# Table 1 Estimated type I error rates, where pw,F is the cumulative probability of stopping for futility at look w or earlier, pE is the probability of stopping early for efficacy and p12m is the probability of stopping for efficacy at the end of the study; N=85, for (a) one look N1=60,N2=45,N3=25, (b) two looks N1=(55,70),N2=(40,55),N3=(20,35) and (c) three looks, N1=(50,65,75),N2=(35,50,60),N3=(15,30,40), ρ=ρ13=ρ23=ρ12 and $$\sigma ^{2}_{1} = \sigma ^{2}_{2} = \sigma ^{2}_{3} = 20$$ (10,000 simulations)

Futility bound ($$\alpha ^{*}_{L}$$)ρpEp1,Fp2,Fp3,Fp12m
(a) One look; $$\alpha ^{*}_{U}=(0.001,0.025)$$
(0.0,0.975)0.00.0020.000--0.025
(0.5,0.975)0.00.0020.504--0.023
(0.0,0.975)0.50.0020.000--0.026
(0.5,0.975)0.50.0020.504--0.026
(b) Two looks; $$\alpha ^{*}_{U}=(0,0.001,0.025)$$
(0.0,0.0,0.975)0.00.0010.0000.000-0.025
(0.2,0.5,0.975)0.00.0010.2020.499-0.025
(0.0,0.0,0.975)0.50.0010.0000.000-0.024
(0.2,0.5,0.975)0.50.0020.1990.505-0.025
(c) Three looks; $$\alpha ^{*}_{U}=(0,0,0.001,0.025)$$
(0.0,0.0,0.0,0.975)0.00.0010.0000.0000.0000.024
(0.1,0.3,0.5,0.975)0.00.0020.1100.3060.5030.025
(0.0,0.0,0.0,0.975)0.50.0010.0000.0000.0000.025
(0.1,0.3,0.5,0.975)0.50.0010.1080.3070.5060.025