Designing optimal mortality risk prediction scores that preserve clinical knowledge.

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.