基于投影的交叉设计下纵向函数数据的显著性检验
Projection-based significance test for longitudinally collected functional data under a crossover design
AI总结：
本研究提出一种基于正交投影的伪广义F检验，用于交叉设计下纵向函数数据中药物疗效的显著性检验，并在美洛昔康对猫活动水平的数据中验证了其有效性和高效性。
摘要：
可穿戴设备用于连续电子健康监测，通常在密集函数设计下以频繁间隔捕获数据。焦点在于纵向函数数据的分析，其中函数轨迹随时间重复观测。本工作受评估非炎症药物美洛昔康在交叉设计下对患有骨关节炎的 household cats 的日常活动水平疗效的兴趣所驱动。加速度计在整个研究期间以分钟级别记录这些活动概况。为此，我们提出了一种基于正交投影的伪广义 F 检验，以在函数加性交叉模型下确定函数治疗效应的显著性，同时考虑残留效应和基线协变量。在温和条件下，我们推导了检验统计量的渐近零分布以及当投影函数从数据中估计时的理论功效函数。数值研究表明，所提出的检验保持了尺寸，在检测美洛昔康的平滑效应方面具有功效，并且与基于自举的替代方法相比表现出高效率。将该检验应用于加速度计活动概况，在调整其他基线协变量后，揭示了美洛昔康对猫的关节疼痛评分的强阳性效应。
英文摘要：
Wearable devices for continuous electronic health monitoring often capture data at frequent intervals under a dense functional design. The focal point is the analysis of longitudinal functional data, wherein functional trajectories are observed repeatedly over time. This work is motivated by the interest in assessing the efficacy of a noninflammatory medication, meloxicam, on the daily activity levels of household cats with a pre-existing condition of osteoarthritis under a crossover design. An accelerometer records these activity profiles at a minute level over the entire study period. To this aspect, we propose an orthogonal projection-based pseudo-generalized F test to determine the significance of the functional treatment effect under a functional additive crossover model while accounting for carryover effects and baseline covariates. Under mild conditions, we derive the asymptotic null distribution of the test statistic and the theoretical power function when the projection function is estimated from the data. Numerical studies demonstrate that the proposed test maintains size, proves powerful in detecting the smooth effect of meloxicam, and exhibits high efficiency compared to bootstrap-based alternatives. Application of the test on the accelerometric activity profiles reveals a strong positive effect of meloxicam on the joint pain score of the cats after adjusting for other baseline covariates.
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