Intensive-Care-Units (ICUs) are time-critical, and sufficient reaction time is crucial. Previous studies of systems for alerting life-threatening events in the ICU, suffer from “immediate” events bias. In this research, we present a new approach for outcome prediction in ICU admissions, which takes into consideration the constraint of an advance notice of a predicted outcome. We showcase the approach over mortality and sepsis-3 predictions and compare it to existing approaches. We’ve created a set of Neural Network models that implement and evaluate the existing and the suggested approaches using the MIMIC-III data. We show that the performance is affected significantly when enforcing a notice period for mortality prediction, but not affected for sepsis-3 prediction. Further, we examine whether models need to be trained for a specific notice period, or whether the approach could be incorporated at the evaluation level. We found that adding notice enforcement post-model training, has no significant performance loss compared to incorporating the notice period during training, within the bounds of the trained lookahead. The concept of adding Alert-Interval could be applied to other clinical scenarios, where having advance notice is essential.