Bias, precision and statistical power of analysis of covariance in the analysis of randomized trials with baseline imbalance: a simulation study

Egbewale, Bolaji E; Lewis, Martyn; Sim, Julius

doi:10.1186/1471-2288-14-49

Table 2 Design effect (ratio of standard errors) in respect of ANCOVA versus ANOVA, CSA versus ANOVA, and ANCOVA versus CSA

From: Bias, precision and statistical power of analysis of covariance in the analysis of randomized trials with baseline imbalance: a simulation study

Ratio	Z′ _T –Z′ _C							Treatment effect
		0.2						0.5						0.8
		ZYcorrelation						ZYcorrelation						ZYcorrelation
		0	0.1	0.3	0.5	0.7	0.9	0	0.1	0.3	0.5	0.7	0.9	0	0.1	0.3	0.5	0.7	0.9
ANCOVA/ANOVA	−1.96	1.00	1.01	0.97	0.86	0.71	0.43	1.02	1.01	0.97	0.88	0.72	0.44	1.05	1.04	1.00	0.90	0.75	0.45
	−1.64	1.00	1.01	0.97	0.87	0.73	0.44	1.01	1.01	0.96	0.88	0.72	0.44	1.04	1.02	0.99	0.90	0.74	0.45
	−1.28	1.00	1.00	0.97	0.87	0.73	0.43	1.01	1.01	0.96	0.87	0.73	0.44	1.03	1.02	0.98	0.89	0.73	0.45
	0.00	1.00	1.00	0.96	0.86	0.71	0.43	1.00	1.00	0.96	0.86	0.71	0.43	1.01	1.00	0.96	0.86	0.71	0.43
	1.28	1.00	1.00	0.97	0.86	0.71	0.43	1.01	1.03	0.93	0.83	0.70	0.43	1.03	1.01	0.97	0.89	0.72	0.45
	1.64	1.00	1.00	0.97	0.86	0.71	0.43	1.01	1.01	0.97	0.86	0.72	0.44	1.04	1.03	0.99	0.90	0.74	0.45
	1.96	1.00	1.00	0.97	0.86	0.71	0.43	1.02	1.00	0.97	0.86	0.72	0.44	1.05	1.04	1.00	0.90	0.75	0.46
CSA/ANOVA	−1.96	1.42	1.36	1.14	1.00	0.79	0.43	1.42	1.34	1.18	1.00	0.77	0.44	1.41	1.34	1.18	1.00	0.77	0.44
	−1.64	1.42	1.36	1.20	1.00	0.79	0.44	1.42	1.34	1.18	1.00	0.77	0.44	1.41	1.32	1.18	1.00	0.77	0.45
	−1.28	1.42	1.36	1.14	1.00	0.79	0.43	1.42	1.34	1.18	1.00	0.77	0.44	1.41	1.34	1.18	1.00	0.76	0.45
	0.00	1.42	1.36	1.14	1.00	0.79	0.43	1.42	1.34	1.19	1.00	0.77	0.44	1.41	1.34	1.18	1.00	0.77	0.45
	1.28	1.42	1.36	1.14	1.01	0.86	0.44	1.42	1.34	1.17	1.00	0.75	0.43	1.41	1.34	1.18	1.00	0.76	0.45
	1.64	1.42	1.37	1.20	1.00	0.79	0.43	1.42	1.34	1.18	1.00	0.77	0.44	1.41	1.34	1.18	1.00	0.76	0.45
	1.96	1.42	1.36	1.14	1.00	0.79	0.43	1.42	1.34	1.18	1.00	0.77	0.44	1.41	1.34	1.18	1.00	0.76	0.45
ANCOVA/CSA	−1.96	0.71	0.75	0.85	0.86	0.91	1.00	0.72	0.75	0.82	0.88	0.94	0.99	0.74	0.78	0.85	0.91	0.97	1.02
	−1.64	0.71	0.75	0.81	0.87	0.93	1.00	0.72	0.75	0.81	0.88	0.94	0.99	0.74	0.77	0.84	0.90	0.96	1.02
	−1.28	0.71	0.74	0.85	0.87	0.93	1.00	0.71	0.75	0.81	0.87	0.93	0.99	0.73	0.76	0.83	0.89	0.97	1.01
	0.00	0.71	0.74	0.84	0.86	0.91	1.00	0.71	0.74	0.81	0.87	0.93	0.97	0.72	0.75	0.81	0.87	0.93	0.99
	1.28	0.71	0.74	0.85	0.85	0.83	0.97	0.71	0.77	0.80	0.83	0.93	0.99	0.73	0.75	0.83	0.89	0.95	1.00
	1.64	0.71	0.73	0.81	0.86	0.91	1.00	0.72	0.75	0.82	0.86	0.94	0.99	0.73	0.77	0.83	0.90	0.98	1.02
	1.96	0.71	0.74	0.85	0.86	0.91	1.00	0.72	0.75	0.82	0.86	0.94	0.99	0.74	0.78	0.84	0.91	0.99	1.02

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