Skip to main content

Table 2 Comparison of standardized bias

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%

0.02

0.73

    

15%

0.03

0.71

0.02

0.17

0.03

0.15

30%

0.01

0.63

0.00

0.18

0.00

0.08

0.01

5.99

0%

0.01

0.34

    

15%

0.00

0.33

0.00

0.02

0.00

0.03

30%

0.00

0.32

0.00

0.01

0.00

0.03

0.05

25.95

0%

0.02

0.15

    

15%

0.02

0.15

0.02

0.08

0.03

0.10

30%

0.02

0.14

0.01

0.05

0.02

0.09

20 (L-Design)

50

0.01

1.49

0%

0.04

0.38

    

15%

0.04

0.37

0.03

0.04

0.06

0.01

30%

0.04

0.36

0.03

0.05

0.08

0.01

0.05

3.45

0%

0.01

0.26

    

15%

0.00

0.24

0.00

0.09

0.03

0.11

30%

0.02

0.13

0.01

0.06

0.03

0.12

0.1

5.90

0%

0.02

0.20

    

15%

0.01

0.19

0.01

0.15

0.05

0.16

30%

0.01

0.19

0.01

0.10

NA

NA

30 (L-Design)

30

0.05

2.45

0%

0.02

0.33

    

15%

0.02

0.32

0.02

0.12

0.02

0.15

30%

0.01

0.14

0.00

0.06

NA

NA

0.1

3.90

0%

0.01

0.23

    

15%

0.01

0.23

0.01

0.18

NA

NA

30%

0.02

0.23

0.02

0.13

NA

NA

0.2

6.80

0%

0.01

0.16

    

15%

0.00

0.15

0.00

0.14

NA

NA

30%

0.01

0.15

0.00

0.16

NA

NA

  1. Standardized bias is defined as the difference between the expectation of the estimator and the parameter, divided by the standard deviation of the estimator. Standardized biases 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.