What would cox regression for continuous covariate looks like? How to interpret it?

Question

[szc002]

Hi, Very new to survival analysis here. I am now trying to correlate the gene expression level with survival and prognosis for patients with lung cancer, and I want to run a cox regression analysis on it. However most of the example I've encountered so far are based on discrete covariate such as sex and I know we can analyze continuous covariate using the coxph function, but I can't see how the actual plot would look like for continuous variable? For instance, for discrete variables you would have the number of regression lines correspond to the number of discrete variables. eg. for gender you'd have two lines on the graph. But what about continuous covariate? Should we first turn the continuous covariate into discrete by assigning quantiles to them? Or else I don't know how to visualize the graph. What are the pros and cons for doing so?

Thanks!

Answer 1

[Kevin Blighe]

I'm not a Professor of Statistics, so, I cannot go into the depths of the equations that are involved. However, one can quite easily produce a Cox model from a single continuous predictor. The hazard ratio (HR) then, via the Beta coefficient, relates to exponential unit change between the y outcome and x predictor.

Many people do di- or tri-chotomise these variables, though, or convert them into quantiles. You can even do what I do here, by first running a 'screen' of the continuous variables via multiple Cox models, and then di-chotomising the statistically significant findings for the purpose of generating a survival curve:

• Survival analysis with gene expression
• https://github.com/kevinblighe/RegParallel#survival-analysis-via-cox-proportional-hazards-regression

Kevin