Accurate Non-Iterative Modelling and Inference of Longitudinal Neuroimaging Data

Despite the growing importance of longitudinal data in neuroimaging, the standard analysis methods make restrictive or unrealistic assumptions. For example, the widely used SPM software package assumes spatially homogeneous longitudinal correlations while the FSL software package assumes Compound Symmetry, the state of all equal variances and equal correlations. While some new methods have been recently pro- posed to more accurately account for such data, these methods can be difficult to specify and are based on iterative algorithms that are generally slow and failure- prone. In this thesis, we propose and investigate the use of the Sandwich Estimator method which first estimates the parameters of interest with a (non-iterative) Ordinary Least Square model and, second, estimates variances/covariances with the “so-called” Sandwich Estimator (SwE) which accounts for the within-subject covariance structure existing in longitudinal data. We introduce the SwE method in its classic form, and review existing and propose new adjustments to improve its behaviour, specifically in small samples. We compare the SwE method to other popular methods, isolating the combination of SwE adjustments that provides valid and powerful inferences. While this result provides p-values at each voxel, it does not provide spatial inferences, e.g. voxel- or cluster-wise family-wise error-corrected p-values. For this, we investigate the use of the non-parametric inference approach called Wild Bootstrap. We again identify the set of procedures and adjustments that provide valid inferences. Finally, in the third and fourth projects, we investigate two ideas to improve the statistical power of the SwE method, by using a shrinkage estimator or a covariance spatial smoothing, respectively. For all the projects, in order to assess the methods, we use intensive Monte Carlo simulations in settings important for longitudinal neuroimaging studies and, for the first two projects, we also illustrate the methods by analysing a highly unbalanced longitudinal dataset obtained from the Alzheimer’s Disease Neuroimaging Initiative.