Multiple Comparison Procedures for Large Correlated Data with Application to Brain Connectivity Analysis

Recent developments in medical imaging and image analysis allow the determination of interregional brain connectivity through diffusion Magnetic Resonance Imaging (MRI) tractography. The brain connectivity is represented by a connection matrix where each cell represents a certain measure of connectivity between two regions of interest of the brain. An important question related to this challenging field of neuroscience is the ability to learn from connection matrices and to perform rigorous statistical analysis to derive new medical results. In particular, we focus on the level of brain regions of interest. The brain connectivity analysis involves the problem of multiplicity correction or the so-called multiple testing or multiple comparisons problem, which is the principal subject of this thesis. The work described in this thesis can be divided into three essential parts. First, the general problem of multiple comparisons. The objective of this part is to develop new multiple comparisons procedures that have optimal behavior. More precisely, we propose a comprehensive family of error rates together with a corresponding family of multiple comparison procedures. The new family generalizes almost all existing error rates. Second, the problem of multiple comparisons for positively dependent data. By supposing that the brain regions of interest that are in the same vicinity or that belong to the same functional subnetwork are positively correlated, we develop new multiple comparison strategies that exploit this additional information in order to increase sensitivity for detecting real effects. Finally, the application of multiple comparisons to brain connectivity matrices. This part is an application of the two previous parts. In addition, we adapt the statistical methods to brain connectivity analysis by estimating the structure of positive dependence. This third part can be seen as a validation of the statistical methods developed in the first and the second part. The thesis represents a complete framework of an adaptive strategy for the statistical analysis of both functional and structural connection matrices ready to be used in single subject analysis or group comparison. The framework is general enough to be used not only in neuroscience but also in many other research domains. In particular, in the brain connectivity context, it will permit an efficient investigation of a large range of pathologies where changes in brain connectivity are a key ingredient of medical interpretation, such as Alzheimer or Schizophrenia