Bayesian networks have become an alternative approach to sur

Bayesian networks have become an alternative approach to survival analysis. They are well-structured, intuitive, while also being theoretically sound [7]. They have the ability to capture expert knowledge, handle model complexity, and offer more flexibility in model interpretation [6]. Researchers can explicitly model dependencies among risk factors. Bayesian networks naturally allow for estimating the survival probability based on partial observations, while the CPH model is not designed for that, even though one could extend it along the lines of BN inference. If we know the Age and SBP of a patient (Fig. 1), we can make a prediction of survival without observing the remaining risk factors. Researchers can also combine an equivalent of multiple CPH models into the same network. For example, Fig. 1 shows an example of a Bayesian network that combines two risk models (Heart-Related Deaths, with risk factors 6 Minute Walking Distance, Age and SBP > 110 mmHg and PAH-Related Deaths with the above risk factors and PVR > 32 WoodUnit) to determine the risk of dying of patients suffering from 3-Deazaadenosine disease and pulmonary arterial hypertension (PAH). Not only we have an equivalent of two CPH models but the BN relaxes the assumption of mutual independence of risk factors (e.g., Age influences both 6 Minute Walking Distance and SBP > 110 mmHg; SBP > 110 mmHg influences PVR > 32 WoodUnit). Moreover, we can use Bayesian network for reasoning from survival nodes to their causes, e.g., when testing a model or predicting values of the risk factors given survival and possibly other risk factors. There are two general approaches to building Bayesian networks for the purpose of risk assessment. Researchers can implement static models that predict risk or survival at a snap-shot of time. For example, Loghmanpour et al. [10] created Bayesian network-based risk assessment models for patient data with the left ventricular assist devices (LVADs). Bayesian networks may estimate the risk at specific points in time, e.g., 30 days, 90 days, 6 months, 1 year, or 2 years, with high accuracy, outperforming traditional risk scores methods. A more complex approach uses dynamic Bayesian networks (DBNs) [11]. Van Gerven et al. [12] implemented a DBN for prognosis of patients who suffer from low-grade midgut carcinoid tumor. Instead of analyzing each time point separately, the DBN model calculates how the state of a patient changes over time under the influence of various therapy choices. This allows for modeling temporal nature of medical problems throughout the course of care and provides detailed prognostic predictions. However, intracellular route requires significantly more effort during model construction, i.e., require expertise to define the causal structure and temporal interactions, large amount of data, and is generally time-consuming [12].
Bayesian network interpretation of the CPH model As we mentioned earlier, the process of building Bayesian networks can take a significant effort, especially when little or no data are available. In this section, we discuss how to use parameters from existing CPH models to create Bayesian networks. This approach is especially useful when very little or no data are available. We assume that the CPH model\'s assumptions are not violated and the risk factors or random variables X are time-independent discrete/binary variables [13].