mvma.hybrid {altmeta}

Hybrid Model for Random-Effects Multivariate Meta-Analysis

Description

Performs a multivariate meta-analysis using the hybrid random-effects model when the within-study correlations are unknown.

Usage

mvma.hybrid(ys, vars, 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.

vars

an n x p numeric matrix containing the observed within-study variances. The n rows represent studies, and the p columns represent the multivariate endpoints. NA is allowed for missing endpoints.

data

an optional data frame containing the multivariate meta-analysis dataset. If data is specified, the previous arguments, ys and vars, 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 "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 their within-study variances form a diagonal matrix \mathbf{D}_i. However, the within-study correlations are unknown. Then, the random-effects hybrid model is as follows (Riley et al., 2008; Lin and Chu, 2018):

\boldsymbol{y}_i \sim N (\boldsymbol{\mu}, (\mathbf{D}_i + \mathbf{T})^{1/2} \mathbf{R} (\mathbf{D}_i + \mathbf{T})^{1/2}),

where \boldsymbol{\mu} represents the overall effect sizes across studies, \mathbf{T} = diag(\tau_1^2, \ldots, \tau_p^2) consists of the between-study variances, and \mathbf{R} is the marginal correlation matrix. Although the within-study correlations are unknown, this model accounts for both within- and between-study correlations by using the marginal correlation matrix.

Value

This function returns a list containing the following elements:

mu.est

The estimated overall effect sizes of the p endpoints.

tau2.est

The estimated between-study variances of the p endpoints.

mar.R

The estimated marginal correlation matrix.

mu.cov

The covariance matrix of the estimated overall effect sizes.

method

The method used to produce the estimates.

Note

The algorithm for maximizing (restricted) likelihood may not converge when the dimension of endpoints is too high or the data are too sparse.

References

Lin L, Chu H (2018), "Bayesian multivariate meta-analysis of multiple factors." Research Synthesis Methods, 9(2), 261–272. <doi: 10.1002/jrsm.1293>

Riley RD, Thompson JR, Abrams KR (2008), "An alternative model for bivariate random-effects meta-analysis when the within-study correlations are unknown." Biostatistics, 9(1), 172–186. <doi: 10.1093/biostatistics/kxm023>

See Also

mvma, mvma.bayesian, mvma.hybrid.bayesian

Examples

data("dat.fib")
y <- dat.fib$y
sd <- dat.fib$sd
mvma.hybrid(y = y, vars = sd^2)