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 4 Type I error probabilities 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 \((X_{C})\)
	\(n_0=n_1=50\)			\(n_0=n_1=75\)
\(\rho _{XY}=0.5, \rho _X=0.6\)	0.0527	0.0517	-	0.05	0.0503	0.0512
\(\rho _{XY}=0.5, \rho _X=0.7\)	0.0526	0.052	-	0.0505	0.0502	0.0506
\(\rho _{XY}=0.5, \rho _X=0.8\)	0.0522	0.0519	-	0.0512	0.0504	0.052
\(\rho _{XY}=0.5, \rho _X=0.9\)	0.052	0.0526	-	0.0508	0.0505	0.0512
\(\rho _{XY}=0.6, \rho _X=0.7\)	0.051	0.0503	-	0.0508	0.0504	0.051
\(\rho _{XY}=0.6, \rho _X=0.8\)	0.0527	0.0517	-	0.0508	0.0503	0.0518
\(\rho _{XY}=0.6, \rho _X=0.9\)	0.0526	0.0511	-	0.0505	0.0494	0.05
\(\rho _{XY}=0.7, \rho _X=0.8\)	0.0508	0.0482	-	0.0506	0.0498	0.0508
\(\rho _{XY}=0.7, \rho _X=0.9\)	0.0499	0.049	-	0.051	0.0488	0.0493
	\(n_0=n_1=100\)			\(n_0=n_1=125\)
\(\rho _{XY}=0.5, \rho _X=0.6\)	0.0479	0.0481	0.0491	0.0476	0.0476	0.0476
\(\rho _{XY}=0.5, \rho _X=0.7\)	0.0498	0.0491	0.0499	0.0494	0.0482	0.0494
\(\rho _{XY}=0.5, \rho _X=0.8\)	0.0488	0.0478	0.0493	0.0496	0.0491	0.05
\(\rho _{XY}=0.5, \rho _X=0.9\)	0.0482	0.0473	0.0484	0.0494	0.0504	0.0506
\(\rho _{XY}=0.6, \rho _X=0.7\)	0.0491	0.0472	0.0485	0.0476	0.0492	0.0503
\(\rho _{XY}=0.6, \rho _X=0.8\)	0.0485	0.0486	0.0492	0.0489	0.0486	0.0498
\(\rho _{XY}=0.6, \rho _X=0.9\)	0.0485	0.0493	0.0492	0.0471	0.0486	0.0487
\(\rho _{XY}=0.7, \rho _X=0.8\)	0.0469	0.0471	0.0482	0.0492	0.0497	0.0516
\(\rho _{XY}=0.7, \rho _X=0.9\)	0.0486	0.0472	0.0478	0.0483	0.049	0.05
	\(n_0=n_1=150\)
\(\rho _{XY}=0.5, \rho _X=0.6\)	0.0486	0.0491	0.0493
\(\rho _{XY}=0.5, \rho _X=0.7\)	0.049	0.0488	0.0488
\(\rho _{XY}=0.5, \rho _X=0.8\)	0.0494	0.0493	0.0485
\(\rho _{XY}=0.5, \rho _X=0.9\)	0.0488	0.048	0.0484
\(\rho _{XY}=0.6, \rho _X=0.7\)	0.0495	0.0492	0.0499
\(\rho _{XY}=0.6, \rho _X=0.8\)	0.0488	0.0499	0.0506
\(\rho _{XY}=0.6, \rho _X=0.9\)	0.0489	0.0486	0.0494
\(\rho _{XY}=0.7, \rho _X=0.8\)	0.0496	0.0504	0.0507
\(\rho _{XY}=0.7, \rho _X=0.9\)	0.051	0.0504	0.051

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