mvma {altmeta}

Multivariate Meta-Analysis

Description

Performs a multivariate meta-analysis when the within-study correlations are known.

Usage

mvma(ys, covs, data, method = "reml", tol = 1e-10)

Arguments

ys

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.

covs

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.

data

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.

method

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).

tol

a small number specifying the convergence tolerance for the estimates by maximizing (restricted) likelihood. The default is 1e-10.

Details

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.

Value

This function returns a list containing the following elements:

mu.est

The estimated overall effect sizes of the p endpoints.

Tau.est

The estimated between-study covariance matrix.

mu.cov

The covariance matrix of the estimated overall effect sizes.

method

The method used to produce the estimates.

References

Jackson D, Riley R, White IR (2011). "Multivariate meta-analysis: potential and promise." Statistics in Medicine, 30(20), 2481–2498. <doi: 10.1002/sim.4172>

See Also

mvma.bayesian, mvma.hybrid, mvma.hybrid.bayesian

Examples

data("dat.fib")
mvma(ys = y, covs = S, data = dat.fib, method = "fe")

mvma(ys = y, covs = S, data = dat.fib, method = "reml")