Resolve conflicting rankings of outcomes in network meta-analysis: Partial ordering of treatments
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Updated: Feb 21, 2026

An R-Based Landscape Validation of a Competing Risk Model
Published on: September 16, 2022
Gerta Rücker1, Guido Schwarzer1
1Faculty of Medicine and Medical Center, Institute for Medical Biometry and Statistics, University of Freiburg, Freiburg, Germany.
Abstract:
Network meta-analysis has evolved into a core method for evidence synthesis in health care. In network meta-analysis, 3 or more treatments for a given medical condition are compared, based on a number of clinical studies, usually randomized controlled trials. Often, many different endpoints are investigated, related to different aspects of the patient's outcome, such as efficacy, safety, acceptability, or costs of a treatment. Different outcomes may lead to different rankings of the treatments. We use the existing theory of partially ordered sets and show how the relations between the treatments in a network meta-analysis can be illustrated by Hasse diagrams, that is, directed graphs showing the partial order relations, and by structured scatter plots and biplots.
Insights
Network meta-analysis synthesizes evidence from multiple treatments and outcomes. This study visualizes treatment comparisons using Hasse diagrams and structured plots for clearer interpretation of complex health data.
Area of Science:
- Health research methodology
- Evidence synthesis
- Biostatistics
Background:
- Network meta-analysis is a key method for synthesizing evidence from multiple treatments for a single condition.
- Clinical studies, often randomized controlled trials, form the basis of network meta-analyses.
- Multiple patient outcomes (efficacy, safety, cost) can lead to varying treatment rankings.
Purpose of the Study:
- To illustrate the complex relationships between treatments in network meta-analysis.
- To apply partially ordered set theory for visualizing treatment comparisons.
- To enhance the interpretation of network meta-analysis results across diverse outcomes.
Main Methods:
- Utilized the theory of partially ordered sets.
- Employed Hasse diagrams (directed graphs) to represent partial order relations between treatments.
- Generated structured scatter plots and biplots for enhanced visualization.
Main Results:
- Demonstrated how Hasse diagrams can effectively illustrate treatment relations in network meta-analysis.
- Showcased structured scatter plots and biplots as valuable tools for visualizing comparative treatment data.
- Provided a novel graphical approach to understanding treatment hierarchies across multiple endpoints.
Conclusions:
- Partially ordered set theory offers a robust framework for visualizing network meta-analysis results.
- Hasse diagrams and structured plots improve the clarity and interpretability of complex evidence synthesis.
- These visualization techniques aid in understanding nuanced treatment comparisons and their implications.
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