= Solution
Calling the effects <exchangeable random variables> means that their joint <prior distribution> is unchanged by permuting study labels. In a <hierarchical Bayesian model>, conditional independent draws $\beta_j\mid\mu,\tau\sim N(\mu,\tau^2)$ achieve this, and integrating shared <hyperparameters> induces dependence between studies. This permits <partial pooling> without asserting that all effects are identical.
The assumption is reasonable when the studies concern comparable treatments, populations, outcomes and follow-up, and no known study characteristic gives one effect a systematically different prior center. Relevant differences can instead enter a <linear regression> for study effects, after which the residual effects may be exchangeable. \b[The numerical table counts deaths], so its event probabilities are mortality probabilities and $\beta_j<0$ indicates a lower mortality <odds ratio>. Interpreting those counts as beneficial responses would reverse the clinical meaning.
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