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Considerable efforts have been made from researchers and policy makers in order to explain road crash occurrence and improve road safety performance of highways. However, there are cases when crashes are so few that they could be considered as rare events. In such cases, the binary dependent variable is characterized by dozens to thousands of times fewer events (crashes) than non-events (non-crashes). This paper attempts to add to the current knowledge by investigating crash likelihood by utilizing real-time traffic data and by proposing a framework driven by appropriate statistical models (Bias Correction and Firth method) in order to overcome the problems that arise when the number of crashes is very low. Under this approach instead of using traditional logistic regression methods, crashes are considered as rare events In order to demonstrate this approach, traffic data were collected from three random loop detectors in the Attica Tollway ("Attiki Odos") located in Greater Athens Area in Greece for the 2008–2011 period. The traffic dataset consists of hourly aggregated traffic data such as flow, occupancy, mean time speed and percentage of trucks in traffic. This study demonstrates the application and findings of our approach and revealed a negative relationship between crash occurrence and speed in crash locations. The method and findings of the study attempt to provide insights on the mechanism of crash occurrence and also to overcome data considerations for the first time in safety evaluation of motorways. [ABSTRACT FROM AUTHOR]