Add Cox Objective

[jordan-melendez]

Would there be any interest in the addition of the Cox Proportional Hazards loss for modeling survival data?

[MarcAntoineSchmidtQC]

Absolutely. This is not on the radar in the short term, but a PR is very welcome if you want to take a shot at it.

[jordan-melendez]

Great -- I just might!

[MatthiasSchmidtblaicherQC]

I thought of giving this a shot, but first we need to clarify something: the Cox partial likelihood is not an EDM. The solvers in glum are built around the EDM assumption, so I don't see how we can easily incorporate this objective.

A Cox Proportional Hazard can be estimated with a Poisson GLM via a data transformation. The Cox objective is equivalent to the Poisson likelihood with a fixed effect for each event time and this fixed effect profiled out, see an explanation here). The transformation is to cut the observation into small subperiods, corresponding to event occurrences (in R, this is survSplit). Is such a data transformation a useful addition to glum or is this too far removed from the core functionality? @MarcAntoineSchmidtQC @tbenthompson