The Global Fragility Index - A Path-Independent Measure of Statistical Fragility

Background: The fragility index quantifies statistical fragility by counting the number of outcome changes needed to reverse statistical significance. However, it depends on arbitrary event definitions and follows specific toggle rules that may not find the actual minimum perturbation. We introduce the global fragility index, a path-independent measure that identifies the minimum number of observation moves across all possible paths in a contingency table. Methods: The global fragility index is defined as the minimum number of single-observation moves between cells of a contingency table, with total sample size fixed, required to reverse statistical significance at α=0.05. Unlike the fragility index, which toggles outcomes within a single arm according to specific rules, the global fragility index evaluates all possible cell-to-cell moves to identify the true global minimum. The global fragility quotient normalizes for sample size by dividing the global fragility index by the total sample size. We present the theoretical framework, computational approach, and worked examples for 2×2 and r×c tables. Results: The global fragility index removes three key dependencies present in existing fragility metrics: (1) event/non-event labeling ambiguity, (2) reference arm selection in balanced designs, and (3) toggle path rules. By definition, the global fragility index will always be less than or equal to the fragility index, since it finds the global minimum while the fragility index follows a predetermined path. The global fragility index naturally extends to multi-group comparisons (r×c tables) using Fisher–Freeman–Halton exact tests. Worked examples demonstrate how the global fragility index provides a more sensitive assessment of study fragility by calculating the global minimum number of single-observation moves required to flip statistical significance. Conclusions: The global fragility index is a more sensitive measure of fragility, removing arbitrary dependencies and identifying the actual minimum perturbation required to reverse statistical findings. While computationally more intensive than the fragility index, the global fragility index provides the definitive answer to the fundamental question: what is the smallest change to the data that would alter the conclusion? This makes the global fragility index a more sensitive measure of fragility for r × c tables. Canonical DOI: 10.2139/ssrn.5709162