Bayesian networks are powerful statistical models to study the probabilistic relationships among sets of random variables with significant applications in disease modeling and prediction. Here, we propose a continuous time Bayesian network with conditional dependencies represented as regularized Poisson regressions to model the impact of exogenous variables on the conditional intensities of the network. We also propose an adaptive group regularization method with an intuitive early stopping feature based on Gaussian mixture model clustering for efficient learning of the structure and parameters of the proposed network. Using a dataset of patients with multiple chronic conditions extracted from electronic health records of the Department of Veterans Affairs, we compare the performance of the proposed network with some of the existing methods in the literature for both short-term (one-year ahead) and long-term (multi-year ahead) predictions. The proposed model provides a sparse intuitive representation of the complex functional relationships between multiple chronic conditions. It also provides the capability of analyzing multiple disease trajectories over time, given any combination of preexisting conditions.
Keywords: Continuous time Bayesian network; Gaussian mixture model; Poisson regression; adaptive group lasso; multiple chronic conditions.