Abstract: We propose a functional joint modeling (FJM) framework for correlating imaging responses with genetic markers and clinical variables. Our FJM consists of a nonlinear multivariate functional principal component analysis (NMFPCA) and a functional multiple-index varying coefficient model (FMVCM). The NMFPCA, with unknown link functions, is used to extract meaningful functional principal component (FPC) scores of genetic markers, while the FMVCM identifies the varying association of the extracted FPC scores and clinical variables with imaging data. We propose an efficient estimation procedure to estimate unknown functions in our FJM and a regularization approach to simultaneously select relevant features from infinite-dimensional functional data and learn the model structure. The asymptotic convergence rate of estimators and model selection consistency are investigated. The proposed method is evaluated through simulation studies and applied to an imaging genetic data set extracted from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) study.

Key words and phrases: Functional joint model, functional principal component, imaging genetics, neuroimaging data analysis, varying coefficient.