II've got a bunch of data on hospital admissions and I'm trying to establish if the number of admissions somebody has had is associated with survival time. I also wish to control for a bunch of other covariates (age, sex, ethnicity...). The cohort consists of everybody who was admitted to a particular hospital for the condition of interest over the course of a 5 year period, and I have since obtained their full history of admissions for the condition. Now the question of interest immediately suggests that a Cox PH model is what I should be fitting. The main thing that I need to account for is that those with a single admission versus those with say, more than 5, are likely to have a shorter follow-up period if their first admission just occurred much later. I've been racking my brain to establish whether a) this is violating any assumption of the Cox model, and b) whether I will even have sufficient data/follow-up for the "single admission" group to be able to compare them to the multiple attenders. There is a lot of right censoring in the data however there is a much larger portion of those with more than one admission who have since died compared to the others.
Modelling time from last admission to death does not seem appropriate since the ones with a single attendance are in the study for a shorter period, hence a lot of censoring in this group, hence overestimation of survival (is this a correct interpretation?). For this reason I'm thinking of trying to fit the number of attendances as a time-dependent covariate and using the index admission as the baseline. I may also categorise the number of admissions into 3 groups.
Does this seem reasonable?