The ability to predict a driver's reaction time to road events could be used in driver safety assistance systems, allowing for autonomous control when a driver may be about to react with sup-optimal performance. In this paper, we evaluate a number of machine learning and feature engineering strategies that we use to predict the reaction time(s) of 24 drivers to road events using EEG (Electroencephalography) captured in an immersive driving simulator. Subject-independent models are trained and evaluated using EEG features extracted from time periods that precede the road events that we predict the reaction times for. Our paper has two contributions: 1) we predict the reaction times corresponding to individual road events using EEG spectral features from a time period before the onset of the road event, i.e. we take EEG data from 2 seconds before the event, and 2) we predict whether a subject will be a slow or fast responder compared to other drivers.