Cox regression: how to get an "average" from multiple cox regression analyses?

Question

I am a medical researcher who has a moderate knowledge of statistics only - mainly because much of the analysis I do is focused on one thing - survival.

let me outline the study I am running so I can explain my question.

Disease A is similar to many other diseases in all but one thing, disease A kills you very quickly. Making a diagnosis of disease A is challenging because it has many mimics at presentation. This has led to many experts believing the best marker of accuracy of diagnosis in a study is mortality.

I have 60 patients of which about 22 have disease A and the others have mimics. I have survival data on them and sure enough, when they first came to the hospital back in 2010 our diagnosis of disease A was pretty accurate because on a survival analysis, our diagnosis of disease A was significantly predictive of mortality (high HR with p<0.0001).

I have taken these 60 cases and got 170 physicians of varying experience and from many countries to evaluate them and make diagnoses. One thing we will measure is diagnostic agreement using the Kappa (and weighted Kappa). Agreement is a surrogate marker of accuracy but only to a point. What we will do is perform survival analysis on each physician's diagnoses (calling disease A "1" and anything thats not disease A "0") and see how prognostic significant it is.

The problem is that I will stratify the physicians based on experience (say,....1-10 years, > 10 but < 20 and >20 years experience. I want to show that OVERALL the prognostic significance of a diagnosis made by an experienced physician is higher than for an inexperienced physician.

My question: is there a way of showing statistically and graphically 50 KM curves (melded together as a sort of "average") for each physician group?

Many thanks

Answer 1

If your data are amenable to Cox proportional hazards analysis, there might be an even more compelling way to document the relation of correct diagnosis to experience.

For each of the 170 physicians, determine the Cox regression coefficient (probably better the coefficient than the associated hazard ratio) for the attempted A classification. Then plot the Cox regression coefficients against actual experience (maybe a log scale of experience). That will avoid the loss of information from binning based on experience, and may indicate the best way to proceed with further analysis to establish the magnitude and significance of experience-related differences. This might also allow evaluation of differences related to the country of the physician.

For display, once significance is evaluated based on analysis of the Cox coefficients, you can simply choose representative examples from each of your binned groups, rather than trying to form melded KM curves.

As you are aware, this isn't strictly a test of ability to diagnose the A disease, but rather the ability to determine which patients will die sooner. So there will be problems if treatment based on diagnosis A is inappropriate for those without A who are nevertheless identified at risk of early death.