br Application of the BN Cox

Application of the BN-Cox model to risk calculation As we mentioned earlier, CPH models are widely used in medical risk assessment and are often reported in the literature. Recently, we proposed a BN-Cox-based risk score calculator to the existing Pulmonary Arterial Hypertension (PAH) risk calculator [20]. The core of the original PAH risk score calculator by Benza et al. [21], the electronic mobile calculator app developed by the United Therapeutics Europe Limited and available at http://www.pah-app.com/, was based on the CPH model. Hence, we replaced the CPH model by a BN-Cox model constructed from the CPH parameters reported in Benza et al. [21] (Table 1). Fig. 3 shows the structure of the BN-Cox model for the BN-Cox-based calculator. In this case, we omitted the time variable, as the purpose of the PAH Risk Calculator is to capture the risk at one point in time (one year). We created the conditional probability table of the survival 3-Deazaadenosine synthesis from Equation (11). We configured all risk factors cases (all binary risk factors generated 219 cases) and created the CPT of the survival node from the 219 cases. This allowed us to reproduce fully the PAH CPH model by means of a Bayesian network (see more details in [20]). This by itself offers no advantages over a CPH model-based calculator but we view it as the first step toward a better calculator that relaxes some of the CPH assumptions and is capable of representing a generalized structure of interactions between risk factors and the survival variables. With the PAH BN-Cox model, we created a risk score calculator using an approach similar to [21]. Equation (11) captures the survival probabilities s given the states of risk factors. We can extract a hidden hazard ratio of each variable by configuring states of other risk factors to be absent. For example, the hazard ratio of a risk factor can be estimated from The term is similar to the baseline survival probability in the CPH model (). Hence, with this equation, we can track back all hazard ratios. Then, we use the same criteria as the original PAH Risk Calculator to convert the hazard rate to a score. Score of 2, for example, indicates at least two-fold increase in risk of mortality compared to the baseline risk. Fig. 8 shows a screen shot of the graphical user interface (GUI) of our prototype of the Bayesian network risk calculator. The left-hand side pane allows for entering risk factors for a given patient. The right-hand side pane shows the calculated score and survival probabilities. Currently, the numerical risks produced by the BN-Cox calculator are identical to those of the original CPH-based PAH Risk Calculator [21]. However, the BN-Cox model makes CPH\'s assumptions explicit and will allow to relax them in the future. One immediate advantage of the BN-Cox representation is that BNs make spores possible to refine the parameters with additional data records.
Making the BN-Cox model computationally efficient One of the challenges to applying the BN-Cox model is an exponential growth of the conditional probability tables (CPT) corresponding to the survival variables, as the number of risk factors increases [22]. When the number of risk factors is high, this table becomes intractable. We evaluated two approaches to mitigate this problem: (1) decomposition of the underlying Bayesian network known as parent divorcing, and (2) simplifying the network structure by removing least influential risk factors.