Scalar-Function Causal Discovery for Generating Causal Hypotheses with Observational Wearable Device Data

Digital health technologies such as wearable devices have transformed health data analytics, providing continuous, high-resolution functional data on various health metrics, thereby opening new avenues for innovative research. In this work, we introduce a new approach for generating causal hypotheses for a pair of a continuous functional variable (e.g., physical activities recorded over time) and a binary scalar variable (e.g., mobility condition indicator). Our method goes beyond traditional association-focused approaches and has the potential to reveal the underlying causal mechanism. We theoretically show that the proposed scalar-function causal model is identifiable with observational data alone. Our identifiability theory justifies the use of a simple yet principled algorithm to discern the causal relationship by comparing the likelihood functions of competing causal hypotheses. The robustness and applicability of our method are demonstrated through simulation studies and a real-world application using wearable device data from the National Health and Nutrition Examination Survey.