*! version 2.0.0 15Jul2020

Title

metafrag -- Fragility index for meta-analysis

Syntax

metafrag
[,
eform
forest[(forestplot)]
]

Before using metafrag you must first use meta esize to compute effect sizes for a two-group comparison of binary outcomes

eform report exponentiated results

forest[(forestplot)] display a forest plot of the studies after modification. Specifying forest without options uses the default forestplot settings.

Description

metafrag is an extension of the fragility index for single studies with a binary outcome (Walsh et al. 2014) to meta-analysis (Atal et al. 2019). The fragility
index for meta-analysis is defined as the minimum number of patients from one or more trials included in the meta-analysis for which a modification
of the event status (ie, changing events to non-events, or non-events to events) would change the statistical significance of the pooled treatment effect (Atal et al. 2019).
As such, a fragility index score of zero indicates that no modification of the event status is necessary to elicit a statistically non-significant pooled treatment effect.
Conversely, a large fragility index score indicates that many modifications to the event status are required to change a statistically significant pooled effect to non-significant
(and thus, the results may be considered more robust).

metafrag is a post estimation command for meta esize, thereby capitalizing on the comprehensive list of options available in official Stata's meta suite for computing effect sizes for binary outcomes.

Options

eform reports exponentiated effect sizes and transforms their respective confidence intervals, whenever applicable.
By default, the results are displayed in the metric declared with meta esize such as log odds-ratios and log risk-ratios.
eform affects how results are displayed, not how they are estimated and stored.

forest[(forestplot)] displays a forest plot of the studies after modification to the events and non-events of included studies,
to move the pooled effect from statistically significant to non-significant (the user can set the level that "significance" represents using the level option
in meta esize). Specifying forest without options uses the default forestplot settings (with only the column headers modified).
Studies that have event modifications are highlighted in blue (when events are added) and red (when events are subtracted).

Remarks

metafrag produces results consistent with those of the R package fragility_ma
and related website http://www.clinicalepidemio.fr/fragility_ma/. However, there are some differences
between the software programs; (1) Stata's meta esize command does not support the combination of random effects with
the Mantel–Haenszel method (see meta_esize), whereas fragility_ma, which utilizes the
metabin
package for computing pooled treatment effects, does support this combination; (2) Stata's meta esize handles zero cells somewhat differently than
metabin, possibly leading to slightly different results between software packages;
and (3) when there are ties between studies in the computed maximum (minimum) confidence level at any iteration, fragility_ma reports
the fragility index that includes the modifications to all tied studies. Conversely, metafrag reports both the fragility index for each
iteration in the loop where any event modification occurs, as well as the total number of modifications if there are ties.

Examples

Load example data

. webuse bcgset, clear

Use meta esize to compute effect sizes for the log risk-ratio using a random effects(REML) model

. meta esize npost nnegt nposc nnegc, esize(lnrratio) studylabel(studylbl)

Generate a forest plot to review the original pooled estimates

. meta forestplot, eform nullrefline

Compute the fragility index for the meta-analysis, specifying that the results be presented in exponentiated form in a forest plot

. metafrag, forest eform

The results indicate that the fragility index is 28 and that 2 trials were modified -- with the first adding 8 events to Group 1 and subtracting 9 events from Group 2,
and the second adding 11 events to Group 1

Acknowledgments

I thank John Moran for advocating that I write this package. I also wish to thank Ignacio Atal for his support in testing the results reported by metafrag
to assess their consistency with his R package fragility_ma and website http://www.clinicalepidemio.fr/fragility_ma/. Finally, I wish to thank
Houssein Assaad at StataCorp for providing details of how Stata and R differ in their respective computations for meta analyses.

Stored results

metafrag stores the following in r():

Scalars

r(frag) fragility index for meta-analysis

r(frag_ties) fragility index for meta-analysis when there are ties

References

Walsh M, Srinathan SK, McAuley DF, Mrkobrada M, Levine O, Ribic C, Molnar AO, Dattani ND, Burke A, Guyatt G et al:
The statistical significance of randomized controlled trial results is frequently fragile: a case for a Fragility Index.
Journal of Clinical Epidemiology 2014;67(6):622-628.

Atal I, Porcher R, Boutron I, Ravaud P. The statistical significance of meta-analyses is frequently fragile: definition of a fragility index for meta-analyses.
Journal of Clinical Epidemiology 2019;111:32-40.

Citation of metafrag

metafrag is not an official Stata command. It is a free contribution
to the research community, like a paper. Please cite it as such:

Linden A. (2019). METAFRAG: Stata module for computing the fragility index of meta-analysis. https://ideas.repec.org/c/boc/bocode/s458717.html.

Authors

Ariel Linden

President, Linden Consulting Group, LLC

alinden@lindenconsulting.org

Also see

Online: meta, meta_esize, meta_summarize, meta_forestplot, fragility (if installed)