Let's say I have discrete events in time, e.g. patients getting sick, and I want to predict whether theses events are indicators of some other underlying event, e.g. a disease outbreak. Usually, one would transform the event based time series into a regular time series by for example aggregating the counts of patients over each week. However, I feel that by this aggregation a lot of information is lost and it is also hard use to multiple features of events, e.g. patients' age, patients' sex, etc. My question is very general: is there a branch of statistics / data science that treats time series as composed of events at arbitrary times rather that aggregated values at evenly distributed intervals?
I tried googling it, but it seemed hard to phrase the question in a way that a search engine understands.