Bayesian Network vs. Cox’s Proportional Hazard Model of PAH Risk: A Comparison
Pulmonary arterial hypertension (PAH) is a severe and often deadly disease, originating from an increase in pulmonary vascular resistance. The REVEAL risk score calculator  has been widely used and extensively validated by health-care professionals to predict PAH risks. The calculator is based on the Cox’s Proportional Hazard (CPH) model, a popular statistical technique used in risk estimation and survival analysis. In this study, we explore an alternative approach to the PAH patient risk assessment based on a Bayesian network (BN) model using the same variables and discretization cut points as the REVEAL risk score calculator. We applied a Tree Augmented Naïve Bayes algorithm for structure and parameter learning from a data set of 2,456 adult patients from the REVEAL registry. We compared our BN model against the original CPH-based calculator quantitatively and qualitatively. Our BN model relaxes some of the CPH model assumptions, which seems to lead to a higher accuracy (AUC = 0.77) than that of the original calculator (AUC = 0.71). We show that hazard ratios, expressing strength of influence in the CPH model, are static and insensitive to changes in context, which limits applicability of the CPH model to personalized medical care.
KeywordsBayesian networks Risk assessment Cox’s proportional hazard model Hazard ratios Pulmonary arterial hypertension
We acknowledge the support of the National Institute of Health (1R01HL134673-01), Department of Defence (W81XWH-17-1-0556), and the Faculty of Information and Communication Technology, Mahidol University, Thailand. Implementation of this work is based on GeNIe and SMILE, a Bayesian inference engine developed at the Decision Systems Laboratory, University of Pittsburgh. It is currently a commercial product but is still available free of charge for academic research and teaching at https://www.bayesfusion.com/. While we are taking full responsibility for any remaining errors and shortcomings of the paper, we would like to thank Dr. Carol Zhao of Actelion Pharmaceuticals US, Inc., for her assistance in learning the TAN model from the REVEAL data set. We also thank the anonymous reviewers for their valuable input that has greatly improved the quality of this paper.
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