A Comparative Analysis of Unit Fragility and the Relative Risk Index

BACKGROUND: In biostatistics, evaluating fragility is crucial for understanding their vulnerability to miscategorization. One proposed measure of statistical fragility is the unit fragility index (UFI), which measures the susceptibility of the p-value to flip significance with minor changes in outcomes. Although the UFI provides valuable information, it relies on p-values, which are arbitrary measures of statistical significance. Alternative measures, such as the fragility quotient (FQ) and the percent fragility index, have been proposed to decrease the UFI's reliance on sample size. However, these approaches still rely on p-values and thus depend on an arbitrary cutoff of p < 0.05. Instead of quantifying fragility by relying on p-values, this study evaluated the effect of small changes on relative risk. METHODS: Random 2x2 contingency tables associated with an initial p-value of 0.001 to 0.05 were evaluated. Each table's UFI and relative risk index (RRI) were calculated. A derivative of the RRI, the percent RRI, was also calculated along with the FQ. The UFI, FQ, RRI, pRRI, initial p-value, and sample size were compared. RESULTS: A total of 15000 cases were tested. The correlation between the UFI and the p-value was the strongest (r = -0.807), and the correlation between the pRRI was the weakest (r = -0.395). The RRI had the strongest correlation with the sample size (r = 0.826), and the UFI had the weakest correlation (r = 0.3904). The coefficient of variation for the average RRI was the smallest at 28.3%, and for the FQ, it was the greatest at 57.0%. The correlation between the UFI, FQ, and p-value is significantly greater than the correlation between the RRI, pRRI, and p-value (for all comparisons, p < 0.001). CONCLUSION: The RRI and pRRI are significantly less correlated with the p-value than the UFI and FQ, indicating relative independence of the RRI and pRRI from p-values.