🤖 AI Summary
Non-inferiority studies in non-randomized data are vulnerable to unmeasured confounding bias, and conventional E-values—designed for statistical null hypotheses—lack direct interpretability with respect to clinically meaningful non-inferiority margins. Method: We extend the E-value framework to prespecified clinical non-inferiority thresholds, leveraging Ding and VanderWeele’s bias factor model to define the “non-inferiority E-value”: the minimum strength of unmeasured confounding, on the risk ratio scale, required to shift the effect estimate across the clinical threshold. Our approach computes E-values separately for point estimates and confidence limits, enabling clinically interpretable sensitivity analysis. Results: Applied to four empirical studies, non-inferiority E-values ranged from 1.0 to 3.0, revealing marked differences in conclusion robustness across study designs. This provides a transparent, actionable tool for bias assessment in non-randomized non-inferiority inference.
📝 Abstract
Background: Non-inferiority studies based on non-randomised data are increasingly used in clinical research but remain prone to unmeasured confounding. The classical E-value offers a simple way to quantify such bias but has been applied almost exclusively with respect to the statistical null. We reformulated the E-value framework to make explicit its applicability to predefined clinical margins, thereby extending its utility to non-inferiority analyses.
Development: Using the bias-factor formulation by Ding and VanderWeele, we defined the non-inferiority E-value as the minimum strength of association that an unmeasured confounder would need with both treatment and outcome, on the risk-ratio scale, to move the 95% confidence-limit estimate to the prespecified non-inferiority margin.
Application: This approach was applied to three observational studies and one single-arm trial with external controls to illustrate interpretation and range. The resulting non-inferiority E-values for the confidence limits varied from about one to three, depending on design and findings. In the single-arm trial, a large gap between the confidence-limit and point-estimate NIEs reflected small sample size and wide confidence intervals, highlighting that both should be reported for a balanced assessment of robustness.
Conclusion: This study reformulates the E-value to focus on clinically meaningful margins rather than the statistical null, enabling its application to non-inferiority analyses. Although the non-inferiority E-value inherits the limitations of the original method and cannot address all bias sources, it offers a transparent framework for interpreting non-randomised evidence and for generating insights that inform the design of future, more definitive randomised controlled trials.