Sample size determination for a binary response in a superiority clinical trial using a hybrid classical and Bayesian procedure

Ciarleglio, Maria M.; Arendt, Christopher D.

doi:10.1186/s13063-017-1791-0

Trials

Table 7 Sample scenarios assuming uniform priors p(π ₁) and p(π ₂) where \(\tau _{1}^{2}=\tau _{2}^{2}\). Hypothesized values of π ₁ and π ₂ set equal to μ ₁ and μ ₂, respectively, under the traditional design. Two-sided α=0.05 and 1−β=0.80 assumed

From: Sample size determination for a binary response in a superiority clinical trial using a hybrid classical and Bayesian procedure

		Traditional design			CEP design
(μ ₁,μ ₂)	\(\tau _{1}^{2}=\tau _{2}^{2}\)	\(\hat {N}\)	Performance	CEP	N ^∗	Performance	E(π ₂−π ₁\|π ₂>π ₁)	P(π ₂>π ₁)	Marginal benefit
(0.1,0.9)	0.001	10	0.638	0.826	10	0.638	0.800	1	0
(0.1,0.8) or (0.2,0.9)	0.001	14	0.643	0.824	14	0.643	0.700	1	0
(0.1,0.7) or (0.3,0.9)	0.001	20	0.680	0.831	20	0.680	0.600	1	0
(0.2,0.8)	0.001	20	0.593	0.811	20	0.593	0.600	1	0
	0.01	20	0.556	0.775	22	0.615	0.600	1	0.030
(0.1,0.6)or (0.4,0.9)	0.001	28	0.633	0.822	28	0.633	0.500	1	0
(0.2,0.7)or (0.3,0.8)	0.001	30	0.599	0.812	30	0.599	0.500	1	0
	0.01	30	0.554	0.763	36	0.650	0.500	1	0.016
(0.1,0.5) or (0.5,0.9)	0.001	40	0.551	0.801	40	0.551	0.400	1	0
(0.2,0.6) or (0.4,0.8)	0.001	46	0.553	0.800	46	0.553	0.400	1	0
	0.01	46	0.535	0.735	62	0.663	0.400	1	0.008
(0.3,0.7)	0.001	48	0.555	0.800	48	0.555	0.400	1	0
	0.01	48	0.536	0.735	64	0.660	0.400	1	0.008
	0.02	48	0.549	0.711	80	0.694	0.407	0.983	0.005
	0.03	48	0.575	0.718	82	0.702	0.427	0.945	0.004
(0.1,0.4) or (0.6,0.9)	0.001	64	0.523	0.787	68	0.589	0.300	1	0.017
(0.2,0.5) or (0.5,0.8)	0.001	78	0.521	0.786	82	0.581	0.300	1	0.015
	0.01	78	0.526	0.704	130	0.689	0.303	0.991	0.003
(0.3,0.6) or (0.4,0.7)	0.001	84	0.506	0.781	90	0.591	0.300	1	0.014
	0.01	84	0.521	0.701	142	0.690	0.303	0.991	0.003
	0.02	84	0.566	0.712	150	0.704	0.330	0.925	0.002
	0.03	84	0.603	0.731	140	0.709	0.357	0.875	0.002
(0.1,0.3) or (0.7,0.9)	0.001	124	0.510	0.764	140	0.600	0.200	1	0.006
(0.2,0.4) or (0.6,0.8)	0.001	164	0.512	0.764	184	0.603	0.200	1	0.005
	0.01	164	0.566	0.713	292	0.703	0.224	0.911	0.001
(0.3,0.5) or (0.5,0.7)	0.001	186	0.504	0.761	210	0.603	0.200	1	0.004
	0.01	186	0.562	0.710	336	0.704	0.224	0.911	0.001
	0.02	186	0.626	0.745	284	0.709	0.263	0.825	0.001
	0.03	186	0.669	0.772	236	0.710	0.295	0.778	0.001
(0.4,0.6)	0.001	194	0.504	0.761	220	0.607	0.200	1	0.004
	0.01	194	0.562	0.709	350	0.704	0.224	0.911	0.001
	0.02	194	0.625	0.745	296	0.708	0.263	0.825	0.001
	0.03	194	0.668	0.771	248	0.711	0.295	0.778	0.001
	0.04	194	0.700	0.792	210	0.712	0.323	0.747	0.001
	0.05	194	0.725	0.809	194	0.725	0.349	0.725	0

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