The optimal pre-post allocation for randomized clinical trials

Table 3 Power of using only baseline (\(S=1\)) or screening and baseline (S=2) for a single continuous outcome, under different sample sizes, \(\rho _{XY}\) and \(\rho _X\)

	\(S=1, T=1\)	\(S=2, T=1\)	\(S=1, T=1\)	\(S=2, T=1\)
	\(n_0=n_1=50\)		\(n_0=n_1=75\)
\(\rho _{XY}=0.5, \rho _X=0.6\)	0.4001	0.4324	0.554	0.5886
\(\rho _{XY}=0.5, \rho _X=0.7\)	0.4008	0.4225	0.554	0.5771
\(\rho _{XY}=0.5, \rho _X=0.8\)	0.4009	0.4132	0.5538	0.5674
\(\rho _{XY}=0.5, \rho _X=0.9\)	0.4019	0.4059	0.5532	0.5592
\(\rho _{XY}=0.6, \rho _X=0.7\)	0.456	0.4978	0.6206	0.6695
\(\rho _{XY}=0.6, \rho _X=0.8\)	0.4568	0.4819	0.6208	0.6526
\(\rho _{XY}=0.6, \rho _X=0.9\)	0.458	0.4692	0.6217	0.6354
\(\rho _{XY}=0.7, \rho _X=0.8\)	0.5428	0.5913	0.7212	0.766
\(\rho _{XY}=0.7, \rho _X=0.9\)	0.5446	0.5666	0.7194	0.7416
	\(n_0=n_1=100\)		\(n_0=n_1=125\)
\(\rho _{XY}=0.5, \rho _X=0.6\)	0.6746	0.7116	0.775	0.8111
\(\rho _{XY}=0.5, \rho _X=0.7\)	0.6741	0.7	0.7736	0.7996
\(\rho _{XY}=0.5, \rho _X=0.8\)	0.6738	0.6908	0.7742	0.7907
\(\rho _{XY}=0.5, \rho _X=0.9\)	0.6748	0.6829	0.7737	0.782
\(\rho _{XY}=0.6, \rho _X=0.7\)	0.7428	0.7873	0.8381	0.8714
\(\rho _{XY}=0.6, \rho _X=0.8\)	0.7449	0.7706	0.8371	0.8586
\(\rho _{XY}=0.6, \rho _X=0.9\)	0.7446	0.7561	0.8371	0.8466
\(\rho _{XY}=0.7, \rho _X=0.8\)	0.8336	0.8744	0.9113	0.9378
\(\rho _{XY}=0.7, \rho _X=0.9\)	0.8334	0.8538	0.9113	0.9244
	\(n_0=n_1=150\)
\(\rho _{XY}=0.5, \rho _X=0.6\)	0.8464	0.8766
\(\rho _{XY}=0.5, \rho _X=0.7\)	0.8469	0.8686
\(\rho _{XY}=0.5, \rho _X=0.8\)	0.8472	0.8603
\(\rho _{XY}=0.5, \rho _X=0.9\)	0.8474	0.8534
\(\rho _{XY}=0.6, \rho _X=0.7\)	0.8991	0.9266
\(\rho _{XY}=0.6, \rho _X=0.8\)	0.899	0.9166
\(\rho _{XY}=0.6, \rho _X=0.9\)	0.8989	0.9082
\(\rho _{XY}=0.7, \rho _X=0.8\)	0.9507	0.9694
\(\rho _{XY}=0.7, \rho _X=0.9\)	0.9507	0.9619

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