Effects and importance of smaller and larger sample sizes on different fragility indices
| Index | Small sample effect (example) | Large sample effect | Explanation and importance |
|---|---|---|---|
| Fragility index (FI) | A small RCT with 50 patients shows that Drug A is significantly better (p = 0.04). Changing 2 non-events to events makes p > 0.05 where FI = 2. | A large RCT with 1,000 patients shows that drug B is significantly better (p = 0.04). Changing 15 non-events to events makes p > 0.05 where FI = 15. | In the small trial (FI = 2), a tiny change in outcomes alters significance, meaning that the results are fragile.In the larger trial (FI = 15), the results are more robust since more changes are needed in order to affect significance. |
| Reverse fragility index (rFI) | A trial with 60 patients shows no significant difference (p = 0.07). Adding 3 new events to the treatment group makes p < 0.05 where rFI = 3. | A large trial with 1,200 patients shows no significant difference (p = 0.07). Adding 20 new events to the treatment group makes p < 0.05 where rFI = 20. | The small study (rFI = 3) is close to significance, requiring just 3 event reversals. The large study (rFI = 20) needs a much bigger shift, showing greater confidence that no real effect exists. |
| Fragility quotient (FQ) | A study with FI = 3 and sample size = 200 results in an FQ = 0.015 (1.5%; 3/200). | A study with FI = 20 and sample size = 2,000 results in an FQ = 0.01 (1%; 20/2,000). | In the small study only 1.5% of the participants changing their outcome can alter significance. In the larger study an FQ = 1% is consistent with greater stability. |
| Incidence fragility index (FIq) | A trial with an FI = 5 and a control group event rate = 10% (15/150 patients), results in an FIq = 0.33 (33%; 5/15). | A larger trial with an FI = 30 and a control group event rate = 12% (360/3,000 patients), results in an FIq = 0.083 (8.3%; 30/360). | In the small study a significant portion of the control group must switch outcomes to change the significance. In the larger trial the result (8.3%) is more reliable across different event rates. |
| Generalized fragility index (GFIq) | A study with an FI = 4, an rFI = 3, a sample size = 250, and a control group event rate = 12% (30/250) uses both the FI and rFI to generate a GFIq. | A study with an FI = 18, an rFI = 15, a sample size = 5,000, and a control group event rate = 10% (500/5,000) results in a more stable GFIq. | The small study has a lower GFIq, meaning both FI and rFI are low, making the results less stable. The large study’ has a higher GFIq demonstrating more resilience to statistical shifts. |