Quantifying ruminal health: A statistical review and application of area and time under the curve in animal science

The concepts of area under the curve (AUC) and time under the curve (TUC), along with their complements area above the curve (AAC) and time above the curve (TAC), provide a powerful statistical framework for quantifying temporal dynamics across various scientific disciplines. These metrics distill complex, time-dependent phenomena into comprehensible values, enabling detailed comparisons of diverse processes. This paper explores the theoretical foundations of these methods and applies them to ruminal pH analysis, a critical indicator of ruminant health, welfare, and productivity. The paper introduces the Area and Time Above and Under the Curve (ATAUC) algorithm, a comprehensive R-based tool designed for analyzing continuous time-series data from multiple sensors. Traditional approaches like the trapezoidal and Simpson's rules are reviewed, alongside advanced methods such as spline interpolation, which better handle irregular data and complex curve behavior. ATAUC integrates robust threshold analysis, smoothing functions for sensor transition, and advanced statistical summaries to ensure accurate and reproducible measurements even in the presence of sampling irregularities or sensor drift. By applying ATAUC to the study of ruminal acidosis, the paper demonstrates the utility of AUC and TUC metrics in capturing the intensity and duration of pH fluctuations relative to critical thresholds. These insights allow researchers and practitioners to evaluate feeding strategies, diagnose metabolic disorders, and optimize animal management practices. AUC-based metrics, supported by the ATAUC algorithm, enable scalable and pragmatic solutions for real-time monitoring and decision-making. This study underscores the relevance of advanced AUC and TUC methodologies for addressing challenges in animal science and beyond. By combining these methods with advancements in data processing, such as machine learning and predictive modeling, the potential for broader applications becomes evident. The findings emphasize that these approaches are not only valuable for quantifying ruminal health but also for understanding and managing complex biological systems across various disciplines. The integration of robust analytical frameworks like ATAUC provides a pathway for improved decision-making, enhanced productivity, and greater welfare in ruminant systems while offering insights applicable to other time-dependent phenomena in science and industry.