META procedure

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


Options

PRINT = strings
Controls output (estimates, overalltest, heterogeneity, confidenceplot, radialplot, monitoring); default esti, over, hete, conf

SELECTION = strings
Which combined estimates to include in the output (fixed, random); default fixe, rand

RMETHOD = string
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
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
Method to use for calculating the confidence interval for random estimates formed by maximum likelihood or REML (approximate, profile); default prof

PRMETHOD = string
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


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.

 

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

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


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.