# Responding to a reviewer: How to apply frailty to a Cox regression analysis in this situation

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 would die or not based upon clinical information provided. I have the survival time and vital status (dead or alive) on each patient.

I am evaluating the prognostic significance of each doctor's prognosis prediction, using Cox regression

(a total of 400 such models)

Some of these docs are university based (about 100), some are community-based (about 300). In a review of a paper I have submitted the reviewer asked the following question:

"Why was the Cox regression for each physician separately rather than using all the data in a frailty model (Cox regression with a physician-specific random intercept?)."

I understand this, taken from the Stata documentation:

"Consider the data from a study of 38 kidney dialysis patients, as described in McGilchrist and Aisbett (1991). The study is concerned with the prevalence of infection at the catheter insertion point. Two recurrence times (in days) are measured for each patient, and each recorded time is the time from initial insertion (onset of risk) to infection or censoring:

Then they say:

"It is reasonable to assume independence of patients but unreasonable to assume that recurrence times within each patient are independent. We could model the correlation by assuming that the correlation is the result of a latent patient-level effect, or frailty. That is, we could fit a frailty model by specifying shared(patient)"

I get all of this. But I cannot see how this could be applied to my situation of doctors predicting death in 60 patients. The example above is a grouping of the patients. How does it make sense to group the doctors based on the logic given above.

Forgive my question if its simple. I cut and pasted Stata documentation because they explain it more clearly than I could.

• Are they the same 60 patients or a different set of 60 patients for each doctor (e.g. their own)? The comment mostly makes sense to me in the latter case. I assume where the reviewer may be going is that predictions from doctors (at least within groups like university based) might vary in a way that could be described according to some distribution (e.g. normal) on the log-hazard for death. One could attempt estimate and describe this distribution, but in the former case the proposed model would seem not quite right for answering that question (and I am not sure it is in the latter case). – Björn May 2 '17 at 19:29
• Same 60 for all doctors. That way we could compare their "performance" – GhostRider May 2 '17 at 19:56
• I think it's an interesting question. I think it depends on how you evaluate the prognostic significance of each doctor's prognosis prediction. Could you detail on that a bit? – Theodor May 9 '17 at 10:12