Cox regression where patients have differing follow-up times

Question

I posted a question yesterday and have done some research accordingly, however it has left me with a problem I hope your expertise could be of help:

Here is the situation: I am investigating whether the addition of a a biomarker (measured at discharge) improves a multivariable cox model predicting post-discharge outcomes in patients that were admitted in the hospital. In addition to looking at the hazard ratio's and significance levels of the variables in the cox models, I will use the likelihood ratio χ2 test to check if addition of the biomarker significantly improves the model, and will use the C-index as a measure of predictive strength of the final model.

Here is the issue: one of my outcomes is mortality through day 180 post-admission, not discharge. As I am using discharge measurements of the biomarkers and am interested in post-discharge outcomes, I am only looking at patients that survived the initial hospitalization (otherwise they would not have discharge measurements). In order to make prospective predictions for patients at discharge, I substracted the hospitalization time from the total time-to-event time (as naturally their time to event from discharge does not include their time in the hospital). This however has lead to differing maximum follow-up times.

I understand that in survival analysis this is not an issue, as non-events will be right-censored regardless, however as maximum follow-up time is related to time-in-hospital, can I still assume independent right-censoring? (I do not controll for length of stay in the models)

Thanks in advance!

Answer 1

My hunch is that this is not a problem as long as you model the patient heterogeneity. First of all in judging added prognostic value by a biomarker it is necessary to aggressively adjust for known patient risk factors, especially age and severity of disease and comorbidies (e.g., Elixhauser index; not Charlson index). Add duration of hospitalization into these factors as it represents another risk factor. And also consider the number of previous hospitalizations. Be sure not to assume linearity for continuous risk factors. You'll get more input from health services researchers if you post to datamethods.org. Note that the $c$-index is not sensitive enough for judging added value (it is good for quantifying predictive discrimination for a single model). Use these measures: https://fharrell.com/post/addvalue.