Interpreting Non-Inferiority Across Effect Scales: A Bayesian Perspective with Clinical Translation

This study examines how the choice of non-inferiority margins affects the clinical interpretation of interventional studies using the Santos et al. trial comparing high-flow nasal cannula (HFNC) with non-invasive ventilation (NIV) as a case example. We also demonstrate how Bayesian reanalysis improves interpretability by expressing non-inferiority margins on absolute and relative scales, quantifying posterior probabilities of non-inferiority and benefit, and translating these margins into patient-centred measures such as the Number Needed to Harm (NNH).

Secondary Bayesian reanalysis of a previously published randomised controlled trial.

Multicentre paediatric intensive care units participating in the original Santos et al. study.

Infants with acute bronchiolitis were randomised to receive either HFNC or NIV.

Respiratory support via HFNC or NIV.

The primary endpoint was intubation, with the intubation rate reported as a descriptive summary statistic. We re-expressed the original non-inferiority margin on the Absolute Risk Reduction (ARR) and Odds Ratio (OR) scales, estimated Bayesian probabilities of non-inferiority and benefit, and derived patient-centred metrics such as the NNH.

The original analysis concluded non-inferiority using a fixed absolute margin. Our Bayesian reanalysis showed that this margin could correspond to a substantial relative tolerance when baseline risks are low; specifically, the 0.15 non-inferiority ARR margin might imply a doubling of the odds of intubation. When interpreted from a patient-centered perspective, this margin corresponds to an NNH of approximately 6.7. In other words, for every seven infants treated with HFNC instead of NIV, one additional child might require intubation who would not have needed it under standard care.

Non-inferiority margins are typically derived through a combination of statistical evidence and clinical judgment. However, their interpretation may vary depending on the effect scale used, and this may not always be transparent in reporting. For this reason, integrating Bayesian methods and framing multiple noninferiority definitions improves the interpretability of trials.