{smcl}
{* *! version 2.0.0 15Jul2020}{...}
{title:Title}
{p2colset 5 18 19 2}{...}
{p2col:{hi:metafrag} {hline 2}} Fragility index for meta-analysis {p_end}
{p2colreset}{...}
{marker syntax}{...}
{title:Syntax}
{p 8 14 2}
{cmd:metafrag}
[{cmd:,}
{opt ef:orm}
{opt for:est}[{cmd:(}{it:{help meta_forestplot:forestplot}}{cmd:)}]
]
{pstd}
Before using {cmd:metafrag} you must first use {helpb meta_esize:meta esize} to compute effect sizes for a two-group comparison of binary outcomes
{synoptset 22 tabbed}{...}
{synopthdr}
{synoptline}
{synopt :{opt ef:orm}}report exponentiated results{p_end}
{synopt:{opt for:est}[{cmd:(}{it:{help meta_forestplot:forestplot}}{cmd:)}]}display a forest plot of the studies after modification. Specifying {cmd:forest} without options uses the default {help meta_forestplot:forestplot} settings.{p_end}
{synoptline}
{marker description}{...}
{title:Description}
{pstd}
{opt 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).
{pstd}
{opt metafrag} is a post estimation command for {helpb meta_esize:meta esize}, thereby capitalizing on the comprehensive list of options available in official Stata's {helpb meta:meta} suite for computing effect sizes for binary outcomes.
{title:Options}
{p 4 8 2}
{cmd: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.
{cmd:eform} affects how results are displayed, not how they are estimated and stored.
{p 4 8 2}
{opt forest}[{cmd:(}{it:{help meta_forestplot:forestplot}}{cmd:)}] 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 {cmd:level} option
in {helpb meta_esize:meta esize}). Specifying {cmd:forest} without options uses the default {help meta_forestplot: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).
{title:Remarks}
{pstd}
{opt metafrag} produces results consistent with those of the R package {browse "https://github.com/iatal/fragility_ma":fragility_ma}
and related website {browse "http://www.clinicalepidemio.fr/fragility_ma/"}. However, there are some differences
between the software programs; (1) Stata's {helpb meta_esize:meta esize} command does not support the combination of random effects with
the Mantelâ€“Haenszel method (see {help meta_esize##remethod}), whereas {browse "https://github.com/iatal/fragility_ma":fragility_ma}, which utilizes the
{browse "https://www.rdocumentation.org/packages/meta/versions/4.9-7/topics/metabin":metabin}
package for computing pooled treatment effects, does support this combination; (2) Stata's {helpb meta_esize:meta esize} handles zero cells somewhat differently than
{browse "https://www.rdocumentation.org/packages/meta/versions/4.9-7/topics/metabin":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, {browse "https://github.com/iatal/fragility_ma":fragility_ma} reports
the fragility index that includes the modifications to all tied studies. Conversely, {cmd:metafrag} reports both the fragility index for each
iteration in the loop where {it:any} event modification occurs, as well as the total number of modifications if there are ties.
{title:Examples}
{pstd}Load example data{p_end}
{p 4 8 2}{stata "webuse bcgset, clear":. webuse bcgset, clear}{p_end}
{pstd}Use {help meta_esize:meta esize} to compute effect sizes for the log risk-ratio using a random effects(REML) model {p_end}
{p 4 8 2}{stata "meta esize npost nnegt nposc nnegc, esize(lnrratio) studylabel(studylbl)": . meta esize npost nnegt nposc nnegc, esize(lnrratio) studylabel(studylbl)}{p_end}
{pstd}Generate a forest plot to review the original pooled estimates {p_end}
{p 4 8 2}{stata "meta forestplot, eform nullrefline ": . meta forestplot, eform nullrefline}{p_end}
{pstd}Compute the fragility index for the meta-analysis, specifying that the results be presented in exponentiated form in a forest plot {p_end}
{p 4 8 2}{stata "metafrag, forest eform":. metafrag, forest eform}{p_end}
{pstd} 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 {p_end}
{title:Acknowledgments}
{p 4 4 2}
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 {cmd:metafrag}
to assess their consistency with his R package {cmd:fragility_ma} and website {browse "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.
{marker results}{...}
{title:Stored results}
{pstd}
{cmd:metafrag} stores the following in {cmd:r()}:
{synoptset 16 tabbed}{...}
{p2col 5 16 20 2: Scalars}{p_end}
{synopt:{cmd:r(frag)}}fragility index for meta-analysis{p_end}
{synopt:{cmd:r(frag_ties)}}fragility index for meta-analysis when there are ties{p_end}
{p2colreset}{...}
{title:References}
{p 4 8 2}
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.
{it: Journal of Clinical Epidemiology} 2014;67(6):622-628. {p_end}
{p 4 8 2}
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.
{it:Journal of Clinical Epidemiology} 2019;111:32-40. {p_end}
{marker citation}{title:Citation of {cmd:metafrag}}
{p 4 8 2}{cmd:metafrag} is not an official Stata command. It is a free contribution
to the research community, like a paper. Please cite it as such: {p_end}
{p 4 8 2}
Linden A. (2019). METAFRAG: Stata module for computing the fragility index of meta-analysis. {browse "https://ideas.repec.org/c/boc/bocode/s458717.html"}.{p_end}
{title:Authors}
{p 4 4 2}
Ariel Linden{break}
President, Linden Consulting Group, LLC{break}
alinden@lindenconsulting.org{break}
{title:Also see}
{p 4 8 2} Online: {helpb meta}, {helpb meta_esize}, {helpb meta_summarize}, {helpb meta_forestplot}, {helpb fragility} (if installed) {p_end}