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Nonattainability of the Fragility Index
1Medical Education and Clinical Sciences, Washington State University Spokane, Spokane, USA.
Cureus
|May 8, 2026
Summary
The fragility index (FI), a measure of statistical significance robustness, is not always attainable for significant trial results. This limitation stems from the FI algorithm
Area of Science:
- Biostatistics
- Clinical Trial Design
- Statistical Significance
Background:
- The fragility index (FI) quantifies the number of outcome changes needed to nullify a statistically significant trial result.
- A reliable metric should be universally applicable to all valid cases.
- This study investigates the universal attainability of the fragility index.
Purpose of the Study:
- To determine if a fragility value can always be calculated for statistically significant two-arm trial results.
- To identify conditions under which the fragility index is not attainable.
- To assess the structural limitations of the fragility index algorithm.
Main Methods:
- Analyzed FI with baseline significance (p < 0.05) and restricted outcome changes.
- Assessed nonattainability by searching for valid 2x2 tables where no finite FI can be obtained.
- Utilized formal counterexamples, complete enumeration of 2x2 tables (N=60), and empirical evaluation of published trials.
Main Results:
- Demonstrated that valid statistically significant 2x2 tables exist for which FI is unattainable.
- A counterexample involves a table with no available nonevents for the required outcome toggle.
- Unattainable cases were found starting at N=18, affecting 11.5% of tables by N=60 and 2.4% of published trials.
Conclusions:
- The fragility index is not universally attainable.
- This unattainability is an inherent structural property of the FI algorithm.
- Mathematical proof, table enumeration, and published data confirm this limitation.
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