The Internet Medical Association
Every trial you read reports the first number. Almost none report the other two — and without them you cannot tell a finding that will replicate from one that is already indistinguishable from nothing.
Below is a published trial. Judge it the way you normally would, then keep scrolling.
Exhibit one
In a randomised comparison of carotid endarterectomy against stenting, surgical patients had roughly twice the rate of myocardial infarction. The difference was statistically significant.
| Arm | MI | No MI | Rate |
|---|---|---|---|
| Endarterectomy | 28 | 1,212 | 2.26% |
| Stenting | 14 | 1,248 | 1.11% |
Dimension two — fragility
Move a single myocardial infarction from the surgical arm to the stenting arm — one reallocation, out of 2,502 patients — and the finding is no longer significant.
The GFI is the smallest number of cell-to-cell reallocations, anywhere in the table, that flips the significance classification. Neither row nor column totals are held fixed — the search is global.
The FI* reported 2 here because it may only toggle outcomes within the arm that had fewer events. Allowed to search the whole table, the answer is 1. Restricting the search to one arm overstates how stable this classification is — and it does so systematically. We come back to that.
Dimension three — robustness
Fragility tells you the statistical classification is unstable. It does not tell you whether there was much of an effect to begin with. That is a separate question, and it has a separate answer.
RQ — distance from therapeutic neutrality, where neutrality means the two arms are indistinguishable.
The two arms differ by 1.1 percentage points — 2.26% against 1.11%. On the neutrality scale that is RQ = 0.011: the result sits almost exactly on the boundary where treatment and control become indistinguishable.
SFW applies to a claim that an effect exists. A claim that an effect is absent reads the same three dimensions differently: there, a high p-value with a stable classification and a result close to neutrality is what supports the null.
Exhibit two
Tocilizumab for giant cell arteritis. Complete remission at twelve weeks. p = 0.030 — statistically indistinguishable from the trial you just dismantled.
| Arm | Remission | No remission |
|---|---|---|
| Tocilizumab | 17 | 3 |
| Placebo | 4 | 6 |
Both trials on the same neutrality scale:
Fragility flagged both classifications as unstable. Only nb distinguished a finding worth confirming from one worth discarding. No standard reporting requirement asks for it. No other framework computes it.
Exhibit two, continued
Same trial, same thirty people, same drug — complete remission measured at fifty-two weeks instead of twelve. Watch all three numbers move.
| Arm | Remission | No remission |
|---|---|---|
| Tocilizumab | 17 | 3 |
| Placebo | 2 | 8 |
Standard reporting called all three of these results “significant” and stopped. The triplet separated them into discard, replicate, and act.
The framework
Reporting a p-value alone is partial evidence. It answers one question and is silent on two others that determine whether a finding is decision-ready.
Both fr and nb are computed from published summary statistics alone — no raw data, no simulation, no distributional assumptions, no access to the trial team. Any reader can compute them from a table already printed in the paper. Full specification →
Why the global index
The FI* may only toggle outcomes within one arm, holding that arm’s total fixed. The Global Fragility Index searches every cell-to-cell reallocation in the table, with neither margin fixed. Because a within-arm toggle is itself a reallocation, the FI is a constrained special case of that search — so GFI ≤ FI always. That is a mathematical result, not a tendency.
We recomputed both indices from the published 2×2 of 130 trials by exhaustive Fisher’s-exact search. The inequality held every time.
In these nine, the conventional quotient lands at or above the 0.05 cutpoint — stable — while the global quotient lands below it — fragile. Same table, same threshold, opposite verdict. A reader trusting the arm-restricted index would file all nine as secure.†
| Trial | N | FI | FQ | GFI | GFQ |
|---|---|---|---|---|---|
| Taylor 2025Lancet Infect Dis | 50 | 5 | 0.1000stable | 2 | 0.0400fragile |
| Wang 2021J Hematol Oncol | 42 | 4 | 0.0952stable | 2 | 0.0476fragile |
| Lee 2025PLOS ONE | 115 | 8 | 0.0696stable | 4 | 0.0348fragile |
| Guo 2025Phytomedicine | 212 | 15 | 0.0708stable | 10 | 0.0472fragile |
| Guido 2019Anesth Analg | 158 | 10 | 0.0633stable | 6 | 0.0380fragile |
| Zucchelli 1992Kidney Int | 69 | 4 | 0.0580stable | 2 | 0.0290fragile |
| Chevalet 2000J Rheumatol | 97 | 5 | 0.0515stable | 3 | 0.0309fragile |
| Brede 2026Crit Care | 179 | 10 | 0.0559stable | 8 | 0.0447fragile |
| Norgaard-Pedersen 2025BMJ Open | 80 | 4 | 0.0500stable | 3 | 0.0375fragile |
Both quotients use the same 0.05 cutpoint. FQ = FI / N. GFQ = GFI / N.
Across the 83 trials where the two disagreed, the FI ran a median of 42% too high, and as much as 150% too high. Every published fragility analysis that confines its search to a single arm is reporting a number more generous than the truth.
Indices recomputed from each published 2×2 by exhaustive search, not taken from any spreadsheet. Search depth capped at 40 reallocations, which excluded 2 trials of 132. Check any row yourself at fragilitymetrics.org.
Issued by the Internet Medical Association
Statistical evidence is reported completely when all three dimensions are reported together.
The metrics are model-free, computed from published summary statistics, and free to calculate. Compliance costs nothing but candour.
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