Table 2.

Trial scenarios and parameters max sample size=302, # arms=2, balanced burn-in period=50,p₂=0.3, and allocation update frequency=28.

Study Description	Expected Performance Based on BRAR algorithm	Simulation Studies without stopping rules	Simulation Studies with stopping rules
Treatment efficacy profile	p1=0.4	p1=0.4;	Scenario 1: p1=0.3; Scenario 2: p1=0.4; Scenario 3: p1=0.5.
Time-trend (linear)	No trend: δ1=0, δ2=0; Equal trend: δ1=0.1, δ2=0.1; Unequal trend: δ1=0, δ2=0.1.	No trend: δ1=0, δ2=0 Equal trend: δ1=0.1,δ2=0.1 Equal trend: δ1=0.2, δ2=0.2. Unequal trend: δ1=0, δ2=0.1.	No trend: δ1=0, δ2=0; Equal trend: δ1=0.1, δ2=0.1; Equal trend: δ1=0.2, δ2=0.2. Unequal trend: δ1=0, δ2=0.1.
RAR algorithm parameters	$r_j\propto \frac{P_j^{\alpha }Var{(p_j)}^{\beta }}{n_j^{\gamma }}$ α=0 to 1 by 0.1; β=0,0.2,0.5,0.8,1; γ=0, 0.5,1;	BRAR (1/2) BRAR (1/2, σ2) BRAR (n/2N)	BRAR (1/2) BRAR (1/2, σ2) BRAR (n/2N)
Efficacy stopping rule	None	None	$P_j>0.99$
Estimation of type I error	___________	_______________	Proportion of simulation runs with: $P_j>0.99$ under efficacy scenario 1.
Estimator of power	___________	_______________	Proportion of simulation runs with: $P_j>0.99$ under efficacy scenarios 2 and 3.
Simulation iteration	___________	10,000 per scenario	10,000 per scenario.

Note: p_j are the posterior probability of success that arm j is better than the other arms, j=1,2.