I am a medical doctor not a statistician. I have 60 patients who were assessed by 400 doctors (each doctor individually evaluated the clinical data on each patient). The doctor was then asked to say whether the patient had disease A or not. I have the survival time and vital status (dead or alive) on each patient.
There is no diagnostic reference standard for this disease, but some have hypothesised that outcome (or mortality) may be a reasonable way of validating diagnostic accuracy (this is not in question - it has precedence in the literature). Therefore we are using prognostic accuracy as an indication of a doctor's ability to accurately diagnose the disease.
I am evaluating the prognostic significance of each doctor's diagnosis using Cox regression, and I also calculated the c-index for each doctor. For each doctor, I, therefore, have a survival model e.g.
c index = .72748 Hazards ratio = 3.0436 p =.0117 95% CI = 1.2815-7.2288
(a total of 400 such models)
I want to compare them, to see whose categorization of "have disease A or not" is the most prognostic significant. I first thought that this could be simply done by comparing the c-index for each doctor but having looked at previous posts, I suspect this is flawed. See for example
So, the question is, what is the best way to compare the prognostic significance of two survival models?