Methods to model multiple time-to-events

Hello, I am looking for suggestions to model and forecast a multiple time-to-events problem. In particular, I am measuring time to purchase multiple products.

I am tracking the timing of the same set of events for all individuals. I have some individual-level covariates, but they are not of interest. The data are:
ID, y1, y2, y3. Each y corresponds to the time it takes for that ID to purchase product j. But there could be censoring, in which case that y[j] would be null.

There is no budget constraint to worry about and these are not competing or sequential events. But the analysis is trying to argue that there is individual-level specific correlation, since it is believed that someone is an early buyer for product1 and also likely to be an early buyer for product2, etc. So I would like to model these time-to-events together, as opposed to separately.

Finally, if I can build this model successfully, I would like to use this model to forecast the timing for another new product (whose data are yet to be observed) for this same group of individuals. This is why I would like to build this model in a Bayesian manner.


I think there is a time-to-events model in rstanarm that can get you started:

After the rstanarm package you can look at similar models in brms

Then maybe code them up in Stan?