Permutation and parametric tests for effect sizes in voxel-based morphometry of grey matter volume in brain structural MRI

Permutation testing has been widely implemented in voxel-based morphometry (VBM) tools. However, this type of non-parametric inference has yet to be thoroughly compared with traditional parametric inference in VBM studies of brain structure. Here we compare both types of inference and investigate what influence the number of permutations in permutation testing has on results in an exemplar study of how gray matter proportion changes with age in a group of working age adults. High resolution T1-weighted volume scans were acquired from 80 healthy adults aged 25–64 years. Using a validated VBM procedure and voxel-based permutation testing for Pearson product-moment coefficient, the effect sizes of changes in gray matter proportion with age were assessed using traditional parametric and permutation testing inference with 100, 500, 1000, 5000, 10000 and 20000 permutations. The statistical significance was set at P < 0.05 and false discovery rate (FDR) was used to correct for multiple comparisons. Clusters of voxels with statistically significant (PFDR < 0.05) declines in gray matter proportion with age identified with permutation testing inference (N ≈ 6000) were approximately twice the size of those identified with parametric inference (N = 3221 voxels). Permutation testing with 10000 (N = 6251 voxels) and 20000 (N = 6233 voxels) permutations produced clusters that were generally consistent with each other. However, with 1000 permutations there were approximately 20% more statistically significant voxels (N = 7117 voxels) than with ≥ 10000 permutations. Permutation testing inference may provide a more sensitive method than traditional parametric inference for identifying age-related differences in gray matter proportion. Based on the results reported here, at least 10000 permutations should be used in future univariate VBM studies investigating age related changes in gray matter to avoid potential false findings. Additional studies using permutation testing in large imaging databanks are required to address the impact of model complexity, multivariate analysis, number of observations, sampling bias and data quality on the accuracy with which subtle differences in brain structure associated with normal aging can be identified

Tilted Euler characteristic densities for Central Limit random fields, with application to "bubbles"

Local increases in the mean of a random field are detected (conservatively) by thresholding a field of test statistics at a level $u$ chosen to control the tail probability or $p$-value of its maximum. This $p$-value is approximated by the expected Euler characteristic (EC) of the excursion set of the test statistic field above $u$, denoted $\mathbb{E}\varphi(A_u)$. Under isotropy, one can use the expansion $\mathbb{E}\varphi(A_u)=\sum_k\mathcal{V}_k\rho_k(u)$, where $\mathcal{V}_k$ is an intrinsic volume of the parameter space and $\rho_k$ is an EC density of the field. EC densities are available for a number of processes, mainly those constructed from (multivariate) Gaussian fields via smooth functions. Using saddlepoint methods, we derive an expansion for $\rho_k(u)$ for fields which are only approximately Gaussian, but for which higher-order cumulants are available. We focus on linear combinations of $n$ independent non-Gaussian fields, whence a Central Limit theorem is in force. The threshold $u$ is allowed to grow with the sample size $n$, in which case our expression has a smaller relative asymptotic error than the Gaussian EC density. Several illustrative examples including an application to "bubbles" data accompany the theory.Comment: Published in at http://dx.doi.org/10.1214/07-AOS549 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Accurate Non-Iterative Modelling and Inference of Longitudinal Neuroimaging Data

In recent years, increasing efforts have been made to collect longitudinal neuroimaging data in order to study how brains change over time. However, the popular methods used to analyse such kind of data may not always be appropriate (e.g., overly sensitive to model misspecifications, difficult to specify adequately or prohibitively slow to compute) and may sometimes lead to erroneous conclusions. Motivated by these shortcomings, in this dissertation, we have proposed and studied the use of an alternative method, referred to as “the Sandwich Estimator method”, and have demonstrated that it is a fast, easy-to-specify and accurate option to analyse longitudinal or repeated-measures neuroimaging data

Statistical Methods in Neuroimaging Genetics: Pathways Sparse Regression and Cluster Size Inference

In the field of neuroimaging genetics, brain images are used as phenotypes in the search for genetic variants associated with brain structure or function. This search presents a formidable statistical challenge, not least because of the very high dimensionality of genotype and phenotype data produced by modern SNP (single nucleotide polymorphism) arrays and high resolution MRI. This thesis focuses on the use of multivariate sparse regression models such as the group lasso and sparse group lasso for the identification of gene pathways associated with both univariate and multivariate quantitative traits. The methods described here take particular account of various factors specific to pathways genome-wide association studies including widespread correlation (linkage disequilibrium) between genetic predictors, and the fact that many variants overlap multiple pathways. A resampling strategy that exploits finite sample variability is employed to provide robust rankings for pathways, SNPs and genes. Comprehensive simulation studies are presented comparing one proposed method, pathways group lasso with adaptive weights, to a popular alternative. This method is extended to the case of a multivariate phenotype, and the resulting pathways sparse reduced-rank regression model and algorithm is applied to a study identifying gene pathways associated with structural change in the brain characteristic of Alzheimer’s disease. The original model is also adapted for the task of ’pathways-driven’ SNP and gene selection, and this latter model, pathways sparse group lasso with adaptive weights, is applied in a search for SNPs and genes associated with elevated lipid levels in two separate cohorts of Asian adults. Finally, in a separate section an existing method for the identification of spatially extended clusters of image voxels with heightened activation is evaluated in an imaging genetic context. This method, known as cluster size inference, rests on a number of assumptions. Using real imaging and SNP data, false positive rates are found to be poorly controlled outside of a narrow range of parameters related to image smoothness and activation thresholds for cluster formation