Performs a multivariate meta-analysis when the within-study correlations are known.
mvma(ys, covs, data, method = "reml", tol = 1e-10)This function returns a list containing the following elements:
The estimated overall effect sizes of the p endpoints.
The estimated between-study covariance matrix.
The covariance matrix of the estimated overall effect sizes.
The method used to produce the estimates.
an n x p numeric matrix containing the observed effect sizes. The n rows represent studies, and the p columns represent the multivariate endpoints. NA is allowed for missing endpoints.
a numeric list with length n. Each element is the p x p within-study covariance matrix. NA is allowed for missing endpoints in the covariance matrix.
an optional data frame containing the multivariate meta-analysis dataset. If data is specified, the previous arguments, ys and covs, should be specified as their corresponding column names in data.
a character string specifying the method for estimating the overall effect sizes. It should be "fe" (fixed-effects model), "ml" (random-effects model using the maximum likelihood method), or "reml" (random-effects model using the restricted maximum likelihood method, the default).
a small number specifying the convergence tolerance for the estimates by maximizing (restricted) likelihood. The default is 1e-10.
Suppose \(n\) studies are collected in a multivariate meta-analysis on a total of \(p\) endpoints. Denote the \(p\)-dimensional vector of effect sizes as \(\boldsymbol{y}_i\), and the within-study covariance matrix \(\mathbf{S}_i\) is assumed to be known. Then, the random-effects model is as follows: $$\boldsymbol{y}_i \sim N (\boldsymbol{\mu}_i, \mathbf{S}_i);$$ $$\boldsymbol{\mu}_i \sim N (\boldsymbol{\mu}, \mathbf{T}).$$ Here, \(\boldsymbol{\mu}_i\) represents the true underlying effect sizes in study \(i\), \(\boldsymbol{\mu}\) represents the overall effect sizes across studies, and \(\mathbf{T}\) is the between-study covariance matrix due to heterogeneity. By setting \(\mathbf{T} = \mathbf{0}\), this model becomes the fixed-effects model.
Jackson D, Riley R, White IR (2011). "Multivariate meta-analysis: potential and promise." Statistics in Medicine, 30(20), 2481--2498. <tools:::Rd_expr_doi("10.1002/sim.4172")>
mvma.bayesian, mvma.hybrid, mvma.hybrid.bayesian
data("dat.fib")
mvma(ys = y, covs = S, data = dat.fib, method = "fe")
# \donttest{
mvma(ys = y, covs = S, data = dat.fib, method = "reml")
# }
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