  Scoring systems are linear classification models that only require users to
add, subtract and multiply a few small numbers in order to make a prediction.
These models are in widespread use by the medical community, but are difficult
to learn from data because they need to be accurate and sparse, have coprime
integer coefficients, and satisfy multiple operational constraints. We present
a new method for creating data-driven scoring systems called a Supersparse
Linear Integer Model (SLIM). SLIM scoring systems are built by solving an
integer program that directly encodes measures of accuracy (the 0-1 loss) and
sparsity (the $\ell_0$-seminorm) while restricting coefficients to coprime
integers. SLIM can seamlessly incorporate a wide range of operational
constraints related to accuracy and sparsity, and can produce highly tailored
models without parameter tuning. We provide bounds on the testing and training
accuracy of SLIM scoring systems, and present a new data reduction technique
that can improve scalability by eliminating a portion of the training data
beforehand. Our paper includes results from a collaboration with the
Massachusetts General Hospital Sleep Laboratory, where SLIM was used to create
a highly tailored scoring system for sleep apnea screening
