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Table 1 Comparison of empirical standard error

From: Comparison of population-averaged and cluster-specific models for the analysis of cluster randomized trials with missing binary outcomes: a simulation study

Design of CRTs

VIF4

% of missing data

Complete case analysis

Standard MI5

Within-cluster MI6

m1

n2

ρ3

GEE7

RELR8

GEE

RELR

GEE

RELR

5 9 (S-Design)

500

0.001

1.499

0%

0.07

0.10

    

15%

0.08

0.11

0.08

0.07

0.08

0.08

30%

0.08

0.12

0.08

0.08

0.10

0.09

0.01

5.99

0%

0.15

0.12

    

15%

0.15

0.13

0.13

0.12

0.16

0.14

30%

0.15

0.15

0.12

0.11

0.16

0.15

0.05

25.95

0%

0.30

0.15

    

15%

0.30

0.16

0.26

0.24

0.30

0.28

30%

0.30

0.16

0.22

0.20

0.30

0.29

20 (L-Design)

50

0.01

1.49

0%

0.11

0.17

    

15%

0.11

0.17

0.12

0.12

0.13

0.13

30%

0.12

0.19

0.12

0.13

0.15

0.16

0.05

3.45

0%

0.17

0.31

    

15%

0.17

0.34

0.16

0.16

0.18

0.19

30%

0.18

0.39

0.15

0.16

0.20

0.21

0.1

5.90

0%

0.22

0.18

    

15%

0.23

0.21

0.20

0.22

0.23

0.26

30%

0.23

0.22

0.18

0.19

NA

NA

30 (L-Design)

30

0.05

2.45

0%

0.15

0.28

    

15%

0.16

0.33

0.15

0.15

0.17

0.18

30%

0.17

0.37

0.15

0.15

NA

NA

0.1

3.90

0%

0.19

0.33

    

15%

0.20

0.38

0.18

0.19

NA

NA

30%

0.20

0.42

0.17

0.18

NA

NA

0.2

6.80

0%

0.26

0.38

    

15%

0.26

0.40

0.23

0.27

NA

NA

30%

0.26

0.44

0.21

0.23

NA

NA

  1. Empirical standard error is defined as the average of standard errors of the estimated treatment effects across all simulation replications. The empirical standard errors obtained when 0% data are missing are considered as references for comparing with those obtained when 15% or 30% data are missing.
  2. Note: 1. m: Number of clusters per trial arm. 2. n: Number of subjects per cluster.
  3. 3. ρ: intracluster correlation coefficient; 4. VIF: Variance inflation factor, i.e. 1+(m-1)ρ; 5. Standard MI: Standard multiple imputation using logistic regression method.
  4. 6. Within-cluster MI: Within-cluster multiple imputation using logistic regression method, which is not applicable (NA) for some L-design of cluster randomized trials.
  5. 7. GEE: Generalized estimating equations.8. RELR: Random-effects logistic regression.
  6. 9. For CRTs with 5 clusters per arm, modified standard errors are provided.