From: A double SIMEX approach for bivariate random-effects meta-analysis of diagnostic accuracy studies
Random-effects | ρ | \(\overline {\eta }\) | \(\overline {\xi }\) | \(\sigma ^{2}_{\eta }\) | \(\sigma ^{2}_{\xi }\) | ρ | Failure |
---|---|---|---|---|---|---|---|
distribution | bias (s.e.) | bias (s.e.) | bias (s.e.) | bias (s.e.) | bias (s.e.) | rate % | |
Normal-Normal | |||||||
Normal | 0.2 | 0.00 (0.32) | 0.01 (0.22) | -0.16 (0.51) | -0.07 (0.22) | -0.02 (0.27) | 0.5 |
0.6 | 0.00 (0.32) | 0.01 (0.21) | -0.19 (0.49) | -0.09 (0.21) | -0.07 (0.20) | 0.0 | |
0.8 | 0.01 (0.33) | 0.01 (0.21) | -0.15 (0.51) | -0.08 (0.21) | -0.08 (0.14) | 0.3 | |
Binomial-Normal | |||||||
0.2 | 0.02 (0.33) | 0.00 (0.22) | -0.09 (0.54) | -0.04 (0.23) | 0.00 (0.30) | 1.0 | |
0.6 | 0.00 (0.33) | 0.00 (0.22) | -0.11 (0.53) | -0.05 (0.23) | -0.01 (0.22) | 1.4 | |
0.8 | 0.01 (0.34) | 0.00 (0.22) | -0.05 (0.56) | -0.04 (0.23) | -0.01 (0.14) | 4.0 | |
SIMEX | |||||||
0.2 | 0.03 (0.34) | -0.01 (0.22) | 0.00 (0.54) | 0.02 (0.24) | -0.02 (0.28) | 0.0 | |
0.6 | 0.01 (0.33) | -0.01 (0.22) | -0.02 (0.53) | 0.01 (0.23) | -0.06 (0.21) | 0.0 | |
0.8 | 0.02 (0.34) | -0.01 (0.22) | 0.03 (0.55) | 0.01 (0.23) | -0.07 (0.14) | 0.0 | |
Normal-Normal | |||||||
t | 0.2 | -0.04 (0.40) | 0.01 (0.27) | 0.44 (0.83) | 0.21 (0.37) | -0.02 (0.25) | 0.5 |
0.6 | -0.01 (0.39) | 0.03 (0.27) | 0.35 (0.78) | 0.20 (0.36) | -0.09 (0.20) | 0.2 | |
0.8 | -0.01 (0.39) | 0.02 (0.27) | 0.39 (0.80) | 0.21 (0.36) | -0.08 (0.14) | 0.2 | |
Binomial-Normal | |||||||
0.2 | -0.01 (0.44) | -0.01 (0.28) | 0.80 (1.01) | 0.32 (0.42) | 0.00 (0.28) | 1.3 | |
0.6 | 0.01 (0.42) | 0.01 (0.28) | 0.70 (0.95) | 0.32 (0.42) | -0.03 (0.21) | 1.2 | |
0.8 | -0.01 (0.43) | 0.00 (0.29) | 0.81 (1.01) | 0.36 (0.43) | -0.01 (0.13) | 2.7 | |
SIMEX | |||||||
0.2 | -0.01 (0.44) | -0.03 (0.29) | 0.92 (0.96) | 0.43 (0.42) | -0.02 (0.26) | 0.0 | |
0.6 | 0.02 (0.43) | 0.00 (0.29) | 0.81 (0.91) | 0.42 (0.42) | -0.08 (0.20) | 0.0 | |
0.8 | 0.00 (0.43) | -0.01 (0.29) | 0.87 (0.94) | 0.47 (0.44) | -0.07 (0.13) | 0.0 | |
Normal-Normal | |||||||
Skew-normal | 0.2 | -0.55 (0.27) | 0.13 (0.21) | -0.45 (0.37) | -0.09 (0.21) | 0.09 (0.26) | 1.0 |
(low skewness) | 0.6 | -0.44 (0.29) | -0.02 (0.21) | -0.38 (0.40) | -0.09 (0.21) | -0.05 (0.20) | 0.4 |
0.8 | -0.41 (0.29) | -0.11 (0.21) | -0.34 (0.42) | -0.10 (0.21) | -0.09 (0.14) | 0.2 | |
Binomial-Normal | |||||||
0.2 | -0.55 (0.28) | 0.12 (0.21) | -0.41 (0.38) | -0.07 (0.22) | 0.12 (0.28) | 1.8 | |
0.6 | -0.45 (0.30) | -0.03 (0.22) | -0.32 (0.42) | -0.06 (0.23) | 0.02 (0.21) | 1.8 | |
0.8 | -0.42 (0.31) | -0.12 (0.22) | -0.27 (0.45) | -0.06 (0.23) | -0.01 (0.15) | 5.9 | |
SIMEX | |||||||
0.2 | -0.55 (0.28) | 0.11 (0.22) | -0.35 (0.38) | -0.01 (0.22) | 0.09 (0.26) | 0.0 | |
0.6 | -0.45 (0.30) | -0.04 (0.22) | -0.26 (0.42) | 0.01 (0.23) | -0.04 (0.20) | 0.0 | |
0.8 | -0.42 (0.31) | -0.14 (0.22) | -0.21 (0.45) | 0.01 (0.23) | -0.08 (0.14) | 0.0 | |
Normal-Normal | |||||||
Skew-normal | 0.2 | -0.51 (0.28) | 0.34 (0.19) | -0.41 (0.39) | -0.16 (0.17) | 0.26 (0.22) | 1.0 |
(high skewness) | 0.6 | -0.32 (0.31) | 0.23 (0.20) | -0.27 (0.45) | -0.11 (0.20) | 0.09 (0.15) | 0.1 |
0.8 | -0.20 (0.31) | 0.15 (0.21) | -0.21 (0.48) | -0.09 (0.21) | -0.01 (0.11) | 0.2 | |
Binomial-Normal | |||||||
0.2 | -0.51 (0.29) | 0.33 (0.19) | -0.36 (0.41) | -0.15 (0.18) | 0.31 (0.20) | 2.9 | |
0.6 | -0.32 (0.31) | 0.23 (0.21) | -0.21 (0.48) | -0.08 (0.21) | 0.17 (0.16) | 4.1 | |
0.8 | -0.20 (0.33) | 0.15 (0.22) | -0.11 (0.53) | -0.05 (0.23) | 0.07 (0.10) | 8.5 | |
SIMEX | |||||||
0.2 | -0.51 (0.29) | 0.32 (0.20) | -0.30 (0.40) | -0.10 (0.18) | 0.27 (0.22) | 0.0 | |
0.6 | -0.32 (0.32) | 0.22 (0.21) | -0.13 (0.48) | -0.03 (0.21) | 0.11 (0.15) | 0.0 | |
0.8 | -0.20 (0.33) | 0.14 (0.22) | -0.05 (0.52) | -0.01 (0.22) | 0.00 (0.11) | 0.0 |