On the Detection of Population Heterogeneity in Causation Between Two Variables: Finite Mixture Modeling of Data Collected from Twin Pairs

Causal inference is inherently complex and relies on key assumptions that can be difficult to validate. One strong assumption is population homogeneity, which assumes that the causal direction remains consistent across individuals. However, there may be variation in causal directions across subpopulations, leading to potential heterogeneity. In psychiatry, for example, the co-occurrence of disorders such as depression and substance use disorder can arise from multiple sources, including shared genetic or environmental factors (common causes) or direct causal pathways between the disorders. A patient diagnosed with two disorders might have one recognized as primary and the other as secondary, suggesting the existence of different types of comorbidity. For example, in some individuals, depression might lead to substance use, while in others, substance use could lead to depression. We account for potential heterogeneity in causal direction by integrating the Direction of Causation (DoC) model for twin data with finite mixture modeling, which allows for the calculation of individual-level likelihoods for alternate causal directions. Through simulations, we demonstrate the effectiveness of using the Direction of Causation Twin Mixture (mixDoC) model to detect and model heterogeneity due to varying causal directions.