Cox PH semi-parametric

[Edward Smith]

What is it exactly that makes the Cox PH semi-parametric? Does the parametric come from the fact that the baseline hazard has an exponential shape?

 

[Dave Johnson]

Hi

The Cox model is sometimes referred to as semi-parametric because it doesn't require knowledge of the baseline hazard function to fit the vector Beta. A fully parametric model would fit the baseline hazard too, and hence give a full formula of mortality for all classes of lives. The strength of the Cox model is that, as printed in the Core Reading, we may care more about the proportionality of mortality across lives than the underlying hazard function, for example if we are testing the efficacy of a medical treatment.

Hope that helps

Dave

 

[Dave Johnson]

Just putting this in simpler terms, I could use a Cox model to show that men have higher mortality than women (say) without determining the underlying pattern of mortality for men or women. All I need to assume is that mortality is proportional.