[Feature] Cox baseline and predicitions

[lrnv]

@sofia-maitri Now that we have cox models, it would be interesting to extract prediction from them.

This article here : https://missingdatasolutions.rbind.io/2022/12/cox-baseline-hazard/ discusses the matter, first talking about the baseline hazard function (also see previous discussion in #10 ) that you will need for prediction, and then discusses the different types of predictions that exists.

Your goal is to implement functions that do does predictions for each of the prediciton type that exists:

predict(C::Cox, type = :lp)
predict(C::Cox, type = :risk)
predict(C::Cox, type = :expected)
predict(C::Cox, type = :terms)
predict(C::Cox, type = :survival)

The first step is probably to implement the baseline hazard that you will need for these prediciton, and use the article to contruct test cases (to ensure that we have the same values outputed).

Tell me if something is not clear enough :)

[sofia-maitri]

did a new branch and i put my first try for the baseline function. it works for centered = false, but it doesn't give the good results for centered = true and i can't find why. all the test are in the cox.md file because i also wrote the formula in the documentation

[lrnv]

Well done !

Maybe you could:

1. Move your tests to the test folder
2. Push your branch online as a pull-request

so that i can take a look at eh centered case ?

[sofia-maitri]

done!

[lrnv]

So what is the problem ? Your test does not compre the obtained values to anything, are you expected a certian result that you do nt obtained ?

[sofia-maitri]

i used the same example from the article that you sent, so i compared my results to that. for centered = true they obtain 2.780815e-02, 4.800566e-01, 4.800566e-01, 8.858118e+00, 1.532636e+02, 1.532636e+02, 5.369326e+03, 7.641106e+04, like the R function on the same dataframe