mvmeta (version 1.0.3)

mvmeta.ml: ML and REML Estimators for mvmeta Models

Description

These functions implement maximum likeliihood (ML) and restricted maximum likelihood (REML) estimators for random-effects multivariate and univariate meta-analysis and meta-regression. They are meant to be used internally and not directly run by the users.

Usage

mvmeta.ml(Xlist, ylist, Slist, nalist, k, m, p, nall, bscov, control, ...)
mvmeta.reml(Xlist, ylist, Slist, nalist, k, m, p, nall, bscov, 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).

bscov

a string defining the between-study (co)variance structure in likelihood based models. See Details.

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

These functions return 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 \(kp\) fixed-effects coefficients and a number of random-effects parameters defining the between-study (co)variance matrix, depending on the chosen (co)variance structure. Up to \(k(k+1)/2\) parameters are needed for an unstructured form, while a smaller set are required for structed matrices

The hybrid estimation procedure is based first on few runs of iterative generalized least square algorithm and then quasi-Newton iterations, using specific likelihood functions, until convergence. The estimation algorithm adopts a profiled (or concentrated) approach, that is expressed only in terms of the random-effects parameters. Cholesky and and QR decompositions are used for computational stability and efficiency, and for assuring the positive-definiteness of the estimated between-study (co)variance matrix. See the help page for the likelihood functions for further details. 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].

Pinheiro JC and Bates DM (2000). Mixed-Effects Models in S and S-PLUS. New York, Springer Verlag.

Lindstrom MJ and Bates DM (1988). Newton-Raphson and EM algorithms for linear mixed-effects models for repeated-measures data. Journal of the American Statistical Association. 83(404):1014--1022.

White IR (2009). Multivariate random-effects meta-analysis. Stata Journal. 9(1):40--56.

White IR (2011). Multivariate random-effects meta-regression: updates to mvmeta. Stata Journal. 11(2):255-270.

Goldstein H (1986). Multilevel mixed linear model analysis using iterative generalized least squares. Biometrika. 73(1):43.

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 {
# REML ESTIMATOR: UNIVARIATE MODEL
model <- mvmeta(yC,S=SCC,data=smoking)
summary(model)

# REML ESTIMATOR: REPRODUCE THE RESULTS IN WHITE (2011)
y <- as.matrix(smoking[11:13])
S <- as.matrix(smoking[14:19])
model <- mvmeta(y,S)
summary(model)

# ML ESTIMATOR: REPRODUCE THE RESULTS IN BERKEY ET AL. (1998)
year <- berkey98$pubyear - 1983
model <- mvmeta(cbind(PD,AL)~year,S=berkey98[5:7],data=berkey98,method="ml")
print(summary(model),digits=3)
round(model$Psi,3)

# UNSTRUCTURED AND STRUCTURED BETWEEN-STUDY (CO)VARIANCE
y <- as.matrix(fibrinogen[2:5])
S <- as.matrix(fibrinogen[6:15])
model <- mvmeta(y,S)
summary(model)
model <- mvmeta(y,S,bscov="diag")
summary(model)
model <- mvmeta(y,S,bscov="hcs")
summary(model)

# SEE help(mvmetaCovStruct) for additional info and examples
# }