Modelling the continuum of serious traffic injuries in police-hospital linked data by applying the random parameters hazard-based duration model

•Police and hospital road injury records are linked.•Random parameters hazard-based duration model with heterogeneity-in-means is applied.•Speeding, impaired driving, and heavy vehicles tend to produce more serious injuries.•Summertime crashes are more likely to be less serious than crashes during winter.•Injuries to the head region are positively associated with a prolonged hospital stay.