Bidirectional fragility is a step forward but not far enough: the case for a global fragility index

Abstract

Commentary responding to Kahana, Perets, and Emile (Journal of Clinical Epidemiology, 2026; doi:10.1016/j.jclinepi.2026.112255), who propose a bidirectional fragility index (bFI) for 2×2 contingency tables. This paper demonstrates that the bFI, while a genuine improvement over the unidirectional fragility index, inherits structural limitations: (1) it restricts perturbations to within-arm toggles (fixed row margins), which is a subset of the full perturbation space; (2) it is mathematically incomplete (not attainable for some valid tables); and (3) it conflates classification stability with robustness. The Global Fragility Index (GFI) resolves the first two limitations by searching all cell-to-cell reallocations without fixing any marginal totals. Exhaustive enumeration of all valid 2×2 tables (N = 7–30, 45,230 tables) confirms that GFI ≤ bFI always, GFI < bFI in 21.5% of cases, and GFI is attainable for every table in the domain. The Risk Quotient (RQ) addresses the third limitation by providing a normalized robustness metric orthogonal to fragility. Includes the R enumeration code and complete output dataset.