hi all!

I'm not too experienced with survival analysis, so I'm hoping to get some feed back regarding our design / study:

Start Date: Date enrolling in an educational program.

Event of Interest: At a maximum of 8 months post enrollment date, did the student make an appointment to write an examination.

Covariates: Gender, other fixed effects.

So, students enter the educational program, and we follow them for a maximum of 8 months to see if they make an appointment to write the exam or we censor them at the 8 month mark. This is the basis of our design.

In between the enrollment and the possible event, we hypothesize that some students will seek additional tutoring services (such as those LSAT/GRE/SAT prep classes). We would like to control for (a) whether this happens at all and (b) what is the intensity of the services? For intensity of the services we would get information such as how many classes they took, how long they were, etc.

I'd like to control for the intensity but this seems random. I'm wondering if it is kosher to take something like a simple rate over the risk period. For example:

Student A enrolls and by month 6 he schedules to write the exam (our event of interest). however, during that 6 month period, we have information that says he had 4 extra ''outside'' tutoring prep classes. Would it make sense to calculate 4/6 as his intensity rate and include that as a covariate in studying the association to time to our event?