A bivariate extreme value model for estimating crash frequency by severity using traffic conflicts

•Extreme value models are used to estimate crash frequency-by-severity from traffic conflict indicators.•Bivariate extreme value method for joint frequency and severity estimation is superior to the univariate method.•Modified Time to Collision (MTTC) is a better indicator of crash frequency than Time To Collision (TTC)•Combined site models are more accurate and precise than site-specific models.•Longer duration of conflict observations improves the performance of extreme value models. Estimating crash frequency by severity levels using traffic conflicts remains relatively unexplored in conflict-based traffic safety assessment, limiting its application scope and appeal compared to traditional methods. No studies to date have predicted the frequency of severe and non-severe crashes utilizing traffic conflicts. This study aims to address this critical gap and stimulate discussion and development in this critical area. The study estimates the frequency of severe crashes and non-severe crashes by jointly modeling the indicators of crash frequency, namely, Time to Collision (TTC) and Modified Time to Collision (MTTC), and crash severity, namely, predicted post-collision change in velocity (Delta-V or Δv), using bivariate Extreme Value. Severe crashes here are defined as crashes with a Maximum Abbreviated Injury Scale rating of greater than or equal to 3. Rear-end conflict data (TTC ≤ 3.0 s) were collected for two days (12 h each day) from two four-legged signalized intersections in Brisbane, Australia. Bivariate peak-over-threshold models for both TTC and MTTC indicators, combined with Delta-V, were estimated. Alternatively, another univariate approach was also attempted where the probability of crash occurrence was estimated using the univariate peak-over-threshold model with TTC (or MTTC) and then multiplied with the injury probability estimated from Delta-V to estimate the frequencies of severe and non-severe injury crashes. The study results demonstrate that the bivariate approach is more advantageous than the univariate approach due to a superior statistical fit to the data and more precise estimations of crash frequencies by severity levels. Both TTC and MTTC indicators, in combination with Delta-V, provide comparable results using the bivariate approach owing to the weak asymptotic dependence between the frequency and severity indicators. Comparing the combined dataset model of the two intersections with the intersection-based models shows that sharing i