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.
| Reiss, Philip T; Ogden, R Todd (2010) Functional generalized linear models with images as predictors. Biometrics 66:61-9 |
