Bayesian averaging over decision tree models: An application for estimating uncertainty in trauma severity scoring

For making reliable decisions, practitioners need to estimate uncertainties that exist in data and decision models. In this paper we analyse uncertainties of predicting survival probability for patients in trauma care. The existing prediction methodology employs logistic regression modelling of Trauma and Injury Severity Score (TRISS), which is based on theoretical assumptions. These assumptions limit the capability of TRISS methodology to provide accurate and reliable predictions.

We adopt the methodology of Bayesian model averaging and show how this methodology can be applied to decision trees in order to provide practitioners with new insights into the uncertainty. The proposed method has been validated on a large set of 447,176 cases registered in the US National Trauma Data Bank in terms of discrimination ability evaluated with receiver operating characteristic (ROC) and precision-recall (PRC) curves.

Areas under curves were improved for ROC from 0.951 to 0.956 (p = 3.89 × 10^-18) and for PRC from 0.564 to 0.605 (p = 3.89 × 10^-18). The new model has significantly better calibration in terms of the Hosmer-Lemeshow Hˆ statistic, showing an improvement from 223.14 (the standard method) to 11.59 (p = 2.31 × 10^-18).

The proposed Bayesian method is capable of improving the accuracy and reliability of survival prediction. The new method has been made available for evaluation purposes as a web application.