= Random-effects meta-analysis
{title2=$y_i\sim N(\mu,v_i+\tau^2)$}
For <independent> study estimates $y_i$ with within-study <variances> $v_i$, a usual approximate model is $y_i\mid\delta_i\sim N(\delta_i,v_i)$ and $\delta_i\sim N(\mu,\tau^2)$. Its <marginal distribution> is $N(\mu,v_i+\tau^2)$, so for fixed heterogeneity $\tau^2$ the <inverse-variance weighted mean> uses weights $(v_i+\tau^2)^{-1}$. Here $\mu$ describes the mean effect across comparable studies; $\tau^2$ represents between-study variation. Estimation and uncertainty for heterogeneity are essential, especially with few studies.
Back to article page
