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. Author manuscript; available in PMC: 2024 Feb 20.
Published in final edited form as: Stat Med. 2022 Dec 24;42(4):559–578. doi: 10.1002/sim.9632

TABLE 5.

Estimated required number of clusters I, subjects per cluster-period N, periods T , empirical type I error when only setting the first effect to zero and when only setting the second effect to zero (e1, e2), empirical power ψ¯¸ predicted power ψ obtained from power formula for given effect size δl/σδl, within-period and between-period endpoint-specific ICCs (ρ0l,ρ1l), within-period and between-period between-endpoint ICCs (ρ0ll,ρ1ll), and intra-subject ICC (ρ2ll) assuming a CAC of 0.5 with L = 2 co-primary endpoints.

ρ212 (ρ01,ρ11) (ρ02,ρ12) (ρ012,ρ112) (δ1/σδ1,δ2/σδ2) I N T (e1, e2) ψ ψ¯
0.2 (0.02, 0.01) (0.02, 0.01) (0.01, 0.005) (0.43, 0.43) 20 13 3 (3.5, 3.0) 84.5 83.0
(0.10, 0.05) (0.01, 0.005) (0.40, 0.38) 12 25 5 (3.8, 4.6) 85.2 86.7
(0.20, 0.10) (0.01, 0.005) (0.39, 0.56) 12 25 4 (3.9, 4.3) 83.6 86.2
(0.10, 0.05) (0.02, 0.01) (0.01, 0.005) (0.38, 0.33) 12 25 5 (3.5, 4.2) 82.6 85.0
(0.1, 0.05) (0.05, 0.025) (0.49, 0.98) 12 15 4 (4.3, 3.7) 85.6 88.1
(0.20, 0.10) (0.05, 0.025) (0.59, 0.99) 12 20 3 (4.6, 4.9) 84.2 84.7
(0.20, 0.10) (0.02, 0.01) (0.01, 0.005) (0.47, 0.22) 20 18 5 (5.5, 4.5) 82.2 82.3
(0.10, 0.05) (0.05, 0.025) (0.92, 0.92) 10 12 3 (3.8, 3.5) 84.1 84.8
(0.20, 0.10) (0.10, 0.05) (0.54, 0.81) 12 25 4 (4.9, 3.9) 83.9 85.8

0.5 (0.02, 0.01) (0.02, 0.01) (0.01, 0.005) (0.30, 0.28) 30 10 4 (4.8, 4.7) 84.4 84.1
(0.10, 0.05) (0.01, 0.005) (0.34, 0.88) 16 22 3 (3.3, 4.2) 82.4 81.3
(0.20, 0.10) (0.01, 0.005) (0.42, 0.83) 8 20 5 (1.2, 3.3) 86.3 86.2
(0.10, 0.05) (0.02, 0.01) (0.01, 0.005) (0.38, 0.55) 21 10 4 (4.8, 5.2) 84.0 84.7
(0.10, 0.05) (0.05, 0.025) (0.52, 0.68) 8 25 5 (3.8, 3.1) 84.8 88.7
(0.20, 0.10) (0.05, 0.025) (0.62, 0.62) 22 8 3 (5.4, 4.9) 83.9 83.9
(0.20, 0.10) (0.02, 0.01) (0.01, 0.005) (0.84, 0.29) 26 18 3 (4.9, 4.7) 84.7 86.8
(0.10, 0.05) (0.05, 0.025) (0.60, 0.60) 12 16 4 (4.7, 5.3) 85.0 85.8
(0.20, 0.10) (0.10, 0.05) (0.32, 0.84) 24 24 5 (5.1, 4.6) 85.7 86.4

0.8 (0.02, 0.01) (0.02, 0.01) (0.01, 0.005) (0.31, 0.55) 12 16 5 (4.1, 5.0) 84.4 82.6
(0.10, 0.05) (0.01, 0.005) (0.29, 0.57) 30 14 3 (4.0, 4.7) 83.1 84.6
(0.20, 0.10) (0.01, 0.005) (0.20, 0.84) 30 17 4 (4.4, 5.4) 81.4 80.2
(0.10, 0.05) (0.02, 0.01) (0.01, 0.005) (0.31, 0.62) 20 13 5 (5.1, 3.2) 84.2 83.5
(0.10, 0.05) (0.05, 0.025) (0.82, 0.92) 8 22 3 (2.9, 2.8) 85.2 87.4
(0.20, 0.10) (0.05, 0.025) (0.45, 0.45) 18 18 4 (5.2, 4.6) 83.7 85.4
(0.20, 0.10) (0.02, 0.01) (0.01, 0.005) (0.99, 0.25) 28 25 3 (5.1, 4.0) 85.6 84.9
(0.10, 0.05) (0.05, 0.025) (0.63, 0.31) 24 17 4 (4.5, 5.6) 84.1 84.6
(0.20, 0.10) (0.10, 0.05) (0.82, 0.82) 8 10 5 (3.2, 2.9) 86.1 89.4