Functional Regress Models with Application in Brain Imaging Studies

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DESCRIPTION (provided by applicant): Brain imaging and other imaging technologies have provided powerful tools for researchers in psychiatry and other medical fields. The ability to measure the density and distribution of various proteins throughout the brain using positron emission tomography (PET) and to determine regional brain function using functional magnetic resonance imaging has yielded important insights as to the physiological basis of major depressive disorder (MDD), Alzheimer's disease (AD), and other neuropsychiatric illnesses. The use of this technology has led to new under- standings of the pathophysiology of such illnesses including, for instance, patterns of differences between normal controls and subjects suffering from MDD. Group-level analysis of imaging data is typically performed using methodology such as Statistical Parametric Mapping (SPM) in which a statistical model is fit separately to each voxel of the co-registered images. A test statistic is computed for each voxel, regarding the imaging data as the "response" variable and the patient-specific information (treatment group, sex, etc.) as predictors. We propose to develop models that reverse the roles of these variables - i.e., to use images as predictors and variables such as response to treatment as outcomes. The primary objectives of this proposal are: 1. to develop methodology for fitting models with two-dimensional and three-dimensional images as predictors and for inference on the estimated model parameters following two general approaches, one based on a spline representation of images and one based on a wavelet decomposition, both involving computationally intensive algorithms for dimension reduction; 2. to validate the methodology by application to simulated data sets and in two real-data situations (one with PET images of the serotonergic system in an MDD study and one with PET images of amyloid plaques in an AD study); 3. to create and make available software for fitting such models. In addition to advances in statistical methodology, this will enable researchers to better understand which areas of the brain are most predictive of various outcomes. PUBLIC HEALTH RELEVANCE: We propose to develop statistical models in which images (in combination with appropriate clinical or biological covariates) serve as predictors of scalar outcome variables. Potential applications include using brain images as predictors of outcomes such as response to a particular treatment for depression, development of Alzheimer's disease, or making a suicide attempt. Once developed and validated, this methodology could be applied to data from any imaging modality, including structural and functional magnetic resonance imaging and diffusion tensor imaging.