https://arxiv.org/pdf/0811.1645.pdf

My recollection (feel free to correct me) is that statistical survival models are (can be?) created as a series of logistic regressions, one for each of several forecast horizons. One could keep that same structure, substituting any classifier (induced decision tree; neural network, ...) which produces an estimated probability for those logistic regressions.

Bayesian networks spring to mind, with wanting to identify what contributes to the death event and whatnot.

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Random survival forests is exactly what I clicked on this thread to suggest, yep.

If I understood correctly, rather than actually predicting survival time your goal is to see whether certain parameters have influence on the survival time. Besides the other things already mentioned, one approach might be trying to predict survival time via a black box algorithm and trying to explain the decision of the algorithm. One paper that covers this topic would be this one.

Seconded.

There are a lot of ways to tackle this problem. But it will really help if you could share a data sample. How many samples do you have? How many attributes are you studying? So on and so forth. The rang is from a simple decision tree to a new experimental algorithm.

you are right, I want to know, wether our „new“ parameter is a good predictor or not

I can try to extract a small data sample. I have around 3000 patients, and their „time till death“ or „time till end of study“, and around 10 predictors

Whatever you do to make a model, I would created benchmarks datasets where you random shuffle the survival info between patients. Then, any model fitting and testing you do, also do it on these randomised datasets. This will give you good insights about the statistical significance of anything you’ll find in your data.

This is what I wanted to say too. Bayesian nets are good for identifying how strongly a parameter affects the outcome

I recently finished Pearl's "Book of Why" and iirc BNNs do not capture causal relationships between variables. So finding a strong association between a lab value and years of survival does not necessarily indicate that one led to the other.

In other words, a strongly associated lab or clinical value might actually be the result of a longer survival (or other compounding factors) and not the other way around.

Entirely not an expert, but this question sounds exactly like a problem for causal inference as described in the book. Of course, there is also the issue that only observational data seems to be available, so CI may not actually be possible. Maybe it's worth it to check out this entry point to the subject.

When you say "has any influence", I'm assuming you mean causal influence, rather than just being correlated with a particular outcome. This puts us in the domain of causal inference. I suggest you go through a causal inference tutorial or two to get some domain knowledge. See https://causalinference.gitlab.io/kdd-tutorial/ and https://economics.mit.edu/sites/default/files/inline-files/causal_tutorial_1.pdf. Econometric modeling revolves heavily around this, so you're probably going to find more sources that are econometric rather than medical.

My personal approach: Train an xgboost model (or really any ML model) using the appropriate hazard function and bayesian optimization for hyperparameter tuning, then compare the log likelihood function of the parameter at its actual values vs counterfactual values. If the counterfactual values provide a similar fit, you're looking at something that is not likely causal.

ML methods people are talking about are mostly focused on prediction. Collinearity and confounding problems you describe will mess with those methods too, though it’ll be harder to recognize and diagnose. “feature importance” measures are generally as vague as the name implies. You’re doing it the right way, just keep working within that feedback loop of analyzing your data and improving your model.

The sample would help a lot. You have a good number of entries. So there could be quite a few ways to go.

Edit: Give "weka" a try it's free to use and has a lot of options. It's great for getting a good overall view of the direction the project should take.

On that note there is a library that extends xgboost's parameters with survival analysis capabilities specifically. Here is a tutorial: https://loft-br.github.io/xgboost-survival-embeddings/how_xgbse_works.html

Good call, didn't know about that