Statistical Fragility and Robustness in Pharmaceutical Trials

This preprint, prepared as a book chapter, presents the p–fr–nb framework for evaluating statistical evidence in pharmaceutical trials. Conventional reporting treats the p-value, confidence interval, and effect size as a complete account of a trial result; this chapter defines that account as partial evidence because it measures significance and magnitude but not the stability of the significance classification or the distance of the estimated effect from therapeutic neutrality. Complete statistical evidence is defined as the triplet p–fr–nb: the p-value for significance, a native fragility quotient (fr) for classification stability, and a neutrality-boundary robustness metric (nb) for separation from no effect. The chapter sets out a taxonomy of statistical fragility distinguishing analysis, resampling, perturbation, and scaling fragility; defines the fragility index, global fragility index, fragility distance, resampling fragility, number needed to reverse, sample-size fragility multiplier, and risk quotient; and works each concept through published trials in coronary artery disease, giant cell arteritis, type 2 diabetes, and amyotrophic lateral sclerosis. All metrics are model-free and computable from published counts, allowing any reader to complete the evidence a trial report begins. A peer-reviewed version of this work will be submitted for publication.