Rejoinder: “Statistical disease mapping for heterogeneous neuroimaging studies”

We thank all the discussants for sharing their valuable viewpoints on the proposed statistical disease mapping (SDM) framework. In our article, we addressed the issue of imaging heterogeneity at both the global and local scales by efficiently borrowing common information shared among a large number of diseased and normal subjects. Understanding such imaging heterogeneity is critical in the development of urgently needed analytic approaches to the prevention, diagnosis, treatment, and prognosis of many diseases (e.g., Alzheimer's disease, brain cancer, and lung cancer), as well as precision medicine broadly. The discussants emphasized improvements to disease mapping by introducing some alternative modelling strategies and many possible future directions in this research topic. The sections of this rejoinder are organized by discussant to address each of their comments separately.