Counterfactual Closing-Acceleration Risk: An Anticipatory Surrogate Safety Measure for the Blind Region of Car-Following

Abstract

Surrogate safety measures allow road-safety assessment from trajectory data in which crashes are absent, yet the dominant proximity measures - time-to-collision (TTC) and its variants - assume invariant motion and are undefined whenever the following vehicle is not yet faster than its leader, so a large fraction of car-following carries no risk reading at all. This paper introduces Counterfactual Closing-Acceleration Risk (CCAR), an anticipatory surrogate measure that scores how exposed a follower is to a rear-end conflict if its leader were to brake, conditioned on the follower's current gap-closing acceleration. CCAR is evaluated on 745,540 expressway car-following frames from the SQM-W-1 trajectory dataset. Conventional measures leave 51% of frames unscored because the follower is not yet faster; across this blind region CCAR returns a graded, non-trivial risk in 98.8% of frames. CCAR is not redundant with existing measures (Spearman correlation 0.54 with modified TTC; top-decile risk-set overlap 0.19), and at fixed gap and speed its risk rises monotonically with closing acceleration. A controlled simulation with a reactive Intelligent Driver Model follower and a scripted leader brake confirms that, holding gap and brake fixed, the actual collision rate rises with closing acceleration, supporting the proposed precursor mechanism. Parameter sensitivity, limitations, and implications for forward-collision-warning systems are discussed.