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.

Imaging genetics is an emerging field for the investigation of neuro-mechanisms linked to genetic variation. Although imaging genetics has recently shown great promise in understanding biological mechanisms for brain development and psychiatric disorders, studying the link between genetic variants and neuroimaging phenotypes remains statistically challenging due to the high-dimensionality of both genetic and neuroimaging data. This becomes even more challenging when studying gene-environment interaction (G×E) on neuroimaging phenotypes. In this study, we proposed a set-based mixed effect model for gene-environment interaction (MixGE) on neuroimaging phenotypes, such as structural volumes and tensor-based morphometry (TBM). MixGE incorporates both fixed and random effects of G×E to investigate homogeneous and heterogeneous contributions of multiple genetic variants and their interaction with environmental risks to phenotypes. We discuss the construction of score statistics for the terms associated with fixed and random effects of G×E to avoid direct parameter estimation in the MixGE model, which would greatly increase computational cost. We also describe how the score statistics can be combined into a single significance value to increase statistical power. We evaluated MixGE using simulated and real Alzheimer's Disease Neuroimaging Initiative (ADNI) data, and showed statistical power superior to other burden and variance component methods. We then demonstrated the use of MixGE for exploring the voxelwise effect of G×E on TBM, made feasible by the computational efficiency of MixGE. Through this, we discovered a potential interaction effect of gene ABCA7 and cardiovascular risk on local volume change of the right superior parietal cortex, which warrants further investigation.

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There is great interest in elucidating the cluster structure of brain networks in terms of modules, blocks or clusters of similar nodes. However, it is currently challenging to handle data on multiple subjects since most of the existing methods are applicable only on a subject-by-subject basis or for analysis of a group average network. The main limitation of per-subject models is that there is no obvious way to combine the results for group comparisons, and of groupaveraged models that they do not reflect the variability between subjects. Here, we propose two novel extensions of the classical Stochastic Blockmodel (SBM) that use a mixture model to estimate blocks or clusters of connected nodes, combined with a regression model to capture the effects on cluster structure of individual differences on subject-level covariates. Multi-subject Stochastic Blockmodels (MS-SBM) can flexibly account for between-subject variability in terms of a homogenous or heterogeneous effect on connectivity of covariates such as age or diagnostic status. Using synthetic data, representing a range of block sizes and cluster structures, we investigate the accuracy of the estimated MS-SBM parameters as well as the validity of inference procedures based on Wald, likelihood ratio and Monte Carlo permutation tests. We show that multi-subject SBMs recover the true cluster structure of synthetic networks more accurately and adaptively than standard methods for modular decomposition. Permutation tests of MS-SBM parameters were more robustly valid for statistical inference and Type I error control than tests based on standard asymptotic assumptions. Applied to analysis of multi-subject resting state fMRI networks (13 healthy volunteers; 12 people with schizophrenia; N = 268 brain regions), we show that the Heterogeneous Stochastic Blockmodel estimates 'core-on-modules' architecture. The intra-block and inter-block connection weights vary between individual participants and can be modelled as a logistic function of subject-level covariates like age or diagnostic status. Multi-subject Stochastic Blockmodels are likely to be useful tools for statistical analysis of individual differences in human brain graphs and other networks whose prior cluster structure needs to be estimated from the data.

We report a case of cluster-like headache in a patient with a trigeminal neurinoma. Symptomatic cluster headache was suspected because of the absence of typical periodicity and the persistence of background headache. Magnetic resonance imaging findings were consistent with a trigeminal neurinoma. Key words: cluster headache, trigeminal neurinoma, cavernous sinus (Headache 1995;35:48-49) In a recent review on cluster headache (CH), Mathew described the association of cluster-like headache with various cephalic vascular and non-vascular lesions such as arteriovenous malformation of the occipital lobe, vertebral artery dissection, nasopharyngeal carcinoma, pituitary adenoma and upper cervical meningioma. 1 We report the occurrence of cluster-like headache in a patient with a trigeminal neurinoma. CASE HISTORYA 45-year-old man had a 2-year history of recurrent headaches. The headaches were invariably left-sided; mainly orbital, nasal, and temporal. At the onset of the disease, he had one to three headaches per day that were rapidly relieved by oral analgesic drugs. The pain was moderate, characterized as throbbing and burning without associated symptoms or signs. He had two remission periods, one after a dental extraction performed 3 months after the onset of pain and one during the previous summer holiday. These pain free periods lasted only 1 month. In September 1993, the headaches became very intense. The patient had two or three headaches per day, each lasting 2 to 3 hours. He frequently had attacks between 1 a.m. and 3 a.m., awakening him from his sleep. The headaches were described as intolerably severe. The location of the pain remained unchanged, but attacks were associated with conjunctival injection, nasal congestion, rhinorrhea and ptosis. A certain degree of background headache persisted between episodes of severe pain. Analgesics, including aspirin, were of no benefit. Neurological examination was entirely normal. Corneal reflex was normal and any sign of involvement of the fifth nerve was absent. On methysergide (2 mg three times a day) the patient showed a marked amelioration in the frequency and severity of the headaches. Magnetic resonance imaging (MRI) was obtained at 2 tesla (EIscint). Unenhanced spin echo sagittal T1-weighted scans showed enlargement of the left trigeminal nerve, slightly hypointense to brain parenchyma The lesion was isointense to slightly hyperintense on T2-weighted images. Sagittal, axial and coronal T1-weighted images were performed after gadolinium DTPA, showing enhancement of the lesion. ( Figure 1A). The lesion involved the cisternal portion of the trigeminal nerve, the trigeminal ganglion within Meckel's cave, and extended into the cavernous sinus in close contact to the internal carotid artery ( Figure 1B). Digital subtraction angiography was performed. Selec-

Statistical inference on neuroimaging data is often conducted using a mass-univariate model, equivalent to fitting a linear model at every voxel with a known set of covariates. Due to the large number of linear models, it is challenging to check if the selection of covariates is appropriate and to modify this selection adequately. The use of standard diagnostics, such as residual plotting, is clearly not practical for neuroimaging data. However, the selection of covariates is crucial for linear regression to ensure valid statistical inference. In particular, the mean model of regression needs to be reasonably well specified. Unfortunately, this issue is often overlooked in the field of neuroimaging. This study aims to adopt the existing Confounder Adjusted Testing and Estimation (CATE) approach and to extend it for use with neuroimaging data. We propose a modification of CATE that can yield valid statistical inferences using Principal Component Analysis (PCA) estimators instead of Maximum Likelihood (ML) estimators. We then propose a non-parametric hypothesis testing procedure that can improve upon parametric testing. Monte Carlo simulations show that the modification of CATE allows for more accurate modelling of neuroimaging data and can in turn yield a better control of False Positive Rate (FPR) and Family-Wise Error Rate (FWER). We demonstrate its application to an Epigenome-Wide Association Study (EWAS) on neonatal brain imaging and umbilical cord DNA methylation data obtained as part of a longitudinal cohort study. Software for this CATE study is freely available at http://www.bioeng.nus.edu.sg/cfa/Imaging_Genetics2.html.

Rationale: For people with Chronic Obstructive Pulmonary Disease (COPD), improvements in breathlessness from pulmonary rehabilitation are neither long lasting nor guaranteed. Previously, we showed that pulmonary rehabilitation induced brain activity changes akin to those seen in exposure based cognitive behavioural therapies (CBT) in other conditions. D-cycloserine is a partial NMDA-receptor agonist which has been shown to enhance CBT. Objectives: Here, we tested whether D-cycloserine would augment the effects of pulmonary rehabilitation on activity in brain areas that process breathlessness expectation. Methods: 72 participants with mild-to-moderate COPD were recruited to a double-blind experimental medicine study running parallel to a pulmonary rehabilitation course. Participants were randomised to 250mg D-cycloserine or matched placebo, administered 15-30 minutes prior to the first four sessions of pulmonary rehabilitation. Brain functional magnetic resonance imaging, self-report questionnaires and clinical measures of respiratory function were collected at three time points: before, during (2-3 weeks) and after pulmonary rehabilitation (6-8 weeks). Measurements: Primary and secondary outcome measures were difference in mean and voxel-wise brain activity across key brain regions of interest. An exploratory analysis determined the interaction with breathlessness-anxiety. Main results: No difference was observed in either primary or secondary outcome measures. However, in the exploratory analysis, D-cycloserine attenuated the relationship between brain activity and breathlessness-anxiety within prefrontal cortex, superior frontal gyrus and precuneus. Conclusions: The observed effects suggest that D-cycloserine augments pulmonary rehabilitation by dampening reactivity to breathlessness cues in brain areas associated with breathlessness expectation and anxiety. This work highlights the opportunity to test brain-active drugs in the context of augmenting behavioural interventions.