Evaluating a survival analysis model against a binary classifier

Question

I'm new to survival analysis and looking to use it to help a telcom company better identify clients at risk of churning. Their current model predicts risk of churning in time windows (1month, 2months, etc) with a GBoost binary classifier, so by using survival analysis I'm hoping to provide a richer continuous risk function (or values) for their clients across time.

I've read some articles and tutorials online, and began experimenting with the Cox Proportional Hazards model, but I have some questions on how can I fairly compare both model's performance. They mainly use the lift score, so I was thinking about using the same metric on the risk scores from the Cox model. However, since the survival model wasn't trained on discrete time windows, I don't know how I could do this comparison using the lift score (or other metric). Do you guys have any suggestion on how I can achieve this?

Note: In case it help, I'll leave here how I compute the event and duration target features for my dataset:

where client_join is the date of when the client joined a service, snapshot is the date when all the current covariates were recorded, study_period is the end of the study period (for my analysis im considering 12 months), so basically any churn event before this date is considered a positive event (event=1), negative otherwise (event=0). For a given snapshot, there can't be churn events before the snapshot. Churn1 and Churn2 are from two different clients!

Answer 1

Sorry if this is answering a different question, but rather than doing that, I would repurpose their classifier as a discrete time survival model.

ie use xgboost to predict p(survive month x| survive to month x-1)

this will give you all the advantages of a survival model ( assuming you don't actually care about continuous time).

(then to predict survive month 3| at month 0, you multiply the individual probabilities: P(survive month 3|2) :P(survive month 2|1): P(survive month 1|0)