A sensitivity analysis for non-inferiority studies with non-randomised data

TL;DR

This paper extends the E-value framework to non-inferiority studies with non-randomised data, providing a tool to assess unmeasured confounding relative to clinical margins, aiding interpretation of observational research.

Contribution

It reformulates the E-value to focus on clinical non-inferiority margins, enabling bias assessment in non-randomised studies and improving interpretation of their robustness.

Findings

Non-inferiority E-values ranged from about one to three across studies.

The approach highlights the importance of reporting both point estimates and confidence intervals.

The method offers a transparent way to interpret non-randomised evidence in clinical research.

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.