Bayesian latent factor on image regression with nonignorable missing data.

Medical imaging data have been widely used in modern health care, particularly in the prognosis, screening, diagnosis, and treatment of various diseases. In this study, we consider a latent factor-on-image (LoI) regression model that regresses a latent factor on ultrahigh dimensional imaging covariates. The latent factor is characterized by multiple manifest variables through a factor analysis model, while the manifest variables are subject to nonignorable missingness. We propose a two-stage approach for statistical inference. At the first stage, an efficient functional principal component analysis method is applied to reduce the dimension and extract useful features/eigenimages. At the second stage, a factor analysis mode is proposed to characterize the latent response variable. Moreover, an LoI model is used to detect influential risk factors, and an exponential tiling model applied to accommodate nonignoreable nonresponses. A fully Bayesian method with an adjust spike-and-slab absolute shrinkage and selection operator (lasso) procedure is developed for the estimation and selection of influential features/eigenimages. Simulation studies show the proposed method exhibits satisfactory performance. The proposed methodology is applied to a study on the Alzheimer's Disease Neuroimaging Initiative data set.