Last chance! 50% off unlimited learning
Sale ends in
Last chance! 50% off unlimited learning
Sale ends in
rma.uni function (with alias rma) provides a general framework for fitting the various models. The function can be used in conjunction with any of the usual effect size or outcome measures used in meta-analyses (e.g., log odds ratios, log risk ratios, risk differences, mean differences, standardized mean differences, raw correlation coefficients, correlation coefficients transformed with Fisher's r-to-z transformation, and so on). For details on these effect size or outcome measures, please see the documentation of the escalc function. The notation and models underlying the rma.uni function are explained below.
For a set of $i = 1, \ldots, k$ independent studies, let $y_i$ denote the observed value of the effect size or outcome measure in the $i^{th}$ study. Let $\theta_i$ denote the corresponding (unknown) true effect or outcome in the $i^{th}$ study, such that $y_i | \theta_i \sim N(\theta_i, v_i)$. In other words, the observed effects or outcomes are assumed to be unbiased and normally distributed estimates of the corresponding (unknown) true effects or outcomes with sampling variances equal to $v_i$. The $v_i$ values are assumed to be known.
The fixed-effects model conditions on the true effects or outcomes and therefore provides a conditional inference about the set of $k$ studies included in the meta-analysis. This implies that the fitted model provides an estimate of $\sum_{i=1}^k w_i \theta_i / \sum_{i=1}^k w_i$, that is, the weighted average of the true effects in the set of $k$ studies, with weights equal to $w_i = 1/v_i$. One can also employ an unweighted estimation method, which provides an estimate of the unweighted average of the true effects in the set of $k$ studies (i.e., an estimate of $1/k \sum_{i=1}^k \theta_i$).
Moderators can be included in the fixed-effects model, yielding a fixed-effects with moderators model. Again, since the model conditions on the set of $k$ studies included in the meta-analysis, the regression coefficients from the fitted model estimate the weighted least-squares relationship between the true effects and the moderator variables within the set of $k$ studies included in the meta-analysis (again using weights equal to $w_i = 1/v_i$). The (unweighted) least-squares relationship between the true effects and the moderator variables can be obtained when using the unweighted estimation method.
The random-effects model does not condition on the true effects. Instead, the $k$ studies included in the meta-analysis are assumed to be a random selection from a hypothetical population of studies. One can envision this hypothetical population as an essentially infinite set of studies comprising all of the studies that have been conducted, that could have been conducted, or that may be conducted in the future. The true effects or outcomes in this population of studies are assumed to be normally distributed with $\mu$ denoting the average effect and $\tau^2$ denoting the variance of the true effects in the population ($\tau^2$ is therefore often referred to as the rma.uni function. Functions to handle multivariate situations and correlated outcomes will be included in the package at a later point.rma.mh function. It can be used in combination with odds ratios, risk ratios, and risk differences. The Mantel-Haenszel method is always based on a weighted estimation approach.rma.peto function. It is a weighted estimation approach for the combination of odds ratios.