Low-rank Latent Matrix Factor-Analysis Modeling for Generalized Linear Regression with High-dimensional Imaging Biomarkers

Medical imaging has been recognized as a phenotype associated with various clinical traits in diagnostics and prognosis of clinical trials and cancer studies. Imaging data used to be converted and stored into high-dimensional matrices in medical imaging data preprocessing. For the imaging predictor expressed in the form of a high-dimensional matrix variate, the mainstream tackling approaches tend to vectorize the matrix-valued predictor into a long regressor array plus a specific regularization scheme. Such vectorization may suffer the loss of information of intrinsic structure. Motivated by the cutting-edge matrix factor analysis modeling, we propose a new latent matrix factor generalized regression tool named FamGLM, which relates a scalar treatment outcome with predictors including imaging variate. The FamGLM enjoys high prediction capability since the extracted matrix factor score refines the structural effect of the matrix-valued predictor and circumvents over dimension reduction. Inspired by 2nd-order tensor principal component analysis, we develop a matrix SVD-based estimation procedure and algorithm through generalized low rank approximation of matrices, which has a much lower computation cost compared with existing statistical approaches. The proposed FamGLM also achieves higher prediction capability than existing methods. In numerical analysis, we evaluate the finite sample performance of FamGLM in classification and prediction compared with existing statistical approaches under various GLM scenarios. The FamGLM outperforms in discriminant power in analysis of a COVID-CT image data set.