I use Cox regression (proportional hazards) to model survival for a cohort of patients. Patients are censored (alive (0), dead (1)).
I was wondering how Cox regression uses censored data intuitively. I thought when alive (0), Cox model will just ignore them, but apparently it is not so simple.
For example, I used the Cox model with all patients (both alive and dead), and the Cox model with only the patients annotated as dead. Apparently, the results were quite different (likelihood ratio test for the whole model, Wald test for the individual covariates).
In brief, intuitively, how does the Cox model uses the censored data and how the censoring affects the results?