Appendix Table 1.

CPU time (in seconds) taken for calculating the power under a given sample size for DF-3 with varying the number of endpoints (K), the number of analyses (L) and common correlation ρ. The given sample sizes of 516 for K =2 and 586 for K =3 are enough to detect a joint effect on all endpoints (assuming a common effect size Δ = Δ_k = 0.2 and zero correlations among the endpoints) with the power of 80 % at the significance level of 2.5% for a one-sided test in the fixed sample design. The O’Brian-Fleming-type boundary is commonly selected for efficacy and futility on all of the endpoints, with equally spaced increments of information. The number of replications for power evaluation by Monte-Carlo simulation is 100,000.

		K =2		K =3
# of analyses L	Correlation ρ	Numerical integration	Monte-Carlo simulation	Numerical integration	Monte-Carlo simulation
2	0.0	0.14	44.59	0.78	75.69
	0.3	0.28	43.82	0.97	74.35
	0.5	0.39	42.73	2.36	73.02
	0.8	0.44	41.64	11.54	70.65
3	0.0	0.67	49.14	2.56	85.72
	0.3	0.87	48.06	3.81	82.96
	0.5	1.12	47.11	5.74	80.96
	0.8	1.37	45.72	11.39	77.42
4	0.0	1.01	55.27	40.06	97.31
	0.3	1.47	54.13	41.54	93.73
	0.5	1.23	52.96	43.23	91.34
	0.8	2.31	50.95	51.53	85.97
5	0.0	5.66	61.67	381.78	108.78
	0.3	6.29	60.06	383.92	104.40
	0.5	6.75	58.70	388.93	101.24
	0.8	8.89	56.53	411.05	101.24