mvmeta: Multivariate fixed-effects meta-analysis via generalized...

In gap: Genetic Analysis Package

Multivariate fixed-effects meta-analysis via generalized least squares

Description

Performs multivariate meta-analysis by pooling study-specific parameter estimates using generalized least squares (GLS) under a fixed-effects model.

Usage

mvmeta(b, V)

Arguments

b	Matrix of study estimates (studies × parameters).
V	may be supplied with a matrix of upper-triangular rows a list of covariance matrices a 3D array (p × p × k)

Details

The function accepts a matrix of parameter estimates and the corresponding within-study covariance matrices (stored in upper-triangular vector form).

This approach is appropriate when combining correlated effect estimates, for example correlation coefficients of SNPs across studies.

The function fits a multivariate fixed-effects meta-analysis using generalized least squares (GLS).

For study i = 1,\dots,k, let d_i be the vector of observed parameter estimates and \Psi_i the corresponding within-study covariance matrix:

d_i \sim N(\beta,\; \Psi_i)

where \beta is the vector of common (pooled) parameters.

The study estimates are stacked into a single vector

d = (d_1^T,\dots,d_k^T)^T

with block-diagonal covariance matrix

\Psi = \mathrm{blockdiag}(\Psi_1,\dots,\Psi_k).

The model can then be written in GLS regression form

d = X\beta + \varepsilon, \qquad \varepsilon \sim N(0,\Psi)

where X is a block design matrix that repeats an identity matrix for each study (intercept-only multivariate meta-analysis). Missing outcomes are automatically removed when constructing d, \Psi and X.

The pooled estimator is the GLS estimator

\hat{\beta} = (X^T \Psi^{-1} X)^{-1} X^T \Psi^{-1} d.

Heterogeneity is assessed using the multivariate Cochran Q statistic

Q = (d - X\hat{\beta})^T \Psi^{-1} (d - X\hat{\beta}),

which is asymptotically \chi^2_{N-p}, where N is the number of observed estimates and p the number of pooled parameters.

This implementation corresponds to the multivariate fixed-effects model described in Hartung et al. (2008, Example 11.3).

Value

An object of class "mvmeta" with the following elements:

• beta: pooled estimates

• vcov: covariance matrix of pooled estimates

• se: standard errors

• z: z statistics

• pval: p values

• ci: 95% confidence intervals

• X2, df, p: heterogeneity test

• logLik: model log-likelihood

• k: number of studies

• p_outcomes: number of pooled outcomes

Author(s)

Jing Hua Zhao

References

\insertRef

hartung08gap

See Also

metareg

Examples

## Not run: 
# Example 11.3 from Hartung et al.
b <- matrix(c(
0.808, 1.308, 1.379, NA, NA,
NA, 1.266, 1.828, 1.962, NA,
NA, 1.835, NA, 2.568, NA,
NA, 1.272, NA, NA, 2.038,
1.171, 2.024, 2.423, 3.159, NA,
0.681, NA, NA, NA, NA), ncol=5, byrow=TRUE)

psi1 <- psi2 <- psi3 <- psi4 <- psi5 <- psi6 <- matrix(0,5,5)
psi1[1,1] <- 0.0985; psi1[1,2] <- 0.0611; psi1[1,3] <- 0.0623
psi1[2,2] <- 0.1142; psi1[2,3] <- 0.0761; psi1[3,3] <- 0.1215

psi2[2,2] <- 0.0713; psi2[2,3] <- 0.0539; psi2[2,4] <- 0.0561
psi2[3,3] <- 0.0938; psi2[3,4] <- 0.0698; psi2[4,4] <- 0.0981

psi3[2,2] <- 0.1228; psi3[2,4] <- 0.1119; psi3[4,4] <- 0.1790
psi4[2,2] <- 0.0562; psi4[2,5] <- 0.0459; psi4[5,5] <- 0.0815

psi5[1,1] <- 0.0895; psi5[1,2] <- 0.0729; psi5[1,3] <- 0.0806
psi5[1,4] <- 0.0950; psi5[2,2] <- 0.1350; psi5[2,3] <- 0.1151
psi5[2,4] <- 0.1394; psi5[3,3] <- 0.1669; psi5[3,4] <- 0.1609
psi5[4,4] <- 0.2381

psi6[1,1] <- 0.0223

V <- rbind(psi1[upper.tri(psi1,diag=TRUE)],
           psi2[upper.tri(psi2,diag=TRUE)],
           psi3[upper.tri(psi3,diag=TRUE)],
           psi4[upper.tri(psi4,diag=TRUE)],
           psi5[upper.tri(psi5,diag=TRUE)],
           psi6[upper.tri(psi6,diag=TRUE)])

fit <- mvmeta(b, V)
summary(fit)
logLik(fit)
AIC(fit)
BIC(fit)

## End(Not run)

gap documentation built on May 28, 2026, 9:07 a.m.