Logistic regression with PET brain images as predictors

描述(申请人提供)：统计学的最新发展扩展了Logistic回归模型，纳入了功能数据，如代表每个人的时间序列的曲线，作为预测值。该项目的目标是进一步扩展这项工作，允许由5-羟色胺受体密度的体素测量组成的二维或三维脑图像作为Logistic回归的输入，以对治疗的反应概率作为输出。虽然标准的Logistic回归产生的系数表明每个预测因素对结果的影响程度，但拟议的分析将产生一个系数函数，其本身可以用图像表示，它将指示大脑区域的血清素受体密度对反应最具预测性。同样的模型可以应用于任何与抑郁相关的感兴趣的二元结果。拟议的方法将补充现有的方法，如统计参数映射，这些方法通过将图像作为结果变量的模型来区分不同的组。它还将改进将图像视为预测器的两种方法-偏最小二乘法和样条法-结合两者的优点。

DESCRIPTION (provided by applicant): Recent developments in statistics have extended the logistic regression model to incorporate functional data, such as curves representing time series for each individual, as predictors. The goal of this project is to extend this work further to allow two- or three-dimensional brain images, consisting of voxel-wise measures of serotonin receptor density, to serve as inputs in a logistic regression, with probability of response to treatment as output. Whereas a standard logistic regression produces coefficients indicating the extent to which each predictor influences the outcome, the proposed analysis will produce a coefficient function, itself representable as an image, which will indicate which brain regions' serotonin receptor density is most predictive of response. The same model could be applied to any depression-related binary outcome of interest. The proposed methodology will complement existing approaches, such as statistical parametric mapping, which distinguish between groups via a model treating the images as the outcome variable. It will also improve on two approaches which treat the image as a predictor-partial least squares and spline methods--by combining the advantages of both.