mvmeta (version 1.0.3)

mvmeta.fixed: Fixed-Effects Estimator for mvmeta Models

Description

This function implements a generalized least square estimator for fixed-effects multivariate and univariate meta-analysis and meta-regression. It is meant to be used internally and not directly run by the users.

Usage

mvmeta.fixed(Xlist, ylist, Slist, nalist, k, m, p, nall, control, ...)

Arguments

Xlist

a \(m\)-dimensional list of study-specific design matrices for the fixed-effects part of the model. Rows corresponding to missing outcomes have been excluded.

ylist

a \(m\)-dimensional list of study-specific vectors of estimated outcomes. Entries corresponding to missing outcomes have been excluded.

Slist

a \(m\)-dimensional list of within-study (co)variance matrices of estimated outcomes. Rows and columns corresponding to missing outcomes have been excluded.

nalist

a \(m\)-dimensional list of \(k\)-dimensional study-specific logical vectors, identifying missing outcomes.

k, m, p, nall

numeric scalars: number of outcomes, number of studies included in estimation (equal to the length of lists above), number of predictors (including the intercept), number of observations (excluding missing).

control

list of parameters for controlling the fitting process, usually internally set to default values by mvmeta.control.

…

further arguments passed to or from other methods. Currently not used.

Value

This function returns an intermediate list object, whose components are then processed by mvmeta.fit. Other components are added later through mvmeta to finalize an object of class "mvmeta".

Details

The estimation involves only the \(kp\) fixed-effects coefficients.

The routine is based on a standard generalized least square (GLS) algorithm implemented in the internal function glsfit. The between-study (co)variance matrix is set to zero, so the marginal (co)variance matrix, composed only by elements of the within-study component, is assumed as completely known. Similarly to the likelihood-based estimators implemented in mvmeta.ml and mvmeta.reml, the computation involves Cholesky and and QR decompositions for computational stability and efficiency. The method is described in details in Gasparrini and collaborators (2012) (see references below).

References

Sera F, Armstrong B, Blangiardo M, Gasparrini A (2019). An extended mixed-effects framework for meta-analysis.Statistics in Medicine. 2019;38(29):5429-5444. [Freely available here].

Gasparrini A, Armstrong B, Kenward MG (2012). Multivariate meta-analysis for non-linear and other multi-parameter associations. Statistics in Medicine. 31(29):3821--3839. [Freely available here].

Berkey, CS, Anderson JJ, Hoaglin DC (1996). Multiple-outcome meta-analysis of clinical trials. Statistics in Medicine. 15(5):537--547.

Berkey, CS, Hoaglin DC, et al. (1998). Meta-analysis of multiple outcomes by regression with random effects. Statistics in Medicine. 17(22):2537--2550.

See Also

See 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 glsfit. See mvmeta-package for an overview of the package and modelling framework.

Examples

# NOT RUN {
# UNIVARIATE FIXED-EFFECTS MODEL
model <- mvmeta(yC,S=SCC,data=smoking,method="fixed")
summary(model)

# MULTIVARIATE FIXED-EFFECTS MODEL
y <- as.matrix(smoking[11:13])
S <- as.matrix(smoking[14:19])
model <- mvmeta(y,S,method="fixed")
summary(model)

# MULTIVARIATE FIXED-EFFECTS MODEL: REPLICATE THE RESULTS IN BERKEY ET AL. 1998
model <- mvmeta(cbind(PD,AL)~I(pubyear-1983),S=berkey98[5:7],
  data=berkey98,method="fixed")
summary(model)
# }