I want to know if it is not only possible to handle left-truncation of data in a survival model, but to know/predict the hazard function (probability of event) before the start point, i.e. the point of truncation.
I have species observations for many sampling sites (locations) and years. For each site-year combination there is a start point of the sampling. I want to model/predict the first observation time of a particular species, across all sites and years. I have read that the hazard function only extends after the start point, but I am interested in how the species might have occurred before the sampling started to see what the sampling potentially missed.
Shifting the starting point earlier is not enough, because the model has to know that the data could only occur after the first sampling time.
Is survival analysis appropriate for this? If so, how can I get the hazard function before the truncation point? If not, do you know of any approaches to this type of problem?
Thanks in advance.