NOTEARS-M: Causal Bayesian Network Structure Learning of Mixed Type Data and Its Application in Identifying Disease Risk Factors

Abstract

Background Identifying and understanding disease risk factors is crucial in epidemiology, particularly for chronic and noncommunicable diseases that often have complex interrelationships. Traditional statistical methods struggle to capture these complexities, necessitating more sophisticated analytical frameworks. Bayesian networks and directed acyclic graphs (DAGs) provide powerful tools for exploring the complex relationships between variables. However, existing DAG structure learning algorithms still have limitations in handling mixed-type data (including continuous and discrete variables), which restricts their practical utility. Therefore, developing DAG structure learning methods that can effectively handle mixed data is highly important for obtaining an in-depth understanding of disease risk factors and pathogenic mechanisms. Methods This study proposes an extension of the NOTEARS algorithm, termed NOTEARS-M, which is designed for Bayesian network structure learning with mixed-type data. The algorithm integrates continuous and categorical variables through a tailored loss function, enhancing its applicability to real-world epidemiological datasets. Results Extensive simulations were conducted across eight distinct scenarios, specifically, variations in the number of nodes, changes in the proportion of categorical nodes, different sample sizes, levels of categorical nodes, variations in edge sparsity, adjustments to the weight scale, different graph types, and diverse noise distributions. These scenarios demonstrate that NOTEARS-M consistently outperforms existing methods such as MMHC, mDAG, and DAGBagM across key metrics, including precision, recall, F1 score, and structural Hamming distance (SHD). Furthermore, the robustness of NOTEARS-M is validated through its application to the National Health and Nutrition Examination Survey (NHANES) dataset, revealing critical causal relationships among risk factors for CHD and diabetes. Conclusions NOTEARS-M provides a powerful and scalable tool for uncovering causal relationships in complex disease networks, with significant implications for risk factor identification and public health research.