Redefining the Risk Quotient: A Generalized Framework for Fragility Analysis Across Study Designs

The Risk Quotient was introduced to normalize the Relative Risk Index, offering an interpretable alternative to fragility metrics tied to P values. However, the initial formulation defined the Risk Quotient as the Relative Risk Index divided by the total sample size, limiting interpretability and comparability. We propose a unified definition: the Relative Risk Index is the average absolute residual between the observed table and the neutrality table (expected counts under therapeutic neutrality), and the Risk Quotient is the Relative Risk Index normalized by the average cell count. This definition yields a Risk Quotient ranging from 0 (perfect neutrality) to 1 (maximum possible deviation), which makes it directly interpretable as the minimum percent of outcomes that must change to eliminate any observed treatment effect. We demonstrate its extension from 2×2 tables to contingency tables of any size, including continuous outcomes reframed as contingency tables. This refinement standardizes the Risk Quotient across study types, resolves definitional conflicts, and enables a common interpretive framework for evidence robustness.