BMC Medical Research Methodology

Table 1 Estimated required number of clusters for HTE test by the direct inflation (\({n}_{0}\)), the proposed formula under MCAR (\({n}_{1}\)), the empirical type I error rate of the Wald test for HTE (\(\psi\)), the predicted power (\({\varphi }_{pre}\)) and empirical power (\({\varphi }_{emp}\)) of the HTE test with a continuous individual-level effect modifier under MCAR. The effect size is \({\updelta }\in \{0.1, 0.25\}\). The missingness ICC is \(\tau =0.05\)

From: Accounting for expected attrition in the planning of cluster randomized trials for assessing treatment effect heterogeneity

				\(\delta =0.10\)					\(\delta =0.25\)
\(m\)	\({\rho }_{x}\)	\({\rho }_{y\|x}\)	\(\pi\)	\({n}_{0}\)	\({n}_{1}\)	\({\varphi }_{pre}\)	\({\varphi }_{emp}\)	\(\psi\)	\({n}_{0}\)	\({n}_{1}\)	\({\varphi }_{pre}\)	\({\varphi }_{emp}\)	\(\psi\)
20	0.1	0.01	0.7	228	228	0.802	0.791	0.047	38	38	0.818	0.811	0.054
		0.01	0.9	178	178	0.803	0.815	0.052	30	30	0.823	0.797	0.052
		0.10	0.7	226	226	0.803	0.802	0.053	36	36	0.801	0.806	0.047
		0.10	0.9	176	176	0.804	0.801	0.052	28	28	0.801	0.803	0.054
	0.5	0.01	0.7	244	240	0.803	0.798	0.045	40	40	0.818	0.801	0.048
		0.01	0.9	190	190	0.804	0.796	0.054	32	32	0.824	0.781	0.051
		0.10	0.7	318	302	0.802	0.798	0.050	52	50	0.815	0.802	0.049
		0.10	0.9	248	244	0.803	0.805	0.049	40	40	0.812	0.802	0.051
50	0.1	0.01	0.7	94	92	0.801	0.793	0.049	16	16	0.832	0.829	0.048
		0.01	0.9	72	72	0.801	0.796	0.052	12	12	0.817	0.803	0.043
		0.10	0.7	90	90	0.801	0.802	0.044	16	16	0.841	0.836	0.046
		0.10	0.9	70	70	0.801	0.791	0.048	12	12	0.828	0.824	0.050
	0.5	0.01	0.7	108	104	0.804	0.799	0.045	18	18	0.834	0.787	0.065
		0.01	0.9	84	84	0.808	0.808	0.049	14	14	0.824	0.786	0.060
		0.10	0.7	144	138	0.804	0.796	0.055	24	22	0.802	0.800	0.055
		0.10	0.9	112	110	0.802	0.815	0.049	18	18	0.811	0.808	0.050
100	0.1	0.01	0.7	48	48	0.812	0.813	0.049	8	8	0.827	0.809	0.057
		0.01	0.9	38	38	0.816	0.820	0.053	6	6	0.811	0.799	0.053
		0.10	0.7	46	46	0.810	0.811	0.052	8	8	0.841	0.831	0.051
		0.10	0.9	36	36	0.812	0.814	0.048	6	6	0.828	0.829	0.057
	0.5	0.01	0.7	60	58	0.811	0.788	0.054	10	10	0.839	0.793	0.061
		0.01	0.9	48	46	0.804	0.800	0.053	8	8	0.836	0.792	0.060
		0.10	0.7	76	74	0.804	0.814	0.056	14	12	0.809	0.817	0.051
		0.10	0.9	60	60	0.812	0.818	0.047	10	10	0.828	0.823	0.054

Back to article page

ISSN: 1471-2288

Contact us

General enquiries: journalsubmissions@springernature.com