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

Table 4 Correlations, type I error rates and powers obtained from simulation compared to calculated values

Design	α ₁	ω ₁	From calculation				From simulation
			ρ\|H ₀	ρ\|H ₁	α	ω	$\hat{ρ} \| H_{0}$	$\hat{ρ} \| H_{1}$	$\hat{α}$	$\hat{ω}$
I=D=culture status
(i)	0.50	0.90	0.39	0.39	0.021	0.826	0.38	0.38	0.021	0.828
(ii)	0.50	0.95	0.50	0.50	0.023	0.870	0.50	0.50	0.024	0.872
(iii)	0.20	0.90	0.65	0.65	0.020	0.843	0.64	0.65	0.019	0.847
(iv)	0.20	0.95	0.76	0.76	0.023	0.883	0.76	0.76	0.023	0.885
I= culture status, D = relapse
(v)	0.50	0.90	0.10	0.08	0.015	0.813	0.07	0.06	0.014	0.809
(vi)	0.50	0.95	0.12	0.11	0.015	0.857	0.10	0.09	0.015	0.854
(vii)	0.20	0.90	0.16	0.14	0.008	0.815	0.12	0.11	0.008	0.811
(viii)	0.20	0.95	0.19	0.16	0.009	0.858	0.15	0.12	0.008	0.858

Overall type I error rates, powers and correlations between stages obtained from simulations of designs (i)-(viii) in Tables 2 and 3. Key: α ₁ = stage 1 significance level, ω ₁ = stage 1 power, ρ|H _h = correlation between stages under hypothesis H _h, α = overall type I error rate, ω = overall power. Hats indicate values estimated from simulations.

ISSN: 1471-2288