Transform Survival function of Cox Proportional Hazards Model to single risk score

Question

I am working on a churn prediction in Python using lifelines based on the Telco Dataset. I managed to create survival functions of the subject within the dataset (see screenshot). However, I want to compare my subjects to each other based on a single risk metric, e.g. subject 1 scores 0.8 and subject 2 scores 0.6. This should imply that subject 1 is overall more risky than subject 2. What I can do is use the partial hazards and normalise them for example. However, is this correct or should I consider other options where the baseline is also included?

Answer 1

The Cox regression by itself only gives regression coefficients from which hazard ratios between sets of covariate values can be calculated. That doesn't directly involve estimating a baseline survival.

Survival curves like you show for a Cox regression are themselves based on hazards estimated from the model. You have to go an extra step to extract the baseline survival curve, based for example on the number of events at event times and the model-estimated hazards for individuals still at risk at those times. See this page.

Including the baseline survival curve thus doesn't add anything about differences among individuals based on their covariate values. So hazard ratios are a reasonable way to summarize differences among subjects.