Table 3.

Characteristics of the optimized separate (sep.), simultaneous (sim.) and improved simultaneous (imp.) designs: stopping boundaries, average sample number (ASN) under H ₀(δ _A=δ _B=0), H ₁(δ _A,δ _B), maximum sample size (N) and the conjunctive and disjunctive power under H ₁. The power and, for designs with no futility stopping (where l ₁=−∞), the A S N are optimized under the alternative H ₁ specified in the table. For designs with futility stopping, $\overline{\mathrm{ASN}}$, defined as the mean of the ASN under H ₁ and the ASN under the global null hypothesis, is optimized. The maximum sample size N is chosen such that the disjunctive power is 90% given δ _A=0,δ _B=0.5. The columns v _i(v i ′),i = 1,2 denote the stopping boundary v _i for the separate and simultaneous design and the boundary v i ′ for the improved simultaneous design.

	Effect size		Stopping boundaries					ASN			Power
Design	δ A	δ B	l 1	u 1	u 2	v 1(v1′)	v 2(v2′)	H 1	H 0	N	conj.	disj.
Sep.	0.50	0.50	−∞	2.47	2.38	2.05	2.38	225	317	318	0.85	0.97
Sim.	0.50	0.50	−∞	2.41	2.43	2.06	2.37	205	322	324	0.71	0.97
Imp.	0.50	0.50	−∞	2.41	2.43	2.00	2.06	205	322	324	0.76	0.97
Sep.	0.50	0.00	−∞	2.79	2.26	2.11	2.26	279	300	300	0.02	0.90
Sim.	0.50	0.00	−∞	2.42	2.42	2.04	2.42	232	322	324	0.02	0.90
Imp.	0.50	0.00	−∞	2.42	2.42	2.00	2.06	232	322	324	0.02	0.90
Sep.	0.50	0.50	0.91	2.55	2.33	2.07	2.33	228	200	330	0.84	0.97
Sim.	0.50	0.50	0.91	2.51	2.35	2.10	2.28	211	203	336	0.71	0.97
Imp.	0.50	0.50	0.91	2.51	2.35	1.98	2.12	211	203	336	0.76	0.97
Sep.	0.50	0.00	0.94	2.68	2.28	2.10	2.28	235	199	330	0.02	0.90
Sim.	0.50	0.00	0.89	2.58	2.32	2.10	2.28	216	200	330	0.02	0.90
Imp.	0.50	0.00	0.88	2.58	2.32	1.97	2.20	216	201	330	0.02	0.90