mvma.hybrid | R Documentation |
Performs a multivariate meta-analysis using the hybrid random-effects model when the within-study correlations are unknown.
mvma.hybrid(ys, vars, data, method = "reml", tol = 1e-10)
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. |
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. |
data |
an optional data frame containing the multivariate meta-analysis dataset. If |
method |
a character string specifying the method for estimating the overall effect sizes. It should be |
tol |
a small number specifying the convergence tolerance for the estimates by maximizing (restricted) likelihood. The default is |
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{μ}, (\mathbf{D}_i + \mathbf{T})^{1/2} \mathbf{R} (\mathbf{D}_i + \mathbf{T})^{1/2}),
where \boldsymbol{μ} represents the overall effect sizes across studies, \mathbf{T} = diag(τ_1^2, …, τ_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.
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. |
The algorithm for maximizing (restricted) likelihood may not converge when the dimension of endpoints is too high or the data are too sparse.
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>
mvma
, mvma.bayesian
, mvma.hybrid.bayesian
data("dat.fib") y <- dat.fib$y sd <- dat.fib$sd mvma.hybrid(y = y, vars = sd^2)
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