	0.011	0.558	0.378	0.186

Note: The operating characteristics are given under the global null (where the Power corresponds to the type I error rate) and several alternative hypotheses. For the adaptive designs the probabilities of the interim decisions futility stop, full enrichment, partial enrichment and the average sample numbers (across both stages) are given. For all designs the power to reject F and the power to reject S only are reported. Note that the power to reject any null hypothesis is given by the sum of the two.