  Many in-hospital mortality risk prediction scores dichotomize predictive
variables to simplify the score calculation. However, hard thresholding in
these additive stepwise scores of the form "add x points if variable v is
above/below threshold t" may lead to critical failures. In this paper, we seek
to develop risk prediction scores that preserve clinical knowledge embedded in
features and structure of the existing additive stepwise scores while
addressing limitations caused by variable dichotomization. To this end, we
propose a novel score structure that relies on a transformation of predictive
variables by means of nonlinear logistic functions facilitating smooth
differentiation between critical and normal values of the variables. We develop
an optimization framework for inferring parameters of the logistic functions
for a given patient population via cyclic block coordinate descent. The
parameters may readily be updated as the patient population and standards of
care evolve. We tested the proposed methodology on two populations: (1) brain
trauma patients admitted to the intensive care unit of the Dell Children's
Medical Center of Central Texas between 2007 and 2012, and (2) adult ICU
patient data from the MIMIC II database. The results are compared with those
obtained by the widely used PRISM III and SOFA scores. The prediction power of
a score is evaluated using area under ROC curve, Youden's index, and
precision-recall balance in a cross-validation study. The results demonstrate
that the new framework enables significant performance improvements over PRISM
III and SOFA in terms of all three criteria.
