= Meta-regression
{wiki}
Meta-regression relates study effect estimates to study-level explanatory variables. A common <random-effects meta-analysis> extension is $y_i=\alpha+\beta x_i+u_i+\varepsilon_i$, where $\operatorname{Var}(u_i)=\tau^2$ and $\operatorname{Var}(\varepsilon_i)=v_i$. For <log odds ratios>, $e^\beta$ is a ratio of underlying odds ratios per unit of $x$. Few studies, correlated design changes and exploratory variable selection limit interpretation; a study-level association does not identify an individual-level <causal effect>. The interpretation of study-level predictors is also discussed in https://www.cochrane.org/authors/handbooks-and-manuals/handbook/current/chapter-10[the Cochrane methods handbook, section 10.11].
Back to article page
