A multi-arm multi-stage clinical trial design for binary outcomes with application to tuberculosis

Table 6 Absolute bias in arms reaching the final analysis

α ₁	Treatment	θ _D	ω ₁=0.90			ω ₁=0.95
	arm		% Pass	$E ({\hat{θ}}_{D})$	b _D	% Pass	$E ({\hat{θ}}_{D})$	b _D
I = D = culture status at 8 weeks
0.5	A	-5%	35	-3.1%	1.9%	29	-2.2%	2.8%
	B	0%	51	1.4%	1.4%	50	1.8%	1.8%
	C	8%	78	8.6%	0.6%	83	8.7%	0.7%
	D	13%	90	13.3%	0.3%	95	13.2%	0.2%
0.2	A	-5%	6	0.9%	5.9%	5	2.4%	7.4%
	B	0%	20	4.2%	4.2%	20	4.8%	4.8%
	C	8%	65	9.5%	1.5%	73	9.5%	1.5%
	D	13%	90	13.5%	0.5%	95	13.4%	0.4%
I = culture status at 8 weeks, D = relapse
0.5	A	-10%	35	-9.8%	0.2%	30	-9.7%	0.3%
	B	-6%	51	-5.9%	0.1%	51	-5.8%	0.2%
	C	-3%	77	-3.0%	0.0%	83	-2.9%	0.1%
	D	0%	90	0.0%	0.0%	95	0.0%	0.0%
0.2	A	-10%	6	-9.4%	0.6%	5	-9.3%	0.7%
	B	-6%	20	-5.6%	0.4%	20	-5.5%	0.5%
	C	-3%	65	-2.9%	0.1%	73	-2.9%	0.1%
	D	0%	90	0.0%	0.0%	95	0.0%	0.0%

Simulation results showing the proportion of trials which continue to the final stage of the trial (% pass) and the absolute bias in the estimated treatment effect on D at the final analysis. Key: θ _D = underlying treatment effect on the definitive outcome, α ₁ = significance level in stage 1, ω ₁ = nominal power in stage 1, $E ({\hat{θ}}_{D})$ = average treatment effect on the definitive outcome in the final stage, $b_{D} = E ({\hat{θ}}_{D}) - θ_{D}$ = bias in the average treatment effect estimate on the definitive outcome in the final stage.

ISSN: 1471-2288