Performs a multitreatment meta analysis using summary results from individual experiments (V.M. Cave).
Options
PRINT = string tokens 
Controls printed output from the REML analysis (model , components , effects , means , monitoring , vcovariance , deviance , Waldtests , covariancemodels ); default mode , comp , cova , mean 
PSE = string token 
Standard errors to be printed with tables of effects and means (differences , estimates , alldifferences , allestimates , none ); default alle 
EMETHOD = string token 
Specifies whether the EXPERIMENTS main effect is fitted as a fixed or random term in the REML model; default fixe 
VCMODEL = string token 
Specifies the betweenexperiment variancecovariance model (identity , diagonal , cs , hcs , unstructured , faequal1 , faequal2 , fa1 ); default iden for fixed EXPERIMENTS effects and cs for random effects 
INITIAL = scalars, variates, matrices, symmetric matrices or pointers 
Initial parameter values for the variancecovariance model specified by VCMODEL (supplied in the structures appropriate for the model concerned); default generates values automatically 
MAXCYCLE = scalar 
Sets a limit on the number of iterations in the REML analysis; default 30 
Parameters
MEANS = variates 
Supplies the TREATMENTS by EXPERIMENTS means 
TREATMENTS = factors 
Identifier of the treatments factor 
EXPERIMENTS = factors 
Identifier of the experiments factor 
SEDMEANS = variates 
Supplies the (average) standard error of differences in each experiment 
VARIANCES = variates 
Identifier for the variate containing the sampling variance for each experiment 
MODERATOR = factors or variates 
Identifier for a moderator variable 
SAVE = REML save structures 
Saves the details of each analysis for use in subsequent VDISPLAY and VKEEP directives 
Description
VMETA
uses REML
to perform a multitreatment meta analysis, when only the summary results for each treatment (i.e. means and standard error of the difference or sampling variance) are available from the individual experiments. The estimated treatment means for each experiment are supplied, in a variate, using the MEANS
parameter. The TREATMENTS
and EXPERIMENTS
parameters must specify factors indicating the treatment and experiment, respectively, corresponding to each mean.
You must use either the SEDMEANS
parameter to supply the (average) standard error of differences for the experiments, or the VARIANCES
parameter to supply their sampling variances. You can specify these in a variate with the same length as the number of experiments. Alternatively, you can supply them in a variate with the same length as MEANS
. However, this must contain the same value for the treatments in each experiment.
The EMETHOD
option specifies whether the experiment effects are fitted as fixed or random; default fixed. The VCMODEL
option specifies the variancecovariance structure used to model the variation and correlation of the betweenexperiment treatment effects. (See the Method Section below for details.) The variancecovariance models available depend on the EMETHOD
option. When EMETHOD=fixed
, the possibilities are identity (default) and diagonal. When EMETHOD=random
, they are cs
(default), hcs
, unstructured
, faequal1
, faequal2
and fa1
. Initial values for the parameters of the variancecovariance model can be supplied by the INITIAL option, which corresponds to the INITIAL
parameter of the VSTRUCTURE
directive. Default values are generated automatically. For all models, except unstructured, the number of initial values is the number of parameters. However, for the unstructured model, a full covariance matrix of initial values must be given. The initial values must be supplied in the structures appropriate for the model concerned. See the VSTRUCTURE
directive for details.
The MODERATOR
parameter can be used to supply either an experimentlevel factor or a variate that is to be incorporated into the linear mixed model to account for experimentspecific effects on the estimated treatment means. You can specify these in a variate with the same length as the number of experiments. Alternatively, you can supply them in a variate with the same length as MEANS
. However, this must contain the same value for the treatments in each experiment.
The PRINT
and PSE
options controls the output from the REML
analyses, with the same settings as the PRINT
and PSE
options of REML
, respectively. The default setting of PRINT
gives a description of the model and covariance models that have been fitted, plus estimates of the variance components and the predicted means. The default setting of PSE=allestimates
gives the all the standard errors.
The MAXCYCLE
option sets a limit on the number of iterations in the REML
analysis (default 30). The SAVE
parameter can be used to name the REML
save structure for later use with the VKEEP
and VDISPLAY
directives.
Options: PRINT
, PSE
, EMETHOD
, VCMODEL
, INITIAL
, MAXCYCLE
.
Parameters: MEANS
, TREATMENTS
, EXPERIMENTS
, SEDMEANS
, VARIANCES
, MODERATOR
, SAVE
.
Method
VMETA
uses the methods described in Madden et al. (2016). The multitreatment meta analysis (also known as network meta analysis) is performed on summary results for each treatment (i.e. means and standard error of the difference or sampling variance) using a linear mixed model, fitted by VMETA
using the REML
, VCOMPONENTS
and VSTRUCTURE
directives in the usual way.
The treatment term, and if supplied, the moderator term are fitted as fixed, but the experiment term may be fitted as either fixed or random.
The variancecovariance models that can be specified by the VCMODEL
option, and subsequently fitted by REML
using the VSTRUCTURE
directive, are:
Setting 
Description 
Variancecovariance matrix 
Number of parameters 
Fixed experiment effects 


Identity 
C_{i,i} = σ_{μ}^{2 }C_{i,j} = 0, for i ≠ j 
1 

Diagonal matrix (heteroscedastic) 
C_{i}_{,i} = σ_{μ}_{(i)}^{2 }C_{i,j} = 0, for i ≠ j 
m 
Random experiment effects 


Compound symmetry 
C_{i}_{,i} = σ_{β}^{2} + σ_{μ}^{2 }C_{i,j} = σ_{β}^{2}, for i ≠ j 
2 

Heterogeneous compound symmetry 
C_{i}_{,i} = σ_{T}_{(i)}^{2 }C_{i,j} = ρσ_{T}_{(i)}σ_{T}_{(j)}, for i ≠ j 
m + 1 

Unstructured 
C_{i}_{,i} = σ_{T}_{(i)}^{2 }C_{i,j} = σ_{T}_{(ij)}, for i ≠ j 
m(m + 1)/2 

First order factor analytic model with common variance 
C_{i}_{,i} = γ_{i}^{2} + σ_{ν}^{2 }C_{i,j} = γ_{i}γ_{j}, for i ≠ j 
m + 1 

Second order factor analytic model with common variance 
C_{i}_{,i} = γ_{i}^{(1)2} + γ_{i}^{(2)2} + σ_{ν}^{2 }C_{i,j} = γ_{i}^{(1)}γ_{j}^{(1)} + γ_{i}^{(2)}γ_{j}^{(2)}, for i ≠ j 
2m 

First order factor analytic model 
C_{i}_{,i} = γ_{i}^{2} + σ_{ν}_{(i)}^{2 }C_{i,j} = γ_{i}γ_{j}, for i ≠ j 
2m 
In this table i, j = 1 … m, where m is the number of treatments.
Action with RESTRICT
VMETA
will work with restrictions. However, if more than one variate or factor is restricted, they must be restricted in the same way. In addition, parameters SEDMEANS
, VARIANCES
and MODERATOR
may only be restricted if they supply vectors of the same length as the MEANS
variate.
References
Madden, L.V., Piepho, H.P., & Paul, P.A. (2016). Statistical models and methods for network metaanalysis. Phytopathology, 106, 792806.
See also
Directives: REML
, VCOMPONENTS
, VSTRUCTURE
Procedures: META
, VAMETA
, VASMEANS
Commands for: REML analysis of linear mixed models.
Example
CAPTION !t('VMETA example'),\ !t('Metaanalysis of wheat yield from Madden et al. (2016).'),\ !t('~{break}The data set contains the trial ID (factor Trial), the \ treatment ID (factor Trt), the mean yield per treatment in each trial \ (variate Yield) and corresponding withintrial sampling variance (variate \ varyld), and the wheat marketing class (factor cla).'),\ !t('~{break}Reference: Madden L.V., Piepho, H.P., & Paul, P.A. \ (2016). Statistical models and methods for network metaanalysis. \ ~i{Phytopathology} 106(8):792806.'); STYLE=meta,plain,plain,plain SPLOAD [PRINT=*] '%data%/MetaWheat.gsh' CAPTION !t('Fixed trial effects with heterogeneous betweentrial variances');\ STYLE=major VMETA [EMETHOD=fixed; VCMODEL=diagonal] MEANS=Yield; TREATMENTS=Trt;\ EXPERIMENTS=Trial; VARIANCES=varyld CAPTION !t('Random trial effects with a heterogeneous compound symmetry \ betweentrial variancecovariance structure'); STYLE=major VMETA [EMETHOD=random; VCMODEL=hcs] MEANS=Yield; TREATMENTS=Trt;\ EXPERIMENTS=Trial; VARIANCES=varyld