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Frailty Assessment in an Aging Mouse Model

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Published on: September 23, 2025

Nonattainability of the Fragility Index.

Thomas F Heston^1,2

¹Medical Education and Clinical Sciences, Washington State University Spokane, Spokane, USA.

|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

Keywords:

clinical trial methodology contingency tables domain incompleteness fisher's exact test fragility index partial function

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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.