Suppose you are given a set of time series, all with identical time stamps (a vector-valued time-series, if you will). These could be for example measurements of various medical metrics, such as blood pressure, heart rate etc of a single patient. For a pool of patients such time series are given. For each patient there is a certain designated time stamp, where an event happens (e.g., "patient dies"). If the task is to predict when patients die, what is is the (general) name of this data science problem?
Please notice: It is not "time series event prediction", since the fact that the event happens can't be read off the time series values (since the event is given as an additional "label" of a time point) and as far as I know event prediction refers to predicting events that can be read of the time series values (such as predicting the event "heart attack" which can be defined as the "heart rate dropping suddenly below a 20" - I'm not a doctor, so don't quote me on this number).
Could you give me references where I can find standard solutions how such a prediction, with an event given by a time label, can be made?