*! version 4.08 David Fisher 17jun2024
help metan_binary

Title

metan -- Perform meta-analysis of two-group binary data

Syntax

metan event_treat noevent_treat event_ctrl noevent_ctrl [if] [in]
[, model_spec options_binary options_main]

options_binary

Options
rr pool risk ratios (default)

or pool odds ratios

rd pool risk differences

effect(string) user-defined title for "effect size" column in the output

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

cc([#] [, cc_opts]) use continuity correction value other than 0.5 for zero cells;
implement alternative methods of Sweeting (2004)

nocc suppress continuity correction entirely

nointeger allow cell counts to be non-integers

log display log effect sizes and confidence limits (for ratio measures only)

Additional options specific to Mantel-Haenszel odds ratios
(strictly speaking part of model_spec, but repeated here for convenience)
cmh Cochran-Mantel-Haenszel test statistic

breslow Breslow-Day test for homogeneity of odds ratios (Breslow and Day 1980)

tarone Breslow-Day-Tarone test for homogeneity of odds ratios
(preferred to breslow; see e.g. Breslow 1996)

Forest plot and/or saved data
efficacy additionally display odds ratios or risk ratios expressed in terms of vaccine efficacy

counts display data counts (n/N) for treatment and control group

group1(string), group2(string) specify title text for the two columns created by counts

npts display participant numbers in the forest plot

oev display columns containing O_E and V

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 studies comparing a binary outcome between two treatment groups.
If no options are supplied, the default analysis is to pool Risk Ratios (Relative Risks)
using the Mantel-Haenszel method, and with the associated Mantel-Haenszel heterogeneity statistic.

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

Options

effect(string) overrides the default title for the "effect size" column in the output generated by rr, or and rd.

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(#)

With two-group comparison of binary outcomes, the default ci_type is exact giving an exact interval.
Alternatively, options woolf or cornfield may be specified; see cc
(not to be confused with metan's cc() option!).

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

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

If model_spec is mhaenzsel or peto, continuity correction is unnecessary
(see, for example, Bradburn et al 2007) and # is set to zero by default.
Otherwise, metan adds 0.5 to each cell of a study where a zero is encountered, to enable finite variance estimators to be calculated.
Any default behaviour may be over-ridden by explicit specification of # and/or cc_opts.
(Note that studies with zero cells in both treatment groups are always excluded from the analysis.)

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 (usually) 0.5, but other factors may also be used;
including zero, which is equivalent to specifying nocc (see below).

Sweeting (2004) discusses the issue of continuity correction, and suggested two alternatives
to the default approach of adding a constant value to all four cells in the 2x2 table.
In both cases a constant of proportionality is required, which again defaults to 0.5 but may instead be user-specified.
These approaches are specified using cc_opts as follows (not appropriate with proportion):

opposite uses the reciprocal of the opposite group arm size as the correction term.

empirical uses an empirical estimate for the correction term, derived from the remaining studies.
This approach may only be used with Odds Ratios, and requires at least one study not to contain any zero cells.

Finally: the usual, and generally recommended, strategy is to add correction factors only to those studies where a zero cell is found.
However, the following alternative strategy is sometimes used:

allifzero adds correction factors to all studies if at least one study with a zero cell is found.

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

nointeger allows cell counts or sample sizes to be non-integers.
This may be useful for manually implementing other corrective strategies for zero cells;
but may also be used in other circumstances, such as where a cluster-randomised trial is to be incorporated
and the "effective sample size" is less than the total number of observations.

log requests that results using ratio statistics (that is, OR or RR) are reported on the log scale.
The analysis itself is unchanged.

Forest plot and/or saved data

efficacy expresses results as the vaccine efficacy (the proportion of cases that would have been prevented
in the placebo group that would have been prevented had they received the vaccination).
Only available with odds ratios or risk ratios.

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

group1(string), group2(string) are for use with the counts option, and contain names for the two groups.
If these are not supplied, the default names "Treatment" and "Control" are used.

npts displays participant numbers in a column to the left of the forest plot.

oev displays the statistics O-E and V in columns to the right of the graph.

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) 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

Bradburn MJ, Deeks JJ, Berlin JA, Localio AR. 2007.
Much ado about nothing: a comparison of the performance of meta-analytical methods with rare events.
Statistics in Medicine 26: 53-77. doi: 10.1002/sim.2528

Breslow NE, Day NE. 1980. Statistical Methods in Cancer Research: Vol. I - The Analysis of Case-Control Studies.
Lyon: International Agency for Research on Cancer.

Breslow NE. 1996.
Statistics in epidemiology: The case-control study.
Journal of the American Statistical Association 91: 14-28

Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). 2019.
Cochrane Handbook for Systematic Reviews of Interventions, 2nd Edition. Chichester: Wiley.

Sweeting MJ, Sutton AJ, Lambert PC. 2004.
What to add to nothing? Use and avoidance of continuity corrections in meta-analysis of sparse data.
Statistics in Medicine 23: 1351-1375. doi: 10.1002/sim.1761