Neutrality Boundary Robustness for Meta-Analysis
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2026
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| _version_ | 1866901683162841088 |
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| author | Heston, Thomas F |
| author_facet | Heston, Thomas F |
| contents | <p>Abstract<br>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.</p> <p>Objective: To extend NBF robustness assessment to meta-analysis by (1) defining a generic meta-analytic robustness index nbmeta, and (2) illustrating empirical robustness synthesis via the distribution of trial-level nb across a heterogeneous sample of randomized trials.</p> <p><br>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 risk ratio = 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 randomized 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).</p> <p><br>Results: Across N = 161 trials, median nb = 0.147 (IQR 0.038–0.390; range 0.000–0.902). Using empirically validated robustness bands (nb < 0.075 weak; 0.075 ≤ nb <<br>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 exhibited systematically lower nb than<br>continuous-outcome trials. Robustness nb was moderately correlated with − log10(p) (r = 0.35, p < 0.001), confirming that robustness captures geometric distance from<br>neutrality, a dimension distinct from statistical significance.</p> <p>Conclusions: NBF robustness extends naturally to meta-analysis. Even without computing nbmeta, the distribution of trial-level nb provides a simple, cross-design sum-<br>mary of how far the evidence base lies from therapeutic neutrality. This methods note formalizes “nb-type meta-analysis” and motivates integration of robustness assessment alongside p-values in routine evidence synthesis.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18842105 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Neutrality Boundary Robustness for Meta-Analysis Heston, Thomas F statistical robustness NBF Neutrality Boundary Framework meta-analyses meta-analysis complete statistical evidence <p>Abstract<br>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.</p> <p>Objective: To extend NBF robustness assessment to meta-analysis by (1) defining a generic meta-analytic robustness index nbmeta, and (2) illustrating empirical robustness synthesis via the distribution of trial-level nb across a heterogeneous sample of randomized trials.</p> <p><br>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 risk ratio = 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 randomized 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).</p> <p><br>Results: Across N = 161 trials, median nb = 0.147 (IQR 0.038–0.390; range 0.000–0.902). Using empirically validated robustness bands (nb < 0.075 weak; 0.075 ≤ nb <<br>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 exhibited systematically lower nb than<br>continuous-outcome trials. Robustness nb was moderately correlated with − log10(p) (r = 0.35, p < 0.001), confirming that robustness captures geometric distance from<br>neutrality, a dimension distinct from statistical significance.</p> <p>Conclusions: NBF robustness extends naturally to meta-analysis. Even without computing nbmeta, the distribution of trial-level nb provides a simple, cross-design sum-<br>mary of how far the evidence base lies from therapeutic neutrality. This methods note formalizes “nb-type meta-analysis” and motivates integration of robustness assessment alongside p-values in routine evidence synthesis.</p> |
| title | Neutrality Boundary Robustness for Meta-Analysis |
| topic | statistical robustness NBF Neutrality Boundary Framework meta-analyses meta-analysis complete statistical evidence |
| url | https://doi.org/10.5281/zenodo.18842105 |