Alzheimer's disease (AD) is a chronic neurodegenerative disease characterized by a gradual decline in cognitive function over a few decades. The Mini-Mental State Examination (MMSE) is a widely used measure for evaluating global cognitive functioning. Characterizing the longitudinal trajectory of the MMSE in the population of interest is important to detect AD onset for preventive intervention. In this study, we formulate a new class of longitudinal trajectory modeling for MMSE from short-term individual data based on an ordinary differential equation. The proposed method models the relationship between individual decline speed of MMSE and the average MMSE using the fractional polynomial function model and subsequently estimates the longitudinal trajectory of MMSE by solving the ordinary differential equation for the estimated model. The appropriate model for trajectory estimation is selected based on the proposed criterion for quantifying the goodness of trajectory fit. The accuracy of the trajectory estimation of the proposed method was demonstrated via simulation studies. The proposed method was successfully applied to MMSE data from the Japanese Alzheimer's Disease Neuroimaging Initiative study.

中文翻译：

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使用不同疾病阶段的短期数据估计认知功能测量的纵向轨迹：在阿尔茨海默病中的应用

阿尔茨海默病 (AD) 是一种慢性神经退行性疾病，其特征是认知功能在几十年内逐渐下降。简易精神状态检查 (MMSE) 是一种广泛用于评估全球认知功能的测量方法。表征感兴趣人群中 MMSE 的纵向轨迹对于检测 AD 发作以进行预防性干预很重要。在这项研究中，我们基于常微分方程从短期个体数据中为 MMSE 制定了一类新的纵向轨迹建模。该方法使用分数多项式函数模型对MMSE的个体下降速度与平均MMSE之间的关系进行建模，然后通过求解估计模型的常微分方程来估计MMSE的纵向轨迹。根据提出的量化轨迹拟合优度的标准，选择合适的轨迹估计模型。通过仿真研究证明了所提出方法的轨迹估计的准确性。所提出的方法成功地应用于来自日本阿尔茨海默病神经影像学倡议研究的 MMSE 数据。