Statistical & Psychometrics
Clinical Trial Fragility Quotient (FQ) & Attrition-vs-Fragility Audit
Standardize Michael Walsh et al.’s (2014) RCT Fragility Index across trial sample size via Fragility Quotient FQ (%) = (FI / N) * 100 and audit whether Lost-to-Follow-Up exceeds FI!
When p = 0.03 hangs on just 3 events—and 7 patients were lost to follow-up!
Michael Walsh et al. (Journal of Clinical Epidemiology, 2014) shocked clinical medicine by showing that across 399 high-impact "statistically significant" (p < 0.05) randomized controlled trials, the median Fragility Index (FI—the minimum number of non-events in the lower-incidence arm that must flip to events to render Fisher’s exact p >= 0.05) was just 8 patients—and in OVER 50% of trials, patients Lost to Follow-Up (LTFU) exceeded the Fragility Index!
Because raw FI = 3 means very different things in a 60-patient pilot vs. a 3,000-patient megatrial, Ahmed et al. (2016) introduced the sample-size-normalized Fragility Quotient FQ = FI / N_total (expressed as % or events per 100 patients), paired with Walsh’s critical attrition audit LTFU > FI! In an N = 240 trial with FI = 3 and LTFU = 7 dropouts, FQ = 1.25% (1.25 flipped outcomes per 100 patients) AND LTFU > FI flags severe attrition fragility!
| Trial Robustness Scenario (N = 240) | Fragility Quotient FQ (%) | Lost to Follow-Up (LTFU) | Walsh Attrition Audit |
|---|---|---|---|
| FI = 3 Events | N = 240 | 1.250% | 7 Dropouts (> FI!) | "Fragile: Lost-to-Follow-Up Exceeds FI" |
| FI = 12 Events | N = 240 | 5.000% | 5 Dropouts (<= FI) | "Robust Against Attrition (LTFU <= FI)" |
| Invalid FI < 0 or N <= 0 | Undefined | Error Guard | "Invalid Trial Counts" |
Sample-Size Standardized Fragility Quotient FQ (%)
Computes (FI / N_total) * 100 in percent (flips per 100 randomized participants) from Fragility Index B2 and total trial sample size B3.
=IF(OR(B2 < 0, B3 <= 0, B4 < 0), "Invalid Trial Counts", ROUND((B2 / B3) * 100, 3))Walsh Lost-to-Follow-Up vs. Fragility Index Audit
Compares total patients lost to follow-up B4 against Fragility Index B2.
=IF(OR(B2 < 0, B3 <= 0, B4 < 0), "Invalid Trial Counts", IF(B4 > B2, "Fragile: Lost-to-Follow-Up Exceeds FI", "Robust Against Attrition (LTFU <= FI)"))Try the example
Use the original values or change them to test your understanding.