From: Bivariate random-effects meta-analysis and the estimation of between-study correlation
Meta-analysis model | n | No. of the 1000 simulations that converged | Bias of mean 1 | Mean s.e. of 1 | MSE of 1 | Coverage of the 95% CIs for 1 | Bias of mean 2 | Mean s.e. of 2 | MSE of 2 | Coverage of the 95% CIs for 2 | Bias of mean (no. of = 0) | Bias of mean (no. of = 0) | Bias of mean B | % of B = -1 | % of B = 1 |
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Scenario (i): Complete data – zero correlation; within-study variance similar to between-study variance | |||||||||||||||
URMA | 50 | 1000 | -0.005 | 0.102 | 0.010 | 94.8% | 0.001 | 0.107 | 0.0108 | 95.4% | -0.003 (0) | 0.005 (1) | - | - | - |
BRMA | 50 | 1000 | -0.005 | 0.101 | 0.010 | 94.7% | 0.001 | 0.106 | 0.0108 | 95.5% | -0.003 (0) | 0.005 (0) | -0.001 | 0.2% | 0.4% |
URMA | 5 | 1000 | -0.002 | 0.267 | 0.081 | 96.0% | -0.006 | 0.267 | 0.0887 | 94.0% | -0.006 (89) | 0.015 (81) | - | - | - |
BRMA | 5 | 998 | -0.002 | 0.274 | 0.081 | 96.7% | -0.006 | 0.269 | 0.0894 | 95.3% | 0.008 (10) | 0.024 (0) | -0.027 | 29.6% | 29.0% |
Scenario (ii): Complete data – no within-study correlation, high between-study correlation; within-study variance similar to between-study variance | |||||||||||||||
URMA | 50 | 1000 | -0.004 | 0.102 | 0.010 | 95.6% | 0.001 | 0.106 | 0.0114 | 94.4% | 0 (0) | -0.004 (1) | - | - | - |
BRMA | 50 | 1000 | -0.004 | 0.100 | 0.010 | 95.3% | 0 | 0.104 | 0.0107 | 95.4% | 0.001 (0) | -0.001 (0) | -0.005 | 0% | 25.2% |
URMA | 5 | 999 | -0.002 | 0.271 | 0.077 | 97.3% | -0.005 | 0.263 | 0.0826 | 94.2% | 0.004 (80) | 0.005 (104) | - | - | - |
BRMA | 5 | 1000 | -0.002 | 0.279 | 0.077 | 98.1% | -0.008 | 0.268 | 0.0819 | 95.7% | 0.024 (15) | 0.024 (0) | -0.161 | 10.3% | 60.5% |
Scenario (viii): Missing data – no within-study correlation, high between-study correlation; within-study variance smaller than between-study variance | |||||||||||||||
URMA | 50 | 1000 | -0.004 | 0.071 | 0.005 | 94.9% | 0 | 0.099 | 0.0101 | 95.0% | -0.006 (0) | -0.005 (0) | - | - | - |
BRMA | 50 | 1000 | -0.004 | 0.071 | 0.005 | 94.9% | 0 | 0.082 | 0.0068 | 95.2% | -0.006 (0) | -0.007 (0) | -0.001 | 0% | 0% |
URMA | 10 | 1000 | -0.002 | 0.154 | 0.028 | 94.1% | -0.003 | 0.209 | 0.0576 | 93.7% | -0.006 (0) | -0.006 (0) | - | - | - |
BRMA | 10 | 1000 | -0.002 | 0.154 | 0.028 | 94.1% | -0.001 | 0.174 | 0.0427 | 93.3% | -0.006 (0) | 0.006 (0) | -0.040 | 0% | 3.9% |
Scenario (ix): Missing data – no within-study correlation, high between-study correlation; within-study variance similar to between-study variance | |||||||||||||||
URMA | 50 | 1000 | -0.004 | 0.102 | 0.010 | 95.6% | -0.001 | 0.145 | 0.0228 | 94.2% | 0 (0) | -0.003 (6) | - | - | - |
BRMA | 50 | 1000 | -0.004 | 0.101 | 0.010 | 95.8% | -0.003 | 0.137 | 0.0203 | 94.7% | 0.001 (0) | 0.003 (0) | -0.012 | 0.1% | 35.6% |
URMA | 10 | 1000 | -0.001 | 0.218 | 0.045 | 93.9% | -0.005 | 0.263 | 0.0825 | 94.2% | 0.006 (45) | 0.005 (84) | - | - | - |
BRMA | 10 | 997 | -0.001 | 0.222 | 0.045 | 96.5% | -0.007 | 0.255 | 0.0797 | 95.6% | 0.020 (0) | 0.025 (0) | -0.164 | 10.1% | 60.2% |