[Feature] Provide CI and parameter tests on GHM ?

[lrnv]

CC @FJRubio67, Not sure if it is possible ? Do you have the theory for confidence intervals, parameter tests and p-values on both predictors ?

[FJRubio67]

CC @FJRubio67, Not sure if it is possible ? Do you have the theory for confidence intervals, parameter tests and p-values on both predictors ?

@lrnv Since these are regular models, one can use an asymptotic normal approximation for the confidence intervals. These can be calculated using the function ConfInt. Here is an illustration on how to use that function (using my rudimentary style). A more accurate way would be using the profile likelihood, but that is computationally expensive.

P-values can be approximated also using the Wald test $\frac{\hat{\beta}}{\sqrt{I^{-1}(\hat{\beta})}} \sim N(0,1)$, with the Fisher information matrix approximated using numerical differentiation, but I have not implemented it.

Alternatively, one could think of using the likelihood ratio test.

Since the package has not been widely (or at all :) ) used, I have not thought of adding these features, but they would certainly be useful.

Incidentally, one of my PhD students is working on Bayesian variable selection in these models. We will hopefully have a preprint by the end of the year.

Were you thinking of something else?

[lrnv]

@FJRubio67 Thanks for the pointers, this is what we needed. For consistency with other models, we would like to provide such "user-oriented" outputs.

If your student wants, this version of the code is now public and available, and discussions are welcome. As discussed last year, it is much more compact than your first draft and a bit more Julian in the coding style. Also, the Cox code is now optimized for performance, our benchmarks show that it beats R::survival::coxph by a factor 10.

We are also available to add other models to this package, if some usefull ones comes to your mind do not hesitate.

[FJRubio67]

@lrnv Oh wow, that is amazing. Is it only for overall survival, or for relative survival too?

I am also glad to hear that you managed to implement the Cox model in an efficient way, that is a big fundamental step.

Let me know when you release it, and if you post it on social media, I will reshare it. I will also think about potential extensions.

[lrnv]

Is it only for overall survival, or for relative survival too?

Only overall. You caught me there, the junction between NetSurvival.jl and SurvivalModels.jl is still to be done... but hopefully soon enough.