In many modern applications, a dependent functional response is observed for each subject over repeated time, leading to longitudinal functional data. In this paper, we propose a novel statistical procedure to test whether the mean function varies over time. Our approach relies on reducing the dimension of the response using data-driven orthogonal projections and it employs a likelihood-based hypothesis testing. We investigate the methodology theoretically and discuss a computationally efficient implementation. The proposed test maintains the type I error rate, and shows excellent power to detect departures from the null hypothesis in finite sample simulation studies. We apply our method to the longitudinal diffusion tensor imaging study of multiple sclerosis (MS) patients to formally assess whether the brain's health tissue, as summarized by fractional anisotropy (FA) profile, degrades over time during the study period.
翻译:在许多现代应用中,对每个科目都反复观察到依赖功能的响应,从而得出纵向功能数据。在本文中,我们提出一个新的统计程序,以测试平均功能是否随时间而变化。我们的方法依靠使用数据驱动的正方形预测来减少响应的维度,并采用基于可能性的假设测试。我们从理论上调查该方法,并讨论一个计算效率有效的实施。提议的测试保持了I型误差率,并显示了在有限样本模拟研究中发现偏离无效假设的极强力。我们运用了我们的方法,对多发性硬化症患者的纵向扩散高压成像研究进行正式评估大脑健康组织是否在研究期间随着时间的流逝而退化。