Table 4.

Power and ASN under a given MSS and true correlation between the endpoints ${\rho }_{12}^{*}$. The given MSS per intervention group (equally-sized groups: r =1) is calculated to detect a joint effect on the two endpoints with a power of 80% using one-sided test with a significance level of α = 2.5%, with (Δ₁, Δ₂) =(0.2,0.2) and hypothetical correlation ρ₁₂ during planning, where both of efficacy and futility assessments are conducted based on DF-1 and critical boundaries are determined by OF-type boundary using the LD error-spending function with equally-spaced increment in information.

Hypo, correlation	No. of analyses		True correlation	ASN(Δ1,Δ2)
ρ12	L	MSS	${\rho }_{12}^{*}$	Power(%)	(0.2,0.2)	(0.2,0.0)	(0.0,0.0)
0.0	1	516
	2	529	0.0	80.0	500	365	305
			0.3	81.2	492	366	317
			0.5	82.4	486	367	325
			0.8	84.8	474	367	341
			1.0	89.5	456	367	367
	3	548	0.0	80.1	468	345	289
			0.3	81.3	460	345	298
			0.5	82.4	454	346	306
			0.8	84.9	443	346	321
			1.0	89.5	427	346	346
	4	560	0.0	80.0	456	329	277
			0.3	81.3	447	330	285
			0.5	82.4	440	330	292
			0.8	84.9	428	330	306
			1.0	89.5	410	330	330
0.5	1	490
	2	505	0.0	77.3	477	343	287
			0.3	78.7	469	344	298
			0.5	80.0	464	345	306
			0.8	82.8	454	345	321
			1.0	87.9	438	345	345
	3	524	0.0	77.3	448	323	269
			0.3	78.8	441	324	278
			0.5	80.0	435	324	286
			0.8	82.8	425	325	300
			1.0	87.9	410	325	325
	4	536	0.0	77.3	437	308	258
			0.3	78.7	429	309	266
			0.5	80.0	423	310	273
			0.8	82.8	412	310	287
			1.0	87.9	395	310	310
1.0	1	393
	2	415	0.0	64.1	380	263	225
			0.3	66.6	377	265	233
			0.5	68.7	375	266	238
			0.8	72.8	370	267	249
			1.0	80.1	363	267	267
	3	434	0.0	64.1	364	243	198
			0.3	66.6	359	245	206
			0.5	68.6	356	246	213
			0.8	72.8	351	247	226
			1.0	80.0	344	247	247
	4	446	0.0	64.1	357	233	190
			0.3	66.6	351	235	198
			0.5	68.6	348	236	204
			0.8	72.8	342	237	216
			1.0	80.1	333	237	237