Power analysis for stratified cluster randomisation trials with cluster size being the stratifying factor

Figures & data

Figure 1. Percentage increase in sample size (R) versus intraclass correlation coefficient (ρ). The vertical axis corresponds to R and the horizontal axis corresponds to ρ. We assume the numbers of clusters and CVs to be equal across strata. The common CV is set at ξ = 1.

Table 1. Specification of scenarios D₁ and D₂.

	Scenarios		Mean	Variance	CV
Stratum	D1	D2	(θl)	(τ^2l)	(ξl)
1	DU(1, 8)	tNB(17.29, 0.26)	4.5	5.25	0.509
2	DU(9, 24)	tNB(57.31, 0.29)	16.5	21.25	0.279
3	DU(25, 100)	tNB(9.33, 6.70)	62.5	481.25	0.351

Table 2. Empirical power from 10,000 simulations for the fixed cluster size method and proposed method.

			b1
ρ	Method	D	0.20	0.25	0.30
0.01	J^*	D1	89.66% (19)	91.38% (13)	91.67% (9)
		D2	89.12% (19)	91.03% (13)	91.56% (9)
	J	D1	90.64% (20)	91.74% (13)	91.28% (9)
		D2	90.27% (20)	91.29% (13)	91.27% (9)
0.02	J^*	D1	88.20% (25)	88.90% (16)	91.05% (12)
		D2	88.68% (25)	89.05% (16)	91.26% (12)
	J	D1	90.55% (27)	90.27% (17)	91.22% (12)
		D2	90.71% (27)	90.56% (17)	91.12% (12)
0.03	J^*	D1	88.80% (32)	88.70% (20)	89.39% (14)
		D2	88.48% (32)	88.33% (20)	89.00% (14)
	J	D1	90.71% (34)	91.03% (22)	91.04% (15)
		D2	90.72% (34)	91.08% (22)	91.34% (15)
0.05	J^*	D1	87.79% (44)	87.92% (28)	89.11% (20)
		D2	88.09% (44)	87.63% (28)	89.28% (20)
	J	D1	90.37% (48)	90.61% (31)	91.69% (22)
		D2	91.10% (48)	91.14% (31)	91.51% (22)
0.10	J^*	D1	87.71% (75)	87.70% (48)	88.03% (34)
		D2	87.85% (75)	87.26% (48)	88.46% (34)
	J	D1	91.16% (83)	90.70% (53)	90.56% (37)
		D2	90.39% (83)	90.22% (53)	90.36% (37)

Note: In each cell, we present empirical power (number of clusters per stratum) under a combination of trial parameters.