= Solution
A <fixed-effect meta-analysis> models the studies as estimating a common underlying treatment effect. In a generic inverse-variance version, independent <log odds ratios> $y_i$ have approximate distributions $N(\delta,v_i)$ and are pooled with weights $1/v_i$. The supplied <forest plot> instead has the <Mantel–Haenszel pooled odds ratio> weights: for event/nonevent cells $a_i,b_i,c_i,d_i$ and total $n_i$, the normalized weights are proportional to $b_ic_i/n_i$. They reproduce the printed percentages and yield a pooled odds ratio about $2.338$. This is still a common-effect analysis; the two weighting methods should not be silently identified.
A <random-effects meta-analysis> allows different true effects: $y_i\mid\delta_i\sim N(\delta_i,v_i)$ with $\delta_i\sim N(\mu,\tau^2)$. The <between-study heterogeneity> variance $\tau^2$ adds to sampling variance, giving marginal variance $v_i+\tau^2$. Its pooled estimate targets the mean of the study-effect distribution rather than one identical effect. Uncertainty about heterogeneity must also be considered.
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