I'm currently trying to model the time to event, where there are three different events that might happen. It's for telecommunication data, and I want to predict the expected lifetime of unlocked customers, so customers for who their contract period has ended and they can resign now on a monthly basis. They are unlocked customers as soon as their 1- or 2-year contract ends, and as time goes by they can churn, retain (buy a new contract) or stay an unlocked customer (so I will need a competing risk model).
Now what my point of interest is, is the time until one of these events happens. I was thinking to use a Cox regression model to find the influence of covariates on the survival probability, but since the baseline hazard is not defined for Cox, it will be hard to predict the time to event (right?). I was thinking a parametric survival model might work better then, but I can't really make up my mind from what I find on the internet so far.
Is survival analysis the right method to predict time to event?
You can assume a parametric model for baseline by using e.g.
survival::survreg. This way you avoid the baseline. Moreover, you can estimate the non-parametric baseline in-sample with a cox model. See thetype = "expected"argument in?predict.coxph.