From Fragility Index to Fragility Distance in Clinical Trials

Fragility indexes attempt to quantify the minimum perturbation that reverses a sample's statistical significance under an unstated constraint: the trial roster is closed, so only the recorded outcomes of enrolled patients may change. The fragility distance (FD) removes that constraint, defining fragility as the L1 edit distance from the observed 2×2 table to the significance boundary, where one unit is one patient added to or removed from any cell. Because every constrained index bounds the FD from above, the published toggle and transfer indexes become special cases of a single geometric quantity. In a published phase 2 trial reporting no significant difference (p = 0.0903), FD = 1: the removal of a single patient reverses the significance classification, a proximity to the boundary that the global fragility index, also equal to 1 but denominated in two-cell moves, understates by half. Reporting FD with its witness table gives the true minimum perturbation, priced in the one unit that occurs in every real trial: the enrollment, or the loss, of a single patient.