I have a following statistical setup I don't know how to attack:
I have two therapies: say A and B. For some patients A works better, for other B works better. I want to direct patients to their optimal therapy based on some diagnostic test. I have two candidates, say test 1 and test 2 (both continuous scores) and a dataset from an observational study where I have values of both tests, the therapy which was applied to each patient, their survival times after the therapy and a bunch of standard covariates. I want to verify if test 2 is significantly better than test 1. How can I do this?
The assignement of patients to therapies was independent of the results of diagnostic tests, but all three variables (therapy assignment and the results of both diagnostic tests will have substantial correlation) which causes that comparing survival times only for discordant cases (i.e. patients where the two diagnostic tests recommend different therapies) is unsatisfactory due to drastic decrease in sample size (<1% of original sample).