Modeling length of stay as an optimized two-class prediction problem

To develop a predictive model for the outcome length of stay at the Intensive Care Unit (ICU LOS), including the choice of an optimal dichotomization threshold for this outcome. Reduction of prediction problems of this type of outcome to a two-class problem is a common strategy to identify high-risk patients.

Threshold selection and model development are performed simultaneously. From the range of possible threshold values, the value is chosen for which the corresponding predictive model has maximal precision based on the data. To compare the precision of models for different dichotomizations of the outcome, the MALOR performance statistic is introduced. This statistic is insensitive to the prevalence of positive cases in a two-class prediction problem.

The procedure is applied to data from cardiac surgery patients to dichotomize the outcome ICU LOS. The class probability tree method is used to develop predictive models. Within our data, the best model precision is found at the threshold of seven days.

The presented method extends existing procedures for predictive modeling with optimization of the outcome definition for predictive purposes. The method can be applied to all prediction problems where the outcome variable needs to be dichotomized, and is insensitive to changes in the prevalence of positive cases with different dichotomization thresholds.