  A common goal in modern biostatistics is to form a biomarker signature from
high dimensional gene expression data that is predictive of some outcome of
interest. After learning this biomarker signature, an important question to
answer is how well it predicts the response compared to classical predictors.
This is challenging, because the biomarker signature is an internal predictor
-- one that has been learned using the same dataset on which we want to
evaluate it's significance. We propose a new method for approaching this
problem based on the technique of selective inference. Simulations show that
our method is able to properly control the level of the test, and that in
certain settings we have more power than sample splitting.
