Table 1.

The effect of primary outcome delay on power and expected treatment failures (standard deviation) for complete randomization, standard RAR, and the S-P replacement algorithm.

				Complete		Treatment A Optimal allocation	Standard RAR		S-P Replacement algorithm
	pA	pB	N	Power	Failures		Power	Failures	Power	Failures
Delay = 0%	0.9	0.3	24	91	10 (2.4)	63%	90	7 (2.7)	90	7 (2.7)
	0.9	0.7	162	91	32 (5.0)	53%	91	31 (4.7)	91	31 (4.7)
	0.7	0.3	62	90	31 (3.9)	60%	91	28 (3.6)	91	28 (3.6)
	0.5	0.4	1036	90	570 (16.0)	53%	90	567 (15.8)	90	567 (15.8)
	0.2	0.1	532	90	452 (8.2)	59%	90	447 (8.4)	90	447 (8.4)
Delay = 25%	0.9	0.3	24	91	10 (2.4)	63%	92	9 (2.1)	90	8 (2.0)
	0.9	0.7	162	91	32 (5.0)	53%	91	31 (4.7)	91	31 (4.8)
	0.7	0.3	62	90	31 (3.9)	60%	90	30 (3.8)	91	28 (3.5)
	0.5	0.4	1036	90	570 (16.0)	53%	90	567 (16.0)	90	567 (15.9)
	0.2	0.1	532	90	452 (8.2)	59%	91	450 (8.2)	90	447 (8.5)
Delay = 50%	0.9	0.3	24	91	10 (2.4)	63%	92	9 (2.1)	90	8 (2.3)
	0.9	0.7	162	91	32 (5.0)	53%	91	31 (4.7)	91	31 (4.9)
	0.7	0.3	62	90	31 (3.9)	60%	90	30 (3.7)	90	28 (3.6)
	0.5	0.4	1036	90	570 (16.0)	53%	90	568 (16.0)	90	567 (15.8)
	0.2	0.1	532	90	452 (8.2)	59%	90	450 (8.3)	90	447 (8.4)
Delay = 75%	0.9	0.3	24	91	10 (2.4)	63%	92	10 (1.9)	90	7 (2.3)
	0.9	0.7	162	91	32 (5.0)	53%	91	31 (4.8)	91	31 (4.9)
	0.7	0.3	62	90	31 (3.9)	60%	91	31 (3.7)	90	28 (3.6)
	0.5	0.4	1036	90	570 (16.0)	53%	90	569 (16.0)	90	567 (15.9)
	0.2	0.1	532	90	452 (8.2)	59%	90	451 (8.3)	90	448 (8.5)

RAR: response-adaptive randomization; DBCD: doubly-adaptive biased coin design.

The sample size was selected that yielded simulated power of approximately 90% under complete randomization. Both RAR methods implemented DBCD (γ = 2) and targeted optimal allocation. Simulations = 10,000 replications (α = 0.05, two-sided). Surrogate distribution equals primary distribution. Surrogate weight w_s = 0.5.