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 |
LOWER = variates |
Saves lower values of the confidence interval |
UPPER = variates |
Saves upper values of the confidence interval |
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:
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. The RVARIANCE parameter can save a scalar containing the random effect variance. Finally, the LOWER and UPPER parameters can save variates containing the lower and upper values of the confidence interval.
Options: PRINT, SELECTION, RMETHOD, XLABEL, CIPROBABILITY, CIMETHOD, PRMETHOD, MAXCYCLE, TOLERANCE.
Parameters: ESTIMATES, SEESTIMATES, LABELS, FIXEDESTIMATE, SEFIXEDESTIMATE, PRFIXEDESTIMATE, RANDOMESTIMATE, SERANDOMESTIMATE, PRRANDOMESTIMATE, QSTATISTIC, QDF, RVARIANCE, LOWER, UPPER.
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
Directives: REML, VRESIDUAL.
Procedures: VRMETAMODEL, VMETA.
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