*! version 4.07 David Fisher 15sep2023
help metan_proportion

Title

metan -- Perform meta-analysis of single-group proportion data

Syntax

metan n_events n_total [if] [in] , proportion
[model_spec options_proportion options_main]

options_proportion

Options
proportion (Required) pool proportions from a single group

cc(#) use continuity correction value other than 0.5 for zero cells

nocc suppress continuity correction entirely

citype(ci_type) method of constructing confidence intervals for reporting of individual studies (not pooled results)

denominator(#) specify a denominator for presentation of proportion data

nointeger allow cell counts to be non-integers

transform(tr_method) specify a transformation for analysis of proportion data

nopr report effect sizes on transformed scale, not as proportions

Forest plot and/or saved data
counts display data counts (n/N)

group1(string) specify title text for the column created by counts

Description

metan performs meta-analysis of aggregate data; that is, data in which each observation represents a summary of a larger study.
This page describes options specific to a meta-analysis of proportions within a single group.
Option proportion must be supplied in this context, in order to disambiguate n_events n_total
from metan's other two-variable syntax of ES seES.

Click here to return to the main metan help page
and to find documentation for model_spec and options_main.

Options

cc(#) controls continuity correction in the case where studies contain zero cells.

By default, metan adds 0.5 to each cell of a trial where a zero is encountered, to enable finite variance estimators to be calculated.
The exception to this is if transform(ftukey) is used; in this case, continuity correction is unnecessary.
Note that corrections are applied during computation only; the original data are not modified.
However, the new variable _CC may be added to the dataset or results set,
to indicate the studies to which a correction was applied. See also the nointeger option.

# is the correction factor. The default is 0.5, but other factors may also be used, including zero.
In that case, studies containing zero cells may be excluded from the analysis.

nocc is synonymous with cc(0) and suppresses continuity correction.
Studies containing zero cells may be excluded from the analysis.

citype(ci_type) specifies how confidence limits for individual studies should be constructed for display purposes.
This option acts independently of how confidence limits for pooled results are constructed
(which will depend upon model_spec). See also level(#)

For proportion data, the default ci_type is wilson, but can also be exact (a.k.a. Clopper-Pearson),
or any of the alternatives listed under ci for proportions.
If option transform() is specified, ci_type may also be transform,
meaning that individual study confidence limits should be derived via back-transformation as well as the pooled estimate.

If nointeger is specified, a Wald-type interval will be constructed and citype() may not be specified.

denominator(#) specifies a denominator for presenting proportion data, with a default value of 1.
For example, specifying denominator(100) would present the data as percentages between 0 and 100.
Specifying denominator(1000) would present the data as the number of events per 1000 observations.
Note that this option has no effect upon the analysis; it simply scales the results.

nointeger allows cell counts or sample sizes to be non-integers.

transform(tr_method) specifies a method of transforming proportion data to create a distribution closer to normality
and to stabilise variances. The following transformations are available using tr_method:

logit specifies the Logit transform. Estimates and variances are undefined if the proportion is zero or one,
so by default a continuity correction of 0.5 is applied; see cc()

arcsine specifies the Arcsine transform, for which continuity correction is not required.

ftukey specifies the Freeman-Tukey double-arcsine transform. Again, continuity correction is not required.
Schwarzer et al (2019) show that the standard back-transformation using the harmonic mean
can sometimes give misleading results. Hence, sensitivity analyses may be carried out using the extended syntax
transform(ftukey [, arithmetic|geometric]) to specify an alternative mean.
Barendregt et al (2013) suggest another alternative back-transformation based on the inverse-variance
of the pooled transformed effects, which may be specified using transform(ftukey, ivariance).

nopr requests that effect sizes are reported on the transformed scale.
In other words, back-transformation to the proportion scale is not performed.

Forest plot and/or saved data

counts displays data counts n/N for each group in columns to the left of the forest plot.

group1(string) specifies a column heading for the counts column.

Authors

Original authors:
Michael J Bradburn, Jonathan J Deeks, Douglas G Altman.
Centre for Statistics in Medicine, University of Oxford, Oxford, UK

metan v3.04 for Stata v9:
Ross J Harris, Roger M Harbord, Jonathan A C Sterne.
Department of Social Medicine, University of Bristol, Bristol, UK

metan v4.00 and later (including current version):
David Fisher, MRC Clinical Trials Unit at UCL, London, UK.

Email d.fisher@ucl.ac.uk

Acknowledgments

Thanks to Patrick Royston (MRC Clinical Trials Unit at UCL, London, UK) for suggestions of improvements to the code and help file.

Thanks to Vince Wiggins, Kit Baum and Jeff Pitblado of Statacorp who offered advice and helped facilitate the version 9 update.

Thanks to Julian Higgins and Jonathan A C Sterne (University of Bristol, Bristol, UK) who offered advice and helped facilitate this latest update,
and thanks to Daniel Klein (Universität Kassel, Germany) for assistance with testing under older Stata versions.

The "click to run" element of the examples in this document is handled using an idea originally developed by Robert Picard.

References

Barendregt JJ, Doi SA, Lee YY, Norman RE, Vos T. 2013.
Meta-analysis of prevalence.
J Epidemiol Community Health 67: 974–978. doi:10.1136/jech-2013-203104

Schwarzer G, Chemaitelly H, Abu-Raddad LJ, Rücker G. 2019.
Seriously misleading results using inverse of Freeman-Tukey double arcsine transformation
in meta-analysis of single proportions.
Research Synthesis Methods 10: 476–483. doi: 10.1002/jrsm.1348