# Fragility Index Calculator

## Calculates the number of patients required to lose statistical significance

### ClinCalc.com » Statistics » Fragility Index Calculator

### Study Data

**Control Group**

Number WITH primary endpoint | |

Number WITHOUT primary endpoint | -- |

Total number of control patients |

**Experimental Group**

Number WITH primary endpoint | |

Number WITHOUT primary endpoint | -- |

Total number of experimental patients |

A fragility index of 8 indicates that if 8 patients in the experimental group were "converted" from NOT having the primary endpoint to HAVING the primary endpoint, the study would lose statistical significance (p > 0.05). The higher the fragility index, the more robust the results of a study are. Learn more about an "acceptable" fragility index.

Original Study | Fragility Index | "Fragile" Study | |

Control group with outcome (N) | 50 | 50 | |

Control group without outcome (N) | 450 | 450 | |

Experimental group with outcome (N) | 25 | + 8 | 33 |

Experimental group without outcome (N) | 475 | - 8 | 467 |

P value | 0.004 | 0.066 |

### About This Calculator

The **fragility index** is a measure of the robustness (or fragility) of the results of a clinical trial. The fragility index is a number indicating how many patients would be required to convert a trial from being statistically significant to not significant (p ≥ 0.05). The larger the fragility index the better (more robust) a trial's data are. The intent of the fragility index is to be used in conjunction with the P value, 95% confidence interval, and various measures describing benefit or risk (relative risk reduction, absolute risk reduction, etc).

#### How Is the Fragility Index Calculated?

The fragility index is calculated by converting one patient in the group (control or experimental group) from a "non-event" to an "event" outcome and recalculating a two-sided Fisher's exact test until the P value meets or exceeds 0.05. In essence, the calculation describes how many patients would have had to have a different outcome (within the group with the fewest number of events) to make a study's results not statistically significant.

#### What Is an "Acceptable" Fragility Index?

There is no specific fragility index that is accepted as being a "good" (robust) or "bad" (fragile) value. In the manuscript introducing the concept, a convenience sample of 399 randomized controlled trials with statistically significant results were analyzed from five high-impact journals.^{1} This study found the following results, which serves to describe the landscape of fragility index among clinical trials that in general are considered high-quality or "robust" studies:

- The median fragility index was 8 (IQR 3 to 18)
- 25% of trials had a fragility index ≤ 3
- 10% of trials had a fragility index of zero (see Fragility Index of Zero for an explanation)
- When loss to follow-up was reported, 52.9% of trials had a larger fragility index compared to the number of patients lost to follow-up

At least two other publications have summarized the fragility index within other areas of medicine:

#### Median Fragility Index in RCTs

Error bars in the graph above indicate the interquartile range (IQR) of each publication

Aside from comparing a study's fragility index to the fragility index of other trials, another method of interpreting a fragility index is to compare the value against the number of patients lost to follow-up. **As a general rule of thumb, if the number of patients lost to follow-up is greater than the fragility index, the study should be considered less robust.** The three previously mentioned publications also reported the percent of trials in which the number lost to follow-up exceeded the fragility index:

#### Trials with Higher Fragility Index than Number Lost to Follow-Up

#### Fragility Index of Zero

By definition, the fragility index is calculated using a Fisher's exact test.^{1} Other methods, such as a Chi squared test, are commonly used to compare a dichotomous (binary) outcome in clinical trials. Particularly for small trials, the P value from a Fisher's exact test can be discrepant from a Chi squared test. In the cases where a Fisher's exact test produces a non-significant P value (without "converting" a patient from a non-event to an event), the fragility index is reported as '0' and clearly emphasizes the lack of robustness of the trial data.

#### Limitations of the Fragility Index

Because of how a fragility index is calculated, there are several inherent limitations to its use:

**Use of Fisher's exact test for statistical significance**- In the manuscript describing the fragility index,^{1}the authors decided to use a Fisher's exact test for the calculation procedure. In general, this tends to be more conservative (more prone to a type II error) than other methods, such as a Chi squared test. This difference in statistical test can lead to a fragility index of zero even though the original study showed statistically significant results.**Only appropriate for dichotomous (binary) outcomes**- The fragility index cannot be applied to an outcome that is a continuous variable. For example, a primary endpoint using a modified Rankin scale (a scale measuring death or disability between 0 and 6) is not appropriate for a Fisher's exact test (and thus not appropriate for a fragility index calculation). With that said, however, some studies do dichotomize a continuous endpoint. For example, an endpoint of "good outcome" (modified Rankin scale of 0 to 3) versus a "bad outcome" (modified Rankin 4 to 6) converts a continuous variable to a binary variable, in which case a fragility index can be calculated.**Possibly not appropriate for time-to-event outcomes**- Although many time-to-event outcomes are usually dichotomous (eg, mortality), the fragility index does not account for the difference in outcome over time. Particularly in longer studies with variable follow-up time periods and treatment durations, an analysis accounting for time (such as a Kaplan-Meier curve or Cox proportional hazards model) are more appropriate than a simple binary outcome analysis without accounting for time.**No standard fragility index "cut-off"**As discussed above (What Is an "Acceptable" Fragility Index?), there is no specific cut-off or lower limit of the fragility index to classify a study as "fragile" or "robust". To a large extent, the interpretation of the fragility index and the interpretation of the index in conjunction with the trial's results are inherently subjective.

### References and Additional Reading

- Walsh M, Srinathan SK, McAuley DF, et al. The statistical significance of randomized controlled trial results is frequently fragile: a case for a Fragility Index.
*J Clin Epidemiol*. 2014 Jun;67(6):622-8. doi: 10.1016/j.jclinepi.2013.10.019. PMID 24508144 - Evaniew N, Files C, Smith C, et al. The fragility of statistically significant findings from randomized trials in spine surgery: a systematic survey.
*Spine J*. 2015 Oct 1;15(10):2188-97. doi: 10.1016/j.spinee.2015.06.004. PMID 26072464 - Ridgeon EE, Young PJ, Bellomo R, et al. The Fragility Index in Multicenter Randomized Controlled Critical Care Trials.
*Crit Care Med*. 2016 Jul;44(7):1278-84. doi: 10.1097/CCM.0000000000001670. PMID 26963326

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