Trial design-aware funnel plot for publication bias assessment with noninferiority or equivalence objectives

Funnel plots are the most widely used graphical tool for assessing publication bias (PB) in meta-analyses of superiority trials. However, conventional funnel plots are not directly applicable to noninferiority (NI) or equivalence (EQ) objectives, which are governed by distinct inferential frameworks and may be prone to inverse publication bias (IPB), a tendency for studies with results far from the null to be underreported. This pattern contrasts with classical PB, where studies with results close to the null are more likely to be suppressed.

We propose trial design-aware funnel plots, a design-aware visualization that incorporates inferential boundaries specific to NI and EQ objectives. By explicitly delineating regions corresponding to key decision thresholds, the proposed plots facilitate visual assessment of where PB or IPB is most likely to arise. For EQ objectives, the plot distinguishes regions supporting EQ, inferiority, and superiority; for NI objectives, it highlights regions reflecting inferiority and nonsuperiority. The framework also accommodates meta-analyses comprising mixtures of NI, EQ, and superiority trials, enabling coherent bias assessment across heterogeneous study designs.

We illustrate the proposed approach using three real-world meta-analyses: one EQ-only set, one NI-only set, and one mixed superiority-NI set. These examples demonstrate the flexibility and interpretability of the design-aware funnel plots across commonly encountered trial objectives.

The trial design-aware funnel plot offers a flexible and intuitive visualization tool for identifying between-study bias in meta-analyses with NI and EQ objectives. It may be particularly valuable for safety outcomes, where the bias mechanisms may differ from classic PB and carry substantial decision-making consequences. Conclusions regarding possible PB, however, may be strongly margin dependent and should be interpreted in light of the prespecified or clinically justified margin.

Standard funnel plots are commonly used to look for PB in meta-analyses, but they were mainly developed for superiority trials and may not work well for NI or EQ objectives. These trial designs use different decision rules, so the types of missing studies may also differ. In particular, some studies with results far from the null may be less likely to be reported, a pattern we describe as inverse PB. We developed a trial design-aware funnel plot that reflects the specific objectives of NI and EQ objectives and helps researchers visually identify where missing studies may occur. We show how this approach works in three real meta-analyses, including EQ-only, NI-only, and mixed design settings. Importantly, conclusions about possible PB may depend strongly on the margin chosen for NI or EQ. This method may help systematic reviewers and decision-makers better understand possible reporting bias in these increasingly common trial designs.