Suppose initially that I am interested in the death rate of males and females that enter a hospital.
I could fit survival curves and stratify by group (male or female) and obtain two separate survival curves.
I have performed a similar analysis for death rate of patients in a hospital. The patients all start in the same state, but they may be diagnosed with a disease during their stay. This is an example of a simple multi-state model.
There appears to be a clear distinction between the death rates of patients who have the disease compared to those who do not. However, I think my estimates are wrong.
My data looks as follows:
Patient Time Death Disease 1 12 1 0 2 23 1 1 3 4 0 0 4 9 0 1
Note for this made up example patients do not leave the Disease state (it is an untreatable disease).
I have fitted separate models for each of the states: Disease = 0 and Disease =1. This is what I did for the male/female example above, however, in the male/female example, the groups were fixed. I.e., it was easy to see which female patients died and which were right censored, and the same for male patients.
In the disease model, patients who leave the hospital with no disease could catch the disease later in their lives. I.e., patients with Death, Disease = 0 are considered right censored for the model with Disease = 0, however, these patients are still susceptible to the disease. I think this simplistic approach is underestimating the number of right censored patients in the Disease = 1 group.
Are my estimates biased since the grouping factor that I am using is time dependent?