VMETA procedure

Performs a multi-treatment 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 between-experiment variance-covariance 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 variance-covariance 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 multi-treatment 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 variance-covariance structure used to model the variation and correlation of the between-experiment treatment effects. (See the Method Section below for details.) The variance-covariance 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 variance-covariance 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 experiment-level factor or a variate that is to be incorporated into the linear mixed model to account for experiment-specific 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 multi-treatment 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 variance-covariance models that can be specified by the VCMODEL option, and subsequently fitted by REML using the VSTRUCTURE directive, are:

Setting	Description	Variance-covariance matrix	Number of parameters
*Fixed experiment effects*
`identity`	Identity	C_i,i = σ_μ²C_i,j = 0, for i ≠ j	1
`diagonal`	Diagonal matrix (heteroscedastic)	C_i_,i = σ_μ_(i)²C_i,j = 0, for i ≠ j	m
*Random experiment effects*
`cs`	Compound symmetry	C_i_,i = σ_β² + σ_μ²C_i,j = σ_β², for i ≠ j	2
`hcs`	Heterogeneous compound symmetry	C_i_,i = σ_T_(i)²C_i,j = ρσ_T_(i)σ_T_(j), for i ≠ j	m + 1
`unstructured`	Unstructured	C_i_,i = σ_T_(i)²C_i,j = σ_T_(ij), for i ≠ j	m(m + 1)/2
`faequal1`	First order factor analytic model with common variance	C_i_,i = γ_i² + σ_ν²C_i,j = γ_iγ_j, for i ≠ j	m + 1
`faequal2`	Second order factor analytic model with common variance	C_i_,i = γ_i⁽¹⁾² + γ_i⁽²⁾² + σ_ν²C_i,j = γ_i⁽¹⁾γ_j⁽¹⁾ + γ_i⁽²⁾γ_j⁽²⁾, for i ≠ j	2m
`fa1`	First order factor analytic model	C_i_,i = γ_i² + σ_ν_(i)²C_i,j = γ_iγ_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 meta-analysis. Phytopathology, 106, 792-806.

Example

CAPTION !t('VMETA example'),\
        !t('Meta-analysis 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 within-trial 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 meta-analysis. \
~i{Phytopathology} 106(8):792-806.'); STYLE=meta,plain,plain,plain 

SPLOAD [PRINT=*] '%data%/MetaWheat.gsh'

CAPTION !t('Fixed trial effects with heterogeneous between-trial 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 \
between-trial variance-covariance structure'); STYLE=major
VMETA   [EMETHOD=random; VCMODEL=hcs] MEANS=Yield; TREATMENTS=Trt;\
         EXPERIMENTS=Trial; VARIANCES=varyld

Updated on October 29, 2020

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