Table 7.1.

Simulation results comparing our approach with Shih’s approach in the two-sample comparison problem with a binary outcome and a cluster level binary exposure. Sample sizes are for achieving a nominal power 90% to detect different relative risks (p₁/p₀) at 0.05 significance level for different correlations ρ. The reference risk p₀ is fixed at 0.1 and ψ₀ = 0. Empirical powers are based on the Wald test. The “actual” are the sample sizes with empirical powers closest to the nominal power 90%.

		Our approach		Shih’s approach		“Actual”
RR	ρ	m	Power (%)	m	Power (%)	m	Power (%)
2.5	0.20	156	89.82	172	92.43	158	89.96
	0.50	195	89.47	215	92.28	196	90.03
	0.80	234	89.40	258	92.68	238	90.06
3.0	0.20	95	89.32	110	93.65	96	90.11
	0.50	119	89.52	138	93.52	122	90.49
	0.80	142	89.45	165	93.25	144	89.86
3.5	0.20	65	89.11	79	93.85	66	89.87
	0.50	81	88.20	99	94.28	84	89.62
	0.80	97	88.76	118	94.45	100	89.98