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### Table 9Definition of MSE, bias and coverage probability

Mean squared error (MSE) $1500Σi=1500(θ^j,1i-θj,1)2$ $1500Σi=1500(θ^j,2i-θj,2)2$The average squared difference between the true (simulated) mean and its estimate across the 500 simulation replicates in scenario j.
• Desirable to have MSE near zero.
• MSE can be high even if bias is 0, because positive and negative deviations of the estimates from the true mean do not cancel out.
• MSE is the sum of the variance of an estimate plus the square of its bias.
Bias $1500Σi=1500(θ^j,1i-θj,1)$ $1500Σi=1500(θ^j,2i-θj,2)$The average difference between the true (simulated) mean and its estimate across the 500 simulation replicates in scenario j.
• Desirable to have bias near zero.
Coverage probability $1500Σi=1500I(θj,1∈[95%CI of θ^j,1i])$ $1500Σi=1500I(θj,2∈[95%CI of θ^j,2i])$The proportion of times the 95% confidence interval of the estimated summary mean contains the true value.
• Desirable to have coverage near 95%.
• Coverage higher than 95% indicates an inefficient estimator
• Coverage less than 95% indicates an inaccurate estimator

j,1i stands for the meta-analysis estimate in draw i, and analogously for the other outcome.

From: Methods

Empirical and Simulation-Based Comparison of Univariate and Multivariate Meta-Analysis for Binary Outcomes [Internet].
Trikalinos TA, Hoaglin DC, Schmid CH.

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