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Fragility of the fragility index: when calculation becomes impossible

clinical-trials
statistics

Abstract

Background: The Fragility Index (FI) may become unattainable under Fisher's exact test constraints in common clinical trial scenarios, including rare events, balanced small samples, and extreme imbalances.
Methods: We analyzed 14 representative 2×2 tables spanning rare events, balanced designs, and extreme imbalances, and computed alternative fragility metrics.
Results: FI was not attainable in all 14 cases. Risk Quotient (RQ), Percent Fragility Index (PFI), and Relative Risk Index (RRI) computed in 14/14; Robustness Index (RI) in 12/14.
Conclusions: FI is not attainable in everyday scenarios. Robust fragility metrics include the RQ, which quantifies distance to therapeutic neutrality on a bounded 0–1 scale, and the PFI, which quantifies the percentage change needed to flip statistical significance.
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