1. Home
  2. META procedure

META procedure

Combines estimates from individual trials (R.W. Payne & S. Senn).

Options

PRINT = string tokens Controls output (estimates, overalltest, heterogeneity, confidenceplot, radialplot, monitoring); default esti, over, hete, conf
SELECTION = string tokens Which combined estimates to include in the output (fixed, random); default fixe, rand
RMETHOD = string token How to form the random estimate (maxlikelihood, maxremllikelihood, moments, reml); default reml
XLABEL = text Label for the x-axis of the confidence plot; default 'treatment effect'
SMETHOD = string token How to set the sizes of symbols on the confidence plot (equal, inversese); default inve
CIPROBABILITY = scalar Probability level to use for the confidence intervals; default 0.95
CIMETHOD = string token Method to use for calculating the confidence interval for random estimates formed by maximum likelihood or REML (approximate, profile); default prof
PRMETHOD = string token Type of test to use for the overall probability values (greaterthan, lessthan, twosided); default grea
MAXCYCLE = scalar Maximum number of iterations to use with RMETHOD settings maxlikelihood and maxremllikelihood; default 100
TOLERANCE = scalar Convergence criterion to use with RMETHOD settings maxlikelihood and maxremllikelihood; default 10-6

Parameters

ESTIMATES = variates Supplies the estimates to combine
SEESTIMATES = variates Specifies the standard errors of the estimates
LABELS = texts Labels to use for each variate of ESTIMATES in the output
FIXEDESTIMATE = scalars Saves the combined estimate for each variate of ESTIMATES, treating them as fixed effects
SEFIXEDESTIMATE = scalars Saves the standard error of the combined estimate for each variate of ESTIMATES, treating them as fixed effects
PRFIXEDESTIMATE = scalars Saves the probability of the combined estimate for each variate of ESTIMATES, treating them as fixed effects
RANDOMESTIMATE = scalars Saves the combined estimate for each variate of ESTIMATES, treating them as random effects
SERANDOMESTIMATE = scalars Saves the standard error of the combined estimate for each variate of ESTIMATES, treating them as random effects
PRRANDOMESTIMATE = scalars Saves the probability of the combined estimate for each variate of ESTIMATES, treating them as random effects
QSTATISTIC = scalars Saves the statistic Q for the test of heterogeneity across trials
QDF = scalars Saves the degrees of freedom of the statistic Q
RVARIANCE = scalars Saves the random effect variance

Description

META produces a combined estimate of a parameter that has been estimated in several separate trials, using the methods described in Chapter 4 of Whitehead (2002).

The estimates to be combined in the meta analyses must be supplied, in a variate, using the ESTIMATES parameter. Their standard errors must be supplied similarly, using the SEESTIMATES parameter. The LABELS parameter can supply a text with a label to be used for each estimate in the output; if this is not supplied, the default is to use the integers 1, 2 and so on.

Printed output is controlled by the PRINT option, with settings:

    estimates table with the estimates from the individual trials and the combined estimates, with standard errors and confidence intervals;
    overalltest overall tests using the combined estimates;
    heterogeneity test for heterogeneity of the estimates across trials (Whitehead 2002, Section 4.2.3);
    confidenceplot plot of the individual and combined estimates, and their confidence intervals;
    radialplot plot of the standardized estimates against their precision i.e. the reciprocal of the standard error (also known as a Galbraith plot; see Whitehead 2002 Section 7.3.2);
    monitoring monitoring information from the estimation with RMETHOD settings maxlikelihood, maxremllikelihood and reml (see below).

By default PRINT=esti,over,hete,conf.

The SELECTION option controls which combined estimates are presented in the output:

    fixed presents combined estimates formed assuming that the ESTIMATES are fixed (see Whitehead 2002, Section 4.2);
    random presents combined estimates formed assuming that the ESTIMATES are random.

By default SELECTION=fixe,rand.

The method to use to form the combined estimates formed assuming that the ESTIMATES are random, is specified by the RMETHOD option:

    maxlikelihood estimates the variance component of the random effects using maximum likelihood (Hardy & Thompson 1996, also see Whitehead 2002, Section 4.3.8);
    maxremllikelihood estimates the variance component of the random effects by maximizing the REML likelihood (Whitehead 2002, Section 4.3.8);
    moments estimates the variance component of the random effects using the method of moments (DerSimonian & Laird 1986, also see Whitehead 2002, Section 4.3.3);
    reml estimates the variance component of the random effects using the REML directive (Whitehead 2002, Section 4.3.8).

The maxremllikelihood setting is based on the same criterion as the reml setting, but it programs the maximization explicitly, in a FOR loop. It thus provides an alternative to use if the REML directive experiences convergence problems. By default RMETHOD=reml.

The CIMETHOD option specifies how to calculate the confidence interval for a random estimate formed by maximum likelihood or REML. The default is to use profile likelihood (c.f. Hardy & Thompson 1996), but you can set CIMETHOD=approximate to use a Normal approximation instead.

The XLABEL option can supply a label for the x-axis of the confidence plots; the default is 'treatment effect'. By default the sizes of the symbols used to plot the estimates on the confidence plots are inversely proportional to their standard errors, but you can set option SMETHOD=equal to use equal sizes. The CIPROBABILITY option specifies the probability level to use for the confidence intervals; (default 0.95 i.e. 95%). The PRMETHOD option specifies the type of test to use for the overall probability values: greaterthan, lessthan or twosided; the default is greaterthan.

The MAXCYCLE option specifies the maximum number of iterations to use with RMETHOD settings maxlikelihood and maxremllikelihood (default 100). The TOLERANCE option specifies the convergence criterion (default 10-6).

The combined estimate formed assuming that the ESTIMATES are fixed can be saved, in a scalar, using the FIXEDESTIMATE parameter. Its standard error and probability can be saved, each in a scalar, using SEFIXEDESTIMATE and PRFIXEDESTIMATE parameters. Similarly, the combined estimate formed assuming that the ESTIMATES are random can be saved using the RANDOMESTIMATE parameter, and the SERANDOMESTIMATE and PRRANDOMESTIMATE parameters can save its standard error and probability. The QSTATISTIC and QDF parameters can save the statistic Q for the test of heterogeneity across trials and its number of degrees of freedom, again in scalars. Finally, the RVARIANCE parameter can save a scalar containing the random effect variance.

Options: PRINT, SELECTION, RMETHOD, XLABEL, CIPROBABILITY, CIMETHOD, PRMETHOD, MAXCYCLE, TOLERANCE.

Parameters: ESTIMATES, SEESTIMATES, LABELS, FIXEDESTIMATE, SEFIXEDESTIMATE, PRFIXEDESTIMATE, RANDOMESTIMATE, SERANDOMESTIMATE, PRRANDOMESTIMATE, QSTATISTIC, QDF, RVARIANCE.

Method

META uses the algorithms described in Chapter 4 of Whitehead (2002).

Action with RESTRICT

ESTIMATES, SEESTIMATES or LABELS can be restricted to form combined estimates using only a subset of those in ESTIMATES.

References

DerSimonian, R. & Laird, N. (1986). Meta-analysis in clinical trials. Controlled Clinical Trials, 7, 177-188.

Hardy, R.J. & Thompson, S.G. (1996). A likelihood approach to meta-analysis with random effects. Statistics in Medicine, 15, 619-629.

Whitehead, A. (2002). Meta-Analysis of Controlled Clinical Trials. Wiley, Chichester.

See also

Directive: REML, VRESIDUAL.

Procedure: VRMETA.

Commands for: REML analysis of linear mixed models.

Example

CAPTION  'META example',!t('Recovery time after anaethesia',\
         '(Whitehead 2002, Tables 4.24, 4.30 & 4.33)'); STYLE=meta,plain
TEXT     study
READ     study,theta,setheta
'Centre 1'  0.864  0.477
'Centre 2'  0.646  0.318
'Centre 3'  0.272  0.244
'Centre 4'  0.916  0.345
'Centre 5'  0.867  0.350
'Centre 6'  0.819  0.311
'Centre 7'  0.809  0.304
'Centre 8'  1.212  0.477
'Centre 9' -0.273  0.250 :
META     [PRINT=estimates,overalltest,heterogeneity,confidenceplot,\
         radialplot; XLABEL='Absolute mean difference']\
         theta; SEESTIMATES=setheta; LABELS=study
META     [PRINT=estimates; RMETHOD=moments] theta; SEESTIMATES=setheta
META     [PRINT=estimates; RMETHOD=maxlikelihood] theta; SEESTIMATES=setheta
META     [PRINT=estimates; RMETHOD=maxremllikelihood] theta; SE=setheta
Updated on March 7, 2019

Was this article helpful?