Massively Univariate Regression Accounting for Random Regressors

• Activity Number: 463
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Xue Yang*+ and Carolyn Lauzon and Ciprian Crainiceanu and Brian Caffo and Susan M. Resnick and Bennett Landman
• Companies: Vanderbilt University and Vanderbilt University and The Johns Hopkins University and The Johns Hopkins University and National Institutes of Health and Vanderbilt University
• Keywords: massively univariate regression ; model II regression ; GLM

Abstract

Massively univariate regression with the general linear model (GLM) is an essential method for quantitative interpretation of multi-dimensional medical images, such as magnetic resonance imaging (MRI) or positron emission tomography (PET). These mappings enable inferences on image appearance (e.g., tissue characteristics) conditioned on a set of non-image based regressors (e.g., treatment regimen). With modern technology, single subject multi-modal imaging data are increasingly common and regression between two images (e.g., MRI vs. PET) has become highly desirable. Although software tools have been extended to support images as regressors they do not account for randomness in the regressor image or model the joint distribution. Model II regression could address this problem but a general maximum likelihood (MLE) solution is ill conditioned. Here, we combine Model II regression with data-derived prior variances to regularize the MLE solution, producing a model that is inverse consistent. This approach shows substantial improvements in fit and increased statistical power compared to OLS, and provides a logical framework for exploring relationships in multi-modal image analysis.