Neutrality Boundary Robustness for Meta-Analyses

Background: Meta-analyses conventionally report pooled effect sizes, confidence intervals (CIs), and p-values, addressing statistical significance and precision but not distance from therapeutic neutrality on a standardized robustness scale. The Neutrality Boundary Framework (NBF) provides a 0–1 robustness metric (nb) for individual studies, but its extension to meta-analytic evidence has not been formalized. Objective: To demonstrate empirical robustness synthesis across heterogeneous trial designs and propose a theoretical framework for pooled meta-analytic robustness (nbmeta) applicable when study-level effect estimates are available (and, for inverse-variance pooling, their variances/SEs). Methods: We formalize meta-analytic robustness using the NBF formula nbmeta = |T − T0|/(|T − T0| + S), where T is a pooled effect estimate, T0 is therapeutic neutrality (e.g., log(RR) = 0), and S is a cross-study scale parameter (e.g., between-study standard deviation ˆτ or median absolute deviation (MAD)). For empirical illustration, we analyzed a convenience sample of N = 161 clinical trials with pre-computed trial-level nb values, where nb ∈ [0, 1] is the NBF robustness index measuring distance from therapeutic neutrality. We summarized the distribution of nb overall and examined the correlation between nb and − log10(p). Results: Across N = 161 trials, median nb = 0.147 (IQR 0.038–0.390; range 0.000–0.902). Using empirically derived, provisionally recommended robustness bands (nb < 0.075 weak; 0.075 ≤ nb < 0.227 moderate; nb ≥ 0.227 strong), 35.4% of trials showed weak robustness, 24.8% moderate, and 39.8% strong. Binary 2×2 trials tended to show lower nb than continuous-outcome trials. Robustness nb was moderately correlated with − log10(p) (r = 0.35, p < 0.001, n = 137; 24 trials with p = 0 excluded), suggesting that robustness captures geometric distance from neutrality, a dimension distinct from statistical significance. Conclusions: This methods note establishes trial-level nb distribution as a simple robustness synthesis approach and formalizes nbmeta for future implementation when study-level effect estimates are available (and, for inverse-variance pooling, their variances/SEs). Even without computing nbmeta, the distribution of trial-level nb provides a cross-design summary of how far the evidence base lies from therapeutic neutrality. Integrating robustness assessment alongside p-values in routine evidence synthesis yields a more complete picture of evidential strength