You mentioned the typical models for survival analysis and if they are not satisfactory, then their theoretical assumptions are probably not correct in your particular case (or at least in your obtained data). Then I would suggest a non-parametric method. One example which is available in R would be regression trees: library(rpart).

The open-source R-package ePCR and its reference documentation are available at the Central R Archive Network (CRAN): https://CRAN.R-project.org/package=ePCR. R-vignette provides step-by-step examples for the ePCR usage.

ePCR: an R-package for survival and time

The open-source R-package ePCR and its reference documentation are available at the Central R Archive Network (CRAN): https://CRAN.R-project.org/package=ePCR. R-vignette provides step-by-step examples for the ePCR usage

Epilogue.

Thanks for your answers.

I have finally decided to select a survival regression model relying on an assumed exponential distribution. I applied a forward stepwise variable selection and kept only a low number of variables. The selected variables seem relevant regarding the literature on my subject.

Still, I have many variables (>500) which variation is significantly associated with survival variations (univariate Cox Proportional Hazard model, log-rank test). I will pursue with these >500 variable feeding them into weight correlation network analysis as a rank-reduction method to see if I haven't missed essential information that the CoxPH suggests.

Cheers.