Optimal Cut-Point Estimation for functional digital biomarkers: Application to Continuous Glucose Monitoring

Establish optimal cut points plays a crucial role in epidemiology and biomarker discovery, enabling the development of effective and practical clinical decision criteria. While there is extensive literature to define optimal cut off over scalar biomarkers, there is a notable lack of general methodologies for analyzing statistical objects in more complex spaces of functions and graphs, which are increasingly relevant in digital health applications. This paper proposes a new general methodology to define optimal cut points for random objects in separable Hilbert spaces. The paper is motivated by the need for creating new clinical rules for diabetes mellitus disease, exploiting the functional information of a continuous diabetes monitor (CGM) as a digital biomarker. More specifically, we provide the functional cut off to identify diabetes cases with CGM information based on glucose distributional functional representations.