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

Table 2 Examples of two-arm two-stage phase II TB trials

Design	Stage (i)	α _i	ω _i	Length of f/u = 4 weeks				Length of f/u = 8 weeks*				ρ	A _i	Ω _i	Fixed
				n _i	N _i	t _i	ESS \|H ₀	n _i	N _i	t _i	ESS\|H ₀				sample size
(i)	1	0.5	0.90	56	96	0.48	262	56	134	0.67	281	0.39	0.500	0.900	360
	2	0.025	0.90	364	428	2.30		364	428	2.49			0.021	0.826
(ii)	1	0.5	0.95	94	140	0.70	284	94	178	0.89	303	0.51	0.500	0.950	398
	2	0.025	0.90	364	428	2.30		364	428	2.49			0.023	0.870
(iii)	1	0.2	0.90	156	214	1.07	257	156	252	1.26	287	0.65	0.200	0.900	381
	2	0.025	0.90	364	428	2.30		364	428	2.49			0.020	0.843
(iv)	1	0.2	0.95	214	282	1.41	311	214	320	1.60	342	0.77	0.200	0.950	414
	2	0.025	0.90	364	428	2.30		364	428	2.49			0.023	0.883

Characteristics of two-arm two-stage TB trials where I = D = culture status observed 4 or 14 weeks after randomisation. The fixed sample sizes correspond to fixed sample designs with pairwise alpha A ₂ and power Ω ₂. Key: for stage i, α _i = significance level, ω _i = nominal power, n _i = total sample size required for analysis i, N _i = cumulative number of patients recruited by the end of stage i, t _i = predicted timing (in years) of the end of stage i assuming a recruitment rate of 200 patients/year, ESS |H ₀ = expected sample size under the null hypothesis, ρ = correlation between stages, A _i = probability of passing stage i under H ₀, Ω _i = probability of passing stage i under H ₁. *Plus an additional 6 week delay to determine culture status.

ISSN: 1471-2288