Derivation of a Bayesian Network Model from an Existing Risk Score Calculator for Pulmonary Arterial Hypertension

Abstract

Purpose We propose an alternative approach to the extensively validated REVEAL risk score calculator using Bayesian network (BN) modeling. We derived a BN model with the same variables and discretization cut points as the REVEAL risk score calculator and data from the REVEAL registry. This study compared the performance and relative impact of the variables in the two PAH risk assessment tools. Methods 2,456 adult patients from the REVEAL registry were used to develop a Bayesian network model to predict 1-year survival using the Tree Augmented Naive Bayes (TAN) algorithm. We used 10-fold cross validation to measure the BN performance, reported as the area under the Receiver Operating Characteristic curve (AUC). We compared hazard ratios of the variables in the REVEAL calculator to cross entropy between risk factors and the outcome variable in the BN model. Cross-entropy measures the expected change in entropy of the probability distribution of the outcome variable as the risk becomes known and is generally a measure of expected information gain from knowing a risk. Cross-entropy is a dynamic measure and changes as other variables are observed. Results The BN model demonstrated an AUC of 0.77 for predicting one-year survival. This was an improvement to the existing AUC of 0.71 for the original REVEAL calculator. There is a high correlation (r = 0.786) for the hazard ratio and the cross entropy, when all risk factors are absent (Figure 1a). In the same context of variables, the cross-entropy and the hazard ratio capture the similar influences to the outcome. However, when the risk factors are partially known for a given patient (Figure 1b), the cross-entropy changes based on the context of which risk factor are observed. Conclusion BN demonstrated a modest improvement in performance over the REVEAL 1.0 model. Moreover, it improved the understandability of the relationship between risk factors, the dynamic influences of each risk factor, and relaxes the assumption of independence between risk factors.