Right censoring in survival analysis

Question

I work with data at an union. If you are member while studying your monthly fee is 0 or a small amount depending on the type of membership. When you end your studies the fee increases significantly since you become a ‘normal’ member.

I’m currently doing EDA (e.g. Kaplan Meier Survival Curves) trying to figure out whether there is a relationship between e.g. age, type of membership under the studies (the free or the almost free), gender etc and the survival time af becoming a 'normal' member.

The problem is, that for many of the students they continue their study after a while hence returning to the free or low-fee membership. That of course gives extremely high survival rates (since they return to the free or low-fee membership) and make it difficult to find a significant relationship.

I have three ideas for how to deal with this, but don’t know which one to those.

1. combining the periods if the break between studies is e.g. under 6 months

2. censoring them when they return to their studies

3. only use the last of the periods they study

What is pros and cons for each approach? I want to get it right from the start to avoid any p-hacking. Any thoughts or reference to good resources is appreciated. 😊

Answer 1

As @Glen_b noted in a comment, a simple survival model isn't appropriate for this type of data, in which the state of an individual can switch back and forth over time.

There are, however, extensions of simple survival models to multi-state models that can handle your data. This vignette of the R survival package provides a useful introduction. Those tools allow you to model transitions between "student" and "normal" membership in both directions, along with transitions out of the union completely as a terminal event.