A copula-based multivariate extreme value framework for roundabout safety evaluation under mixed traffic

Roundabouts in low- and middle-income countries are not as safe as expected due to non-lane-based traffic behaviors and heterogeneity in traffic conditions. To address the limitations of crash-based analyses, this study developed a proactive, data-driven framework that integrates high-resolution drone-recorded video-based trajectory extraction, multivariate Extreme Value Theory (EVT)-Peak-Over-Threshold (POT) modeling, and probabilistic clustering to identify and classify conflict events at unsignalized roundabouts. Trajectories from videos collected at 22 roundabouts were extracted via advanced computer-vision algorithms and processed in the Surrogate Safety Assessment Model (SSAM) developed by the Federal Highway Administration to compute four surrogate safety measures (SSMs): Time-to-Collision (TTC), Post-Encroachment Time (PET), maximum deceleration (MaxD), and maximum post-collision (hypothetical) velocity change (MaxDeltaV). The quadrivariate EVT-POT model with Gumbel-Hougaard copula was developed to capture joint exceedances of the SSMs and determine context-specific thresholds, i.e., 1.5 s for TTC and PET, -3.0 m/s² for MaxD, and 4.5 m/s for MaxDeltaV, via Mean Residual Life, Threshold Stability, and AIC plots. The copula captured tail dependencies among the SSMs efficiently, marked by its goodness-of-fit diagnostics. Conflicts were mapped spatially, revealing that lane-change interactions constituted ∼ 43 %, rear-end ∼ 38 %, and crossing ∼ 19 % of conflicts, with distinct clustering at approach legs, weaving zones, and pedestrian/bicyclists crossing points. Latent profile analysis using the Gaussian Mixture Model stratified conflicts into five severity levels, i.e., from minor (29.7 %) to critical (7.6 %), enabling prioritized intervention strategies. This framework offers a scalable tool for practitioners to pinpoint high-risk areas and deploy targeted safety countermeasures, enhancing proactive roundabout safety under mixed-traffic conditions.