How to prove predictive use of a biomarker? I have a binary endpoint (cured/not cured) and a continuous biomarker measured on each patient. Every patient recieved one of two treatments. The biomarker predicts the effect of the treatment, if there is an interaction between the biomarker and the treatment effect on the endpoint. One can test for this interaction by logistic regression.
However, the biomarker has to be dichotomized by some cutoff for clinical use. The dichotomized biomarker might perform different.
What is the method of choice to prove that the biomarker predicts the outcome of the treatment after suitable dichotomization? Would one of the approaches below work?

Some approaches I thought of:


*

*Find the cutoff minimizing the $p$-value of the interaction test with the dichotomized biomarker. The biomarker will be validated if this minimal $p$-value is below some threashold reflecting $\alpha$ and the multiplicity involved. (Let's put aside how to adjust; I'll find a way.) What I don't like about this idea is that the distribution of $p$-values favours of course balanced sample sizes (best power for balanced sample sizes), so the cutoff estimation might not be reproducible if the sample distribution of the biomarker is different in another study. 

*Split the dataset in a training and a validation set. Pro: It's easy. Con: In my opinion this wastes sample size. Also, I don't like the result to depend on my arbitrary choice of splitting procedure.

*For regression model validation, Efron suggested a bootstrap method. I would probably prefer this, but I intent cutoff selection and not variable selection, so I'm not sure about the details.

 A: The fact that a decision might have to be go/no go (which is not always the case because timing and dose of treatment can vary by likelihood of disease) has absolutely nothing to do with dichotomizing an input variable.  Does a football coach dichotomize on a fixed cutpoint of running speed when deciding whether to put a player in the football game?  It is easy to show algebraically that if you were to use a cutpoint on a continuous predictor, that cutpoint must necessarily be a function of the continuous values of all the other predictors.  For example, how much to worry about cholesterol depends on age and smoking.  Since you would need to compute a cutpoint for the biomarker based on all the other patient variables in order to cohesively use risk to make optimal decisions, what is the point of dichotomizing in the first place, since it's actually very complex?
The only possible cohesive use of cutpoints comes when in application to the overall predicted risk - a prediction that keeps continuous predictors continuous.  Once you know the utility/loss/cost function you can solve for the risk cutoff that leads to various actions.  Even then, as hinted in my first sentence, the decision does not have to be binary.  One viable decision is to make no decision and acquire more data.
