Patient monitoring algorithms that analyze multiple features from physiological signals can produce an index that serves as a predictive or prognostic measure for a specific critical health event or physiological instability. Classical detection metrics such as sensitivity and positive predictive value are often used to evaluate new patient monitoring indices for such purposes, but since these metrics do not take into account the continuous nature of monitoring, the assessment of a warning system to notify a user of a critical health event remains incomplete. In this article, we present challenges of assessing the performance of new warning indices and propose a framework that provides a more complete characterization of warning index performance predicting a critical event that includes the timeliness of the warning. The framework considers 1) an assessment of the sensitivity to provide a notification within a meaningful time window, 2) the cumulative sensitivity leading up to an event, 3) characteristics on if the warning stays on until the event occurs once a warning has been activated, and 4) the distribution of warning times and the burden of additional warnings (e.g., false-alarm rate) throughout monitoring that may or may not be associated with the event of interest. Using an example from an experimental study of hemorrhage, we examine how this characterization can differentiate two warning systems in terms of timeliness of warnings and warning burden.