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 http://warwick.ac.uk/tenichols/SwE.
Antenatal maternal depressive symptoms influence fetal brain development and increase the risk for depression in offspring. Such vulnerability is often moderated by the offspring's genetic variants. This study aimed to examine whether FKBP5, a key regulator of the hypothalamic-pituitary-adrenal (HPA) axis, moderates the association between antenatal maternal depressive symptoms and in utero brain development, using an Asian cohort with 161 mother-offspring dyads. Antenatal maternal depressive symptoms were measured using the Edinburgh Postnatal Depression Scale (EPDS) during the second trimester of pregnancy. Neonatal structural brain images were acquired using magnetic resonance imaging (MRI) shortly after birth. Maternal and neonatal FKBP5 gene was genotyped using Illumina OmniExpress arrays. A gene set-based mixed effect model for gene-environment interaction (MixGE) was used to examine interactive effects between neonatal genetic variants of FKBP5 and antenatal maternal depressive symptoms on neonatal amygdala and hippocampal volumes, and cortical thickness. Our study revealed that genetic variants in neonatal FKBP5 moderate the association between antenatal maternal depressive symptoms and right hippocampal volume but only show a trend for such moderation on amygdala volumes and cortical thickness. Our findings are the first to reveal that the association between maternal depressive symptoms and in utero neurodevelopment of specific brain regions is modified through complex genetic variation in neonatal FKBP5. Our results suggest that an increased risk for depression may be transmitted from mother to child during fetal life and that the effect is dependent upon neonatal FKBP5 genotype.
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