From:  Considering the fragility index in reporting trials on diverticular disease

 Summary of index calculation

Metric indexCalculation
Fragility index (FI)With a events in Group 1 (total patients = a + b) and c events in Group 2 (total patients = c + d).
Where hypothetically:
EventNon-event
Group 1ab
Group 2cd
When FI is positive patients are moved from a non-event to an event in Group 1. When FI is negative patients are moved from an event to a non-event in Group 1. Changing outcomes preserves the number of patients in each group. FI is based on the number of changes required to render the p value ≥ 0.05.
Where the hypothetical data structure is as:
EventNon-event
Group 1a + f1b – f1
Group 2c + f2d – f2
Reverse fragility index (rFI)Choose the group that has the fewest number of events and then change the events to non-events to render statistical significance. The total number of outcome changes = the rFI.
Fragility quotient (FQ)The FQ is a relative measurement calculated by division as:
Absolute FITotal Sample FI
Incidence fragility index (FIq)FIq is such that any probability q∈1,2 = the minimum number of changes in patient outcome with a probability of at least q in order to reverse statistical significance. This permits only sufficiently likely modifications according to the likelihood threshold value of q.
The minimum modifications are then:
minfi,f2⁡∈Zf1+f2
(based on hypothetical tables above)
Generalized fragility index (GFIq)To generalize the data set:
Where there are n samples (and Y1–Yn observations), a significant (< 0.05) t-test becomes:
lim Y1→∞n(Y--0)/S=n-1/(1-n-1)/(n(n-1))=1
For all modifications with Y as the sample mean and S the SD.
In each case, the one sample t-test =1 (i.e., it is not significant) at the a = 0.05 level for any sample size [52].
Return to article view