Let's say we are given the following problem:
Predict which clients are most likely to stop buying in our shop in next 3 months.
For each client we know the month when one started to buy in our shop and additionally we have many behavioral features in monthly aggregates. The 'eldest' client has been buying for fifty months; let's denote the time since a client began to buy by $t$ ($t \in [0, 50]$). It can be assumed that the number of clients is very large. If a client stops buying for three months and then comes back, then he is treated as a new customer so an event (stop buying) can occur only once.
Two solutions come into my mind:
Logistic regression - For each client and each month (maybe except the 3 newest months), we can say whether a client stopped buying or not, so we can do rolling samples with one observation per client and month. We can use the number of months since beginning as a categorical variable to obtain some equivalent of base hazard function.
Extended Cox model - This problem can be also modeled using the extended Cox model. It seems that this problem is more suited to survival analysis.
Question: What are the advantages of survival analysis in similar problems? The survival analysis was invented for some reason, so there must be some serious advantage.
My knowledge in survival analysis is not very deep and I think that most potential advantages of the Cox model can also be achieved using logistic regression.
- Equivalent of stratified Cox model can be obtained using an interaction of $t$ and the stratifying variable.
- Interaction Cox model can be obtained by diving the population into several sub-populations and estimating LR for every sub-population.
The only advantage I see is that Cox model is more flexible; for example, we can easily calculate the probability that a client will stop buying in 6 months.