  Optimal biomarker combinations for treatment-selection can be derived by
minimizing total burden to the population caused by the targeted disease and
its treatment. However, when multiple biomarkers are present, including all in
the model can be expensive and hurt model performance. To remedy this, we
consider feature selection in optimization by minimizing an extended total
burden that additionally incorporates biomarker measurement costs. Formulating
it as a 0-norm penalized weighted classification, we develop various procedures
for estimating linear and nonlinear combinations. Through simulations and a
real data example, we demonstrate the importance of incorporating
feature-selection and marker cost when deriving treatment-selection rules.
