Pomann Gina-Maria, Staicu Ana-Maria, Lobaton Edgar J, Mejia Amanda F, Dewey Blake E, Reich Daniel S, Sweeney Elizabeth M, Shinohara Russell T
Department of Biostatistics and Bioinformatics, Duke University, Durham, North Carolina 27710, USA.
Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695, USA.
Ann Appl Stat. 2016 Dec;10(4):2325-2348. doi: 10.1214/16-aoas981. Epub 2017 Jan 5.
We propose a lag functional linear model to predict a response using multiple functional predictors observed at discrete grids with noise. Two procedures are proposed to estimate the regression parameter functions: (1) an approach that ensures smoothness for each value of time using generalized cross-validation; and (2) a global smoothing approach using a restricted maximum likelihood framework. Numerical studies are presented to analyze predictive accuracy in many realistic scenarios. The methods are employed to estimate a magnetic resonance imaging (MRI)-based measure of tissue damage (the magnetization transfer ratio, or MTR) in multiple sclerosis (MS) lesions, a disease that causes damage to the myelin sheaths around axons in the central nervous system. Our method of estimation of MTR within lesions is useful retrospectively in research applications where MTR was not acquired, as well as in clinical practice settings where acquiring MTR is not currently part of the standard of care. The model facilitates the use of commonly acquired imaging modalities to estimate MTR within lesions, and outperforms cross-sectional models that do not account for temporal patterns of lesion development and repair.
我们提出了一种滞后泛函线性模型，用于利用在离散网格上观测到的带有噪声的多个泛函预测变量来预测响应。我们提出了两种估计回归参数函数的方法：（1）一种使用广义交叉验证来确保每个时间值的平滑性的方法；（2）一种使用受限最大似然框架的全局平滑方法。我们进行了数值研究，以分析许多现实场景中的预测准确性。这些方法被用于估计多发性硬化症（MS）病变中基于磁共振成像（MRI）的组织损伤测量指标（磁化传递率，即MTR），MS是一种会对中枢神经系统中轴突周围的髓鞘造成损伤的疾病。我们在病变内估计MTR的方法在未获取MTR的研究应用中具有回顾性用途，在目前获取MTR并非标准治疗一部分的临床实践环境中也很有用。该模型有助于使用常见的成像模态来估计病变内的MTR，并且优于不考虑病变发展和修复时间模式的横断面模型。
