Hi everyone! I have a hospitalization dataset that spans an 18 year period. Because of this some individuals are hospitalized multiple times. I am attempting to assess the association of diabetes exposure with in-hospital death among patients hospitalized with a salmonella infection, aka everyone in the dataset has this infection (I do not have any info on whether death occurred outside the hospital, I only know if an individual died in the hospital). Additionally I also have the length of stay of each hospitalization event. I am wondering if a survival analysis would be more appropriate in this case (perhaps a cox proportional hazards model, I have length of stay to act as my time variable?) rather than a logistic regression model? What benefit conceptually does using a cox model give?
First, one aspect I am a bit iffy on is that since my outcome is explicitly in-hospital mortality rather than mortality in general, is the censoring framework really appropriate in this scenario? Since censoring implies that the event (death) could have happened but is simply not observed due to loss to follow up/the end of the study, I am wondering if this is even appropriate in my scenario since by definition they can no longer have an in-hospital death once they leave the hospital and I am not trying to (and cannot due to limitations of the data) assess mortality outside the hospital.
Secondarily, I am wondering if a survival analysis would also be inappropriate since some individuals may have had a hospitalization before the time span of the dataset (aka before 2000) and thus I would be missing these previous hospitalizations. Basically I am afraid that my time origin isn’t actually the start of the risk period for some of the individuals.
For both these reasons I am wondering if logistic regression would be the more appropriate method.
Any advise would be much appreciated!