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 classic fragility index 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. The classic index was overstating 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 conventional index may only toggle outcomes within one arm, in one direction. The Global Fragility Index searches every cell-to-cell reallocation in the table. Because the classic procedure is a constrained special case, GFI ≤ FI always — and the gap is routinely large.
Every published fragility analysis using the conventional index is reporting a number more generous than the truth.
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.
Endorsement is a public statement of practice, not a membership fee. There is nothing to pay and nothing to renew.
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researchers and clinicians have endorsed the Standard.