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Despite the growing importance of longitudinal data in neuroimaging, the standard analysis methods make restrictive or unrealistic assumptions (e.g., assumption of Compound Symmetry--the state of all equal variances and equal correlations--or spatially homogeneous longitudinal correlations). While some new methods have been proposed to more accurately account for such data, these methods are based on iterative algorithms that are slow and failure-prone. In this article, we propose the use of the Sandwich Estimator method which first estimates the parameters of interest with a simple Ordinary Least Square model and second estimates variances/covariances with the "so-called" Sandwich Estimator (SwE) which accounts for the within-subject correlation existing in longitudinal data. Here, we introduce the SwE method in its classic form, and we review and propose several adjustments to improve its behaviour, specifically in small samples. We use intensive Monte Carlo simulations to compare all considered adjustments and isolate the best combination for neuroimaging data. We also compare the SwE method to other popular methods and demonstrate its strengths and weaknesses. Finally, we analyse a highly unbalanced longitudinal dataset from the Alzheimer's Disease Neuroimaging Initiative and demonstrate the flexibility of the SwE method to fit within- and between-subject effects in a single model. Software implementing this SwE method has been made freely available at

Original publication




Journal article



Publication Date





287 - 302


ADNI, Longitudinal Modelling, Marginal Modelling, Sandwich Estimator, Aged, Aged, 80 and over, Algorithms, Alzheimer Disease, Brain, Cognitive Dysfunction, Computer Simulation, Data Interpretation, Statistical, Female, Humans, Image Enhancement, Image Interpretation, Computer-Assisted, Longitudinal Studies, Male, Middle Aged, Models, Statistical, Neuroimaging, Radionuclide Imaging, Reproducibility of Results, Sensitivity and Specificity