Abstract Integrative analysis methods are in great needs as multimodal multi-cohort neuroimaging data rapidly emerge in neuro science. In Alzheimer's Disease (AD) studies, many research relies on multimodal neuroimaging data to identify key image biomarkers for the early diagnosis of AD. Despite great endeavors in data collection, there still lacks rigorous statistical methods and efficient computational tools to properly integrate big neuroimaging data in a statistical model and carry out inference to address practical problems. Important problems such as missing data and adjustment for between-subject heterogeneity still remain unsolved. In this proposal, we propose to build two integrative models, one handles multimodal data and the other handles longitudinal multi-cohort data. They will be built under a generic M-estimation framework that covers many widely used statistical models as its special cases. We will provide various inference tools for these models and develop efficient algorithms to solve the M-estimation problem in presence of block missing values. In Aim 1, we propose a factor-adjusted integrative model for multimodal data and provide a complete set of inference tools. These tools can test the significance of one whole data modality as well as the significance of multiple linear combinations of predictors from one or more modalities. In Aim 2, we provide a powerful computational tool to handle block missing values of multimodal data. Such a tool does not need to perform ad-hoc imputation on missing values, but rather relies on an innovative mini- batch gradient descent algorithm to yield a good estimator. In Aim 3, we will develop an interactive factor model to jointly model longitudinal data coming from multiple cohorts. We show that such a model includes the standard random effects model as a special case and is more flexible modeling the longitudinal data and accounting for the between-subject heterogeneity. The proposed research will likely transform how we analyze neuroimaging data and enhance our understanding of Alzheimer's Disease and its relation to public health.