# General framework of nonlinear factor interactions using bayesian networks for risk analysis applied to road safety and public health

## TL;DR

This paper introduces a new method using Bayesian networks to better understand complex risk interactions in areas like road safety and public health.

## Contribution

A novel Bayesian network framework for analyzing nonlinear risk factor interactions in complex systems.

## Key findings

- The framework accurately captures nonlinear and synergistic risk interactions better than traditional linear models.
- It was successfully applied to road safety and type 2 diabetes risk analysis, showing broader applicability.
- The method reveals how risk factors amplify or mitigate outcomes in complex systems.

## Abstract

In complex systems, understanding the nonlinear interactions among risk factors is essential for accurate risk analysis. However, traditional linear models often fail to capture these complex interdependencies, leading to significant gaps in risk prediction. The aim of this study is to present a novel approach for risk analysis of nonlinear risk interactions using Bayesian networks (BNs), thereby providing a broadly applicable method for risk management and mitigation. Specifically, this study applies a BN-based framework that integrates conditional dependencies and nonlinear effects to illustrate how multifactor risk interactions operate synergistically. Using a step-by-step approach, the interactions among multiple risk factors are first mathematically formalized, and then this framework is applied to a case study of road safety using crash report data. Additionally, a second validation case in public health (type 2 diabetes risk) is included in supplementary materials to illustrate the broader applicability of the framework. The findings demonstrate through BNs and a mathematical framework, how to analyse complex interactions more accurately than traditional methods can, revealing the amplifying or mitigating effects of individual risk factors on outcomes. This approach offers more accurate risk representations and is applicable not only to road safety but also to complex environments, such as healthcare and environmental risk analysis.

The online version contains supplementary material available at 10.1038/s41598-025-13572-5.