Background
Methods
Statistical analysis methods
Generalized estimating equations
Random-effects logistic regression
Missing data strategies
Combination of results from different imputed data sets
Simulation study
Results
Empirical standard error
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 |
Standardized bias
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 |
Root mean squared error
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 | 0.10 | 0.08 | 0.06 | 0.08 | 0.06 | ||||
30% | 0.08 | 0.11 | 0.08 | 0.07 | 0.09 | 0.08 | ||||
0.01 | 5.99 | 0% | 0.14 | 0.17 | ||||||
15% | 0.14 | 0.17 | 0.15 | 0.15 | 0.15 | 0.15 | ||||
30% | 0.15 | 0.17 | 0.15 | 0.15 | 0.15 | 0.15 | ||||
0.05 | 25.95 | 0% | 0.31 | 0.34 | ||||||
15% | 0.31 | 0.34 | 0.31 | 0.32 | 0.31 | 0.33 | ||||
30% | 0.31 | 0.34 | 0.31 | 0.32 | 0.31 | 0.33 | ||||
20 (L-Design) | 50 | 0.01 | 1.49 | 0% | 0.11 | 0.13 | ||||
15% | 0.11 | 0.13 | 0.12 | 0.12 | 0.12 | 0.12 | ||||
30% | 0.12 | 0.14 | 0.14 | 0.12 | 0.13 | 0.13 | ||||
0.05 | 3.45 | 0% | 0.18 | 0.20 | ||||||
15% | 0.18 | 0.21 | 0.18 | 0.19 | 0.18 | 0.19 | ||||
30% | 0.19 | 0.20 | 0.19 | 0.20 | 0.19 | 0.20 | ||||
0.1 | 5.90 | 0% | 0.24 | 0.26 | ||||||
15% | 0.24 | 0.27 | 0.24 | 0.26 | 0.24 | 0.27 | ||||
30% | 0.25 | 0.27 | 0.25 | 0.26 | NA | NA | ||||
30 (L-Design) | 30 | 0.05 | 2.45 | 0% | 0.15 | 0.17 | ||||
15% | 0.16 | 0.18 | 0.16 | 0.16 | 0.15 | 0.17 | ||||
30% | 0.16 | 0.17 | 0.16 | 0.17 | NA | NA | ||||
0.1 | 3.90 | 0% | 0.20 | 0.21 | ||||||
15% | 0.20 | 0.22 | 0.20 | 0.22 | NA | NA | ||||
30% | 0.20 | 0.23 | 0.21 | 0.22 | NA | NA | ||||
0.2 | 6.80 | 0% | 0.27 | 0.30 | ||||||
15% | 0.27 | 0.30 | 0.28 | 0.33 | NA | NA | ||||
30% | 0.28 | 0.30 | 0.28 | 0.31 | NA | NA |
Coverage probability
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% | 0.91 | 0.96 | ||||
15% | 0.92 | 0.97 | 0.93 | 0.97 | 1.00 | 0.99 | ||||
30% | 0.93 | 0.97 | 0.95 | 0.98 | 1.00 | 0.99 | ||||
0.01 | 5.99 | 0% | 0.92 | 0.79 | ||||||
15% | 0.92 | 0.81 | 0.90 | 0.87 | 0.95 | 0.91 | ||||
30% | 0.94 | 0.84 | 0.88 | 0.84 | 0.98 | 0.93 | ||||
0.05 | 25.95 | 0% | 0.91 | 0.49 | ||||||
15% | 0.91 | 0.52 | 0.89 | 0.83 | 0.93 | 0.89 | ||||
30% | 0.93 | 0.52 | 0.83 | 0.77 | 0.96 | 0.90 | ||||
20 (L-Design) | 50 | 0.01 | 1.49 | 0% | 0.94 | 0.98 | ||||
15% | 0.94 | 0.98 | 0.93 | 0.95 | 0.96 | 0.97 | ||||
30% | 0.94 | 0.98 | 0.92 | 0.96 | 0.98 | 0.98 | ||||
0.05 | 3.45 | 0% | 0.93 | 0.91 | ||||||
15% | 0.93 | 0.92 | 0.90 | 0.89 | 0.94 | 0.94 | ||||
30% | 0.93 | 0.93 | 0.87 | 0.88 | 0.95 | 0.96 | ||||
0.1 | 5.90 | 0% | 0.93 | 0.78 | ||||||
15% | 0.93 | 0.82 | 0.89 | 0.88 | 0.93 | 0.93 | ||||
30% | 0.92 | 0.83 | 0.85 | 0.85 | NA | NA | ||||
30 (L-Design) | 30 | 0.05 | 2.45 | 0% | 0.95 | 0.95 | ||||
15% | 0.96 | 0.96 | 0.93 | 0.93 | 0.97 | 0.96 | ||||
30% | 0.95 | 0.96 | 0.91 | 0.92 | NA | NA | ||||
0.1 | 3.90 | 0% | 0.95 | 0.91 | ||||||
15% | 0.95 | 0.93 | 0.92 | 0.92 | NA | NA | ||||
30% | 0.95 | 0.94 | 0.89 | 0.90 | NA | NA | ||||
0.2 | 6.80 | 0% | 0.94 | 0.79 | ||||||
15% | 0.94 | 0.81 | 0.90 | 0.89 | NA | NA | ||||
30% | 0.94 | 0.85 | 0.85 | 0.85 | NA | NA |