CTBN-PH: A continuous-time Bayesian network for individualised diagnostic risk prediction

Continuous-time Bayesian networks (CTBNs) are powerful tools for modelling and predicting complex disease trajectories in continuous-time scenarios. However, their application is often limited by a lack of individualisation in the results, if the covariates significantly influence a patient's diagnostic transitions. To address these challenges, we introduce the CTBN-PH model, which integrates CTBN models with Cox proportional hazards (Cox-PH) models. The proposed model combines the dynamic and probabilistic capabilities of CTBNs with the robust, covariate-driven risk estimation of Cox-PH models. By leveraging causal topologies learned from healthcare trajectories, the method dynamically adjusts transition intensities based on covariate effects, enabling efficient parameter learning in extensive databases. We validated the model using a dataset of over 2.1 million patients and found that it learned complex causal structures associated with multi-morbid conditions such as diabetes and hypertension. Performance comparisons with non-individualised and non-causally inferred networks highlight the model's effectiveness. Our model achieved an integrated Brier score (IBS) of 0.153 for predicting the onset of a single diagnosis over 25 years and an IBS of 0.04 for forecasting the inertia of the entire system over four years. Additionally, we explore the model's utility in simulating patient trajectories that are tailored to specific covariate-defined populations.