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.

翻译：确立最优切点在流行病学和生物标志物发现中起着关键作用，有助于制定有效且实用的临床决策标准。尽管针对标量型生物标志物的最优切点定义已有大量文献，但在函数和图等更为复杂的空间中分析统计对象的一般性方法却明显缺乏，而这些空间在数字健康应用中日益重要。本文提出了一种新的通用方法，用于定义可分希尔伯特空间中随机对象的最优切点。该研究的动机源于利用持续血糖监测仪（CGM）作为数字生物标志物的功能信息，为糖尿病制定新的临床规则。具体而言，我们基于血糖分布函数表示，提供了利用CGM信息识别糖尿病病例的功能性切点。