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I am studying Cox proportional hazard models, and in particular Regularization Paths for Cox's Proportional Hazards Model via Coordinate Descent, by Tibshirani, Hastie and Friedman.

I would like to understand if in this setting we still have to require uninformative censoring or if it is possible to relax such hypothesis.

In other words, in the presence of informative censoring, are we still able to maximize the partial likelihood with the elastic net penalty using coordinate descent?

Thank you in advance!

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The problem with informative censoring in survival analysis is that the assumptions underlying the usual (partial) likelihood formula don't hold. This answer notes that you need non-informative censoring to factor out contributions from the distribution of censoring times to the likelihood. As Klein and Moeschberger say in the context of Nelson-Aalen and Product-Limit nonparametric estimators (page 99):

When this assumption is violated, both estimators are estimating the wrong function and the investigator can be appreciably misled.

So you will be able to optimize something with informative censoring, but it won't necessarily be the right thing.

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