Amanda Mejia

Zen and the art of multiple comparisons

Objective The need for appropriate multiple comparisons correction when performing statistical inference is not a new problem. However, it has come to the forefront in many new modern data-intensive disciplines. For example, researchers in areas such as imaging and genetics are routinely required to simultaneously perform thousands of statistical tests. Ignoring this multiplicity can cause severe problems with false positives, thereby introducing nonreproducible results into the literature. Methods This article serves as an introduction to hypothesis testing and multiple comparisons for practical research applications, with a particular focus on its use in the analysis of functional magnetic resonance imaging data. Results We discuss hypothesis testing and a variety of principled techniques for correcting for multiple tests. We also illustrate potential pitfalls problems that can occur if the multiple comparisons issue is not dealt with properly. We conclude, by discussing effect size estimation, an issue often linked with the multiple comparisons problem. Conclusions Failure to properly account for multiple comparisons will ultimately lead to heightened risks for false positives and erroneous conclusions.

Shrinkage prediction of seed-voxel brain connectivity using resting state fMRI.

Resting-state functional magnetic resonance imaging (rs-fMRI) is used to investigate synchronous activations in spatially distinct regions of the brain, which are thought to reflect functional systems supporting cognitive processes. Analyses are often performed using seed-based correlation analysis, allowing researchers to explore functional connectivity between data in a seed region and the rest of the brain. Using scan-rescan rs-fMRI data, we investigate how well the subject-specific seed-based correlation map from the second replication of the study can be predicted using data from the first replication. We show that one can dramatically improve prediction of subject-specific connectivity by borrowing strength from the group correlation map computed using all other subjects in the study. Even more surprisingly, we found that the group correlation map provided a better prediction of a subjects connectivity than the individuals own data. While further discussion and experimentation are required to understand how this can be used in practice, results indicate that shrinkage-based methods that borrow strength from the population mean should play a role in rs-fMRI data analysis.

Left‐Hemispheric Microstructural Abnormalities in Children With High‐Functioning Autism Spectrum Disorder

Current theories of the neurobiological basis of autism spectrum disorder (ASD) posit an altered pattern of connectivity in large‐scale brain networks. Here we used diffusion tensor imaging to investigate the microstructural properties of the white matter (WM) that mediates interregional connectivity in 36 high‐functioning children with ASD (HF‐ASD) as compared with 37 controls. By employing an atlas‐based analysis using large deformation diffeometric morphic mapping registration, a widespread but left‐lateralized pattern of abnormalities was revealed. The mean diffusivity (MD) of water in the WM of HF‐ASD children was significantly elevated throughout the left hemisphere, particularly in the outer‐zone cortical WM. Across diagnostic groups, there was a significant effect of age on left‐hemisphere MD, with a similar reduction in MD during childhood in both typically developing and HF‐ASD children. The increased MD in children with HF‐ASD suggests hypomyelination and may reflect increased short‐range cortico‐cortical connections subsequent to early WM overgrowth. These findings also highlight left‐hemispheric connectivity as relevant to the pathophysiology of ASD and indicate that the spatial distribution of microstructural abnormalities in HF‐ASD is widespread and left‐lateralized. This altered left‐hemispheric connectivity may contribute to deficits in communication and praxis observed in ASD. Autism Res 2015, 8: 61–72.

Statistical estimation of T1 relaxation times using conventional magnetic resonance imaging.

Quantitative T1 maps estimate T1 relaxation times and can be used to assess diffuse tissue abnormalities within normal-appearing tissue. T1 maps are popular for studying the progression and treatment of multiple sclerosis (MS). However, their inclusion in standard imaging protocols remains limited due to the additional scanning time and expert calibration required and susceptibility to bias and noise. Here, we propose a new method of estimating T1 maps using four conventional MR images, which are intensity-normalized using cerebellar gray matter as a reference tissue and related to T1 using a smooth regression model. Using cross-validation, we generate statistical T1 maps for 61 subjects with MS. The statistical maps are less noisy than the acquired maps and show similar reproducibility. Tests of group differences in normal-appearing white matter across MS subtypes give similar results using both methods.

Independent Association of Severity of Muscle Weakness With Disability as Measured by the Health Assessment Questionnaire Disability Index in Scleroderma

To determine whether the presence and degree of muscle weakness in scleroderma is associated with disability.

Severity of muscle weakness independently associates with disability as measured by the Health Assessment Questionnaire‐Disability Index (HAQ‐DI) in scleroderma

To determine whether the presence and degree of muscle weakness in scleroderma is associated with disability.

Improved estimation of subject-level functional connectivity using full and partial correlation with empirical Bayes shrinkage

&NA; Reliability of subject‐level resting‐state functional connectivity (FC) is determined in part by the statistical techniques employed in its estimation. Methods that pool information across subjects to inform estimation of subject‐level effects (e.g., Bayesian approaches) have been shown to enhance reliability of subject‐level FC. However, fully Bayesian approaches are computationally demanding, while empirical Bayesian approaches typically rely on using repeated measures to estimate the variance components in the model. Here, we avoid the need for repeated measures by proposing a novel measurement error model for FC describing the different sources of variance and error, which we use to perform empirical Bayes shrinkage of subject‐level FC towards the group average. In addition, since the traditional intra‐class correlation coefficient (ICC) is inappropriate for biased estimates, we propose a new reliability measure denoted the mean squared error intra‐class correlation coefficient (ICCMSE) to properly assess the reliability of the resulting (biased) estimates. We apply the proposed techniques to test‐retest resting‐state fMRI data on 461 subjects from the Human Connectome Project to estimate connectivity between 100 regions identified through independent components analysis (ICA). We consider both correlation and partial correlation as the measure of FC and assess the benefit of shrinkage for each measure, as well as the effects of scan duration. We find that shrinkage estimates of subject‐level FC exhibit substantially greater reliability than traditional estimates across various scan durations, even for the most reliable connections and regardless of connectivity measure. Additionally, we find partial correlation reliability to be highly sensitive to the choice of penalty term, and to be generally worse than that of full correlations except for certain connections and a narrow range of penalty values. This suggests that the penalty needs to be chosen carefully when using partial correlations. HighlightsEmpirical Bayes shrinkage methods for functional connectivity are proposed.A novel reliability measure analogous to intraclass correlation is proposed.Shrinkage significantly improves reliability of full and partial correlations.Partial correlation reliability is highly sensitive to ridge regression penalty.Partial correlation reliability is worse overall but better for some connections.

Big Data and Neuroimaging

Big Data are of increasing importance in a variety of areas, especially in the biosciences. There is an emerging critical need for Big Data tools and methods, because of the potential impact of advancements in these areas. Importantly, statisticians and statistical thinking have a major role to play in creating meaningful progress in this arena. We would like to emphasize this point in this special issue, as it highlights both the dramatic need for statistical input for Big Data analysis and for a greater number of statisticians working on Big Data problems. We use the field of statistical neuroimaging to demonstrate these points. As such, this paper covers several applications and novel methodological developments of Big Data tools applied to neuroimaging data.