Suppose I'm Netflix. I'm using survival analysis methods (kaplan-meier curves) to study when my customers decide to cancel their subscription. However, I've noticed that customers that experience problems and have to contact support decide to cancel their subscriptions at a higher rate than those that never contact support.
I'd like to know what my cancellation rate (survival curve) would look like if nobody had problems that required them to contact support. So, I model a competing hazard for first-touch with support. When customers contact support the first time, they are modeled out as a second type of event. My assumption is that this is a more accurate methodology than simply censoring those people at that time point.
Is this an appropriate methodology? Why or why not?
Disclaimer: I don't work for Netflix.
Edit: Another possible methodology
Another way of looking at this would be to model the competing event not as first touch with support, but instead as cancellation after touching support. This makes the events of equivalent types (much like if you had death by cancer vs. death by getting hit by a bus).