# state transition classification on terminal state

I have data on a unit $$i$$ which enters an entry state $$S_0$$. This unit has some covariates $$x_i$$ I would like to predict the probability the unit will reach the terminal state $$S_{pos}$$ or $$S_{neg}$$. The unit can spend time on each state, which affects the probabilities as well. In some time the unit can jump to an intermediate state $$S_j$$ which is not terminal which also changes the probability to get to one of the terminal states.

I have "dimension" data of the unit $$x_i$$ in one table and the state transition and time in a "fact" table.

I would like to build a model $$M(x, s, t)$$ which will predict probability to get to $$S_{pos}$$ given the covariate $$x$$ the state $$s$$ and the time spent in that state $$t$$. My idea was to replicate the data so that each unit $$i$$ I will create $$T$$ rows, one for each of the timestamps it lived until it was terminated and feed this to a general-purpose classifier.

The question is, is this redundant? Is there some representation of the data where I will not have to duplicate rows? Maybe feed this to an RNN? but there I will still need to feed a "nothing happened" time stamp every day until a state has changed.

How would you model this?

Survival analysis seems less relevant as I do not want to predict the duration, just the terminal state.