  We propose a Bayesian model selection approach that allows medical
practitioners to select among predictor variables while taking their respective
costs into account. Medical procedures almost always incur costs in time and/or
money. These costs might exceed their usefulness for modeling the outcome of
interest. We develop Bayesian model selection that uses flexible model priors
to penalize costly predictors a priori and select a subset of predictors useful
relative to their costs. Our approach (i) gives the practitioner control over
the magnitude of cost penalization, (ii) enables the prior to scale well with
sample size, and (iii) enables the creation of our proposed inclusion path
visualization, which can be used to make decisions about individual candidate
predictors using both probabilistic and visual tools. We demonstrate the
effectiveness of our inclusion path approach and the importance of being able
to adjust the magnitude of the prior's cost penalization through a dataset
pertaining to heart disease diagnosis in patients at the Cleveland Clinic
Foundation, where several candidate predictors with various costs were recorded
for patients, and through simulated data.
