I have data consisting of irregular event times and at each event there is either a binary positive or negative result (with approximate probability of a negative result ~5%).
The aim is to assess whether the rate of negative results is changing over time. One option I've thought of, and probably the most common approach, is to bin the events into (e.g. yearly) intervals and calculate a rate for each bin and test whether the annual rate is changing.
However, this obviously throws away some of the richness of the data and may obscure certain temporal relationships. I was wondering if there's some form of Poisson model that that can use the continuous time index?