The optimal pre-post allocation for randomized clinical trials

Ma, Shiyang; Wang, Tianying

doi:10.1186/s12874-023-01893-w

BMC Medical Research Methodology

Table 5 Power of three different logistic regression models for a single binary outcome, under different sample sizes, \(\rho _{XY}\) and \(\rho _X\)

From: The optimal pre-post allocation for randomized clinical trials

	Model 1 (\(X_2\))	Model 2 (\(X_{\text {log}}\))	Model 3 \((X_{C})\)	Model 1 (\(X_2\))	Model 2 (\(X_{\text {log}}\))	Model 3 \((X_{C})\)
	\(n_0=n_1=50\)			\(n_0=n_1=75\)
\(\rho _{XY}=0.5, \rho _X=0.6\)	0.5482	0.5662	-	0.7268	0.7509	0.749
\(\rho _{XY}=0.5, \rho _X=0.7\)	0.5474	0.5624	-	0.7264	0.7454	0.7444
\(\rho _{XY}=0.5, \rho _X=0.8\)	0.5476	0.5584	-	0.7262	0.7394	0.7405
\(\rho _{XY}=0.5, \rho _X=0.9\)	0.5464	0.555	-	0.7292	0.7361	0.7341
\(\rho _{XY}=0.6, \rho _X=0.7\)	0.5708	0.5946	-	0.754	0.7788	0.779
\(\rho _{XY}=0.6, \rho _X=0.8\)	0.5692	0.5896	-	0.7538	0.7732	0.771
\(\rho _{XY}=0.6, \rho _X=0.9\)	0.5668	0.5804	-	0.7558	0.767	0.7664
\(\rho _{XY}=0.7, \rho _X=0.8\)	0.6042	0.638	-	0.7888	0.819	0.818
\(\rho _{XY}=0.7, \rho _X=0.9\)	0.6028	0.6263	-	0.7889	0.808	0.8078
	\(n_0=n_1=100\)			\(n_0=n_1=125\)
\(\rho _{XY}=0.5, \rho _X=0.6\)	0.8442	0.859	0.859	0.9134	0.9272	0.9261
\(\rho _{XY}=0.5, \rho _X=0.7\)	0.8426	0.8567	0.8558	0.9134	0.9244	0.9242
\(\rho _{XY}=0.5, \rho _X=0.8\)	0.8442	0.8536	0.8524	0.9134	0.9211	0.9213
\(\rho _{XY}=0.5, \rho _X=0.9\)	0.8418	0.8488	0.8489	0.9129	0.9182	0.9176
\(\rho _{XY}=0.6, \rho _X=0.7\)	0.8642	0.8864	0.8853	0.9288	0.9433	0.9428
\(\rho _{XY}=0.6, \rho _X=0.8\)	0.8644	0.8811	0.8804	0.9285	0.9396	0.9389
\(\rho _{XY}=0.6, \rho _X=0.9\)	0.8646	0.8765	0.875	0.9292	0.9354	0.9346
\(\rho _{XY}=0.7, \rho _X=0.8\)	0.8924	0.914	0.9139	0.9458	0.9598	0.9592
\(\rho _{XY}=0.7, \rho _X=0.9\)	0.892	0.9064	0.9058	0.9447	0.9552	0.954
	\(n_0=n_1=150\)
\(\rho _{XY}=0.5, \rho _X=0.6\)	0.9536	0.9618	0.9608
\(\rho _{XY}=0.5, \rho _X=0.7\)	0.9529	0.9598	0.9587
\(\rho _{XY}=0.5, \rho _X=0.8\)	0.9522	0.9576	0.9571
\(\rho _{XY}=0.5, \rho _X=0.9\)	0.9531	0.9554	0.955
\(\rho _{XY}=0.6, \rho _X=0.7\)	0.9658	0.9732	0.9733
\(\rho _{XY}=0.6, \rho _X=0.8\)	0.9643	0.9714	0.9711
\(\rho _{XY}=0.6, \rho _X=0.9\)	0.963	0.9683	0.9679
\(\rho _{XY}=0.7, \rho _X=0.8\)	0.9756	0.9834	0.9833
\(\rho _{XY}=0.7, \rho _X=0.9\)	0.9748	0.9815	0.9808

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