mvmeta.vc(Xlist, ylist, Slist, nalist, k, m, p, nall, control, ...)mvmeta.control.mvmeta.fit. Other components are added later through mvmeta to finalize an object of class "mvmeta".
The procedure is based on the estimate of the between-study (co)variance as the difference between the marginal (co)variance and the average within-study (co)variance. This in turn requires the estimate of the marginal (co)variance, obtained by the residuals of the fitted model. The procedure is iterative, with the current estimate of the between-study (co)variance plugged into a generalized least square (GLS) routine. Starting values are provided by a fixed-effects estimator (see mvmeta.fixed). The algorithm is fast and generally converges with few iterations.
Similar versions of this estimator has been previously proposed. Berkey and collaborators (1998) simply called it GLS method, and a non-iterative approach was proposed by Ritz and collaborators (2008), referred to as MVEE3. A non-iterative version for univariate models is discussed in Sidik and Jonkman (2007). The results from Berkey and collaborators (1998) are reproduced in the example below.
In the original approach, the estimate of the marginal (co)variance is obtained from the sum of the residual components using a denominator equal to m-p. Following the development proposed by Kauermann and Carroll (2001) and Fay and Graubard (2001) in the context of sandwich (co)variance estimators, then discussed by Lu and collaborators (2007), an adjusted denominator can be computed as a quantity derived from the hat matrix. This method is expected to perform better in the presence of missing values and small data sets. This alternative adjustment is chosen by default by setting vc.adj=TRUE in the control argument.
The variance component estimator is not bounded to provide a positive semi-definite between-study (co)variance matrix, as shown in the simulation study by Liu and colleagues (2009). Here positive semi-definiteness is forced by setting the negative eigenvalues of the estimated matrix to zero at each iteration. Little is known about the impact of such constraint.
Ritz J, Demidenko E, Spiegelman G (2008). Multivariate meta-analysis for data consortia, individual patient meta-analysis, and pooling projects. Journal of Statistical Planning and Inference. 139(7):1919--1933.
Berkey, CS, Hoaglin DC, et al. (1998). Meta-analysis of multiple outcomes by regression with random effects. Statistics in Medicine. 17(22):2537--2550.
Liu Q, Cook NR, Bergstrom A, Hsieh CC (2009). A two-stage hierarchical regression model for meta-analysis of epidemiologic nonlinear dose-response data. Computational Statistics and Data Analysis. 53(12):4157--4167
Sidik K, Jonkman JN (2007). A comparison of heterogeneity variance estimators in combining results of studies. Statistics in Medicine. 26(9):1964--81.
mvmeta for the general usage of the functions. See mvmeta.control to determine specific parameters of the fitting procedures. Use the triple colon operator (':::') to access the code of the internal functions, such as sumlist. See mvmeta-package for an overview of the package and modelling framework.
# VC ESTIMATOR: UNIVARIATE MODEL
model <- mvmeta(PD~pubyear,S=berkey98[,5],data=berkey98,method="vc")
summary(model)
# VC ESTIMATOR: MULTIVARIATE MODEL
model <- mvmeta(cbind(PD,AL)~pubyear,S=berkey98[5:7],data=berkey98,method="vc")
summary(model)
# VC ESTIMATOR: NON-ITERATIVE VERSION
model <- mvmeta(cbind(PD,AL)~pubyear,S=berkey98[5:7],data=berkey98,method="vc",
control=list(maxiter=1))
summary(model)
# VARIANCE COMPONENTS ESTIMATOR: REPLICATE THE RESULTS IN BERKEY ET AL. (1998)
model <- mvmeta(cbind(PD,AL)~I(pubyear-1983),S=berkey98[5:7],
data=berkey98,method="vc",control=list(vc.adj=FALSE))
summary(model)
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