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Fragility Index Calculator (RCT Robustness)
Test how robust a statistically significant trial result is (the fragility index counts how many outcome events would need to change to lose significance), with the exact R command behind the result. A full guide follows below. Validated against R 4.3.3.
In Simple Words
The fragility index asks a simple question of a significant 2×2 trial result: how many patients in one arm would have had to switch outcome (from non-event to event) for the p-value to cross from below 0.05 to at or above it? A small number means the result hangs on just a few events.
A fragility index of 1 or 2 signals a result that, while statistically significant, is easily overturned by a handful of different outcomes, especially worrying if more patients were lost to follow-up than the index itself. A larger index indicates a more robust finding. The index complements the p-value; it does not replace it.
When to Use the Fragility Index
Use the fragility index to gauge the robustness of a significant binary outcome in a randomised trial, particularly when the sample is small, the event count is low, or the p-value is just under 0.05. It is increasingly reported in systematic reviews to flag fragile evidence.
Interpret it as one piece of context, not a verdict: a low index does not invalidate a trial, and the metric has known limitations, including that trials are often designed to be statistically efficient rather than “robust” by this measure. Read it alongside the p-value, effect size, and confidence interval. Unsure how to present robustness? Our Test Selector can help.
ea <- {ea}; na <- {na}; ec <- {ec}; nc <- {nc}
fp <- function(x1, x0) fisher.test(matrix(c(x1, na - x1, x0, nc - x0), 2, byrow = TRUE))$p.value
p0 <- fp(ea, ec); x1 <- ea; x0 <- ec; fi <- 0
if (p0 < 0.05) while (fp(x1, x0) < 0.05) { if (ea <= ec) x1 <- x1 + 1 else x0 <- x0 + 1; fi <- fi + 1 }
c(fisher_p = p0, fragility_index = if (p0 < 0.05) fi else NA)User guide
When to use. Assess how robust a statistically significant RCT result is.
Assumptions. Binary outcome 2×2 from a randomised trial.
Common mistakes. A low fragility index does not by itself invalidate a trial.
Worked example
Click Load example data above, then Run Analysis to see a fully worked result with figure, formula and interpretation for this test.
References
- Walsh M, et al. The statistical significance of randomized controlled trial results is frequently fragile. J Clin Epidemiol. 2014;67:622-628.
Worked Examples
Example 1: A fragile result
A trial reports 8/50 events in treatment versus 21/50 in control (two-sided Fisher’s exact p = .008). Converting non-events to events in the treatment arm, p stays below 0.05 at 9/50 (p = .016) and 10/50 (p = .030) and crosses it at 11/50 (p = .053): a fragility index of 3, signalling the result rests on few events. The preloaded example (8/50 versus 15/50) is not significant (p = .153), so the calculator reports that the index does not apply.
Example 2: Index versus loss to follow-up
If that fragility index is 3 but the trial lost 10 participants to follow-up, the result is especially fragile: more patients went unaccounted for than would be needed to erase the finding, which should temper confidence in the conclusion.
Assumptions to Check
A 2×2 binary outcome from an RCT. The fragility index is defined for a two-arm trial with a dichotomous outcome analysed by a 2×2 test, not for continuous or time-to-event endpoints.
A statistically significant result. The standard index applies to results that are significant; a reverse fragility index addresses non-significant findings separately.
Equal-sized arms aid interpretation. The index is sensitive to sample size and event rate, so it is most comparable between trials of similar size and balance.
Common Mistakes
Treating a low index as invalidation
A small fragility index flags sensitivity, not error. A robustly designed trial can still have a modest index; the metric is context, not a verdict.
Ignoring loss to follow-up
A fragility index smaller than the number lost to follow-up is a strong caution. Always compare the two.
Applying it outside a 2×2 RCT
The index is defined for binary outcomes in two-arm trials. Using it for continuous or survival outcomes misapplies the method.
Forgetting it is tied to the p-value
Because the index is built around the 0.05 threshold, it inherits the limitations of dichotomous significance testing and should be read with that in mind.
Frequently Asked Questions
What does the fragility index measure?
It is the minimum number of outcome events that would need to change in one arm to move a significant result to non-significant.
Is a low fragility index bad?
It indicates the result is sensitive to a few events, which warrants caution, but it does not by itself mean the trial is wrong.
What is the reverse fragility index?
It is the analogous count for a non-significant result: how many events would need to change to make it significant.
Does the result match R?
Yes. The calculator uses the two-sided Fisher exact test and converts non-events to events, one at a time, in the arm with fewer events until p reaches 0.05; the R approach shown reproduces the count.
Related Calculators
References
- Walsh M, Srinathan SK, McAuley DF, Mrkobrada M, Levine O, et al. The statistical significance of randomized controlled trial results is frequently fragile: a case for a Fragility Index. J Clin Epidemiol. 2014;67(6):622–628. PMID 24508144.
- Cote MP, Lubowitz JH, Rossi MJ, Matzkin E. The Fragility Index is typically misinterpreted and of low value: clinical trials are designed to be fragile. Arthroscopy. 2024;40(12):2738–2741. PMID 39151709.
- Feinstein AR. The unit fragility index: an additional appraisal of “statistical significance” for a contrast of two proportions. J Clin Epidemiol. 1990;43(2):201–209.
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