Distance-based analysis of variance: Approximate inference

Individual differences in delay discounting are associated with dorsal prefrontal cortex connectivity in children, adolescents, and adults

Delay discounting is a measure of impulsive choice relevant in adolescence as it predicts many real-life outcomes, including obesity and academic achievement. However, resting-state functional networks underlying individual differences in delay discounting during youth remain incompletely described. Here we investigate the association between multivariate patterns of functional connectivity and individual differences in impulsive choice in a large sample of children, adolescents, and adults. A total of 293 participants (9-23 years) completed a delay discounting task and underwent 3T resting-state fMRI. A connectome-wide analysis using multivariate distance-based matrix regression was used to examine whole-brain relationships between delay discounting and functional connectivity. These analyses revealed that individual differences in delay discounting were associated with patterns of connectivity emanating from the left dorsal prefrontal cortex, a default mode network hub. Greater delay discounting was associated with greater functional connectivity between the dorsal prefrontal cortex and other default mode network regions, but reduced connectivity with regions in the dorsal and ventral attention networks. These results suggest delay discounting in children, adolescents, and adults is associated with individual differences in relationships both within the default mode network and between the default mode and networks involved in attentional and cognitive control.

Kernel-based genetic association analysis for microbiome phenotypes identifies host genetic drivers of beta-diversity

BACKGROUND

Understanding human genetic influences on the gut microbiota helps elucidate the mechanisms by which genetics may influence health outcomes. Typical microbiome genome-wide association studies (GWAS) marginally assess the association between individual genetic variants and individual microbial taxa. We propose a novel approach, the covariate-adjusted kernel RV (KRV) framework, to map genetic variants associated with microbiome beta-diversity, which focuses on overall shifts in the microbiota. The KRV framework evaluates the association between genetics and microbes by comparing similarity in genetic profiles, based on groups of variants at the gene level, to similarity in microbiome profiles, based on the overall microbiome composition, across all pairs of individuals. By reducing the multiple-testing burden and capturing intrinsic structure within the genetic and microbiome data, the KRV framework has the potential of improving statistical power in microbiome GWAS.

RESULTS

We apply the covariate-adjusted KRV to the Hispanic Community Health Study/Study of Latinos (HCHS/SOL) in a two-stage (first gene-level, then variant-level) genome-wide association analysis for gut microbiome beta-diversity. We have identified an immunity-related gene, IL23R, reported in a previous microbiome genetic association study and discovered 3 other novel genes, 2 of which are involved in immune functions or autoimmune disorders. In addition, simulation studies show that the covariate-adjusted KRV has a greater power than other microbiome GWAS methods that rely on univariate microbiome phenotypes across a range of scenarios.

CONCLUSIONS

Our findings highlight the value of the covariate-adjusted KRV as a powerful microbiome GWAS approach and support an important role of immunity-related genes in shaping the gut microbiome composition. Video Abstract.

Distance-based analysis of variance for brain connectivity

The field of neuroimaging dedicated to mapping connections in the brain is increasingly being recognized as key for understanding neurodevelopment and pathology. Networks of these connections are quantitatively represented using complex structures, including matrices, functions, and graphs, which require specialized statistical techniques for estimation and inference about developmental and disorder-related changes. Unfortunately, classical statistical testing procedures are not well suited to high-dimensional testing problems. In the context of global or regional tests for differences in neuroimaging data, traditional analysis of variance (ANOVA) is not directly applicable without first summarizing the data into univariate or low-dimensional features, a process that might mask the salient features of high-dimensional distributions. In this work, we consider a general framework for two-sample testing of complex structures by studying generalized within-group and between-group variances based on distances between complex and potentially high-dimensional observations. We derive an asymptotic approximation to the null distribution of the ANOVA test statistic, and conduct simulation studies with scalar and graph outcomes to study finite sample properties of the test. Finally, we apply our test to our motivating study of structural connectivity in autism spectrum disorder.

Application of the distance-based F test in an mGWAS investigating β diversity of intestinal microbiota identifies variants in SLC9A8 (NHE8) and 3 other loci

Factors shaping the human intestinal microbiota range from environmental influences, like smoking and exercise, over dietary patterns and disease to the host's genetic variation. Recently, we could show in a microbiome genome-wide association study (mGWAS) targeting genetic variation influencing the β diversity of gut microbial communities, that approximately 10% of the overall gut microbiome variation can be explained by host genetics. Here, we report on the application of a new method for genotype-β-diversity association testing, the distance-based F (DBF) test. With this we identified 4 loci with genome-wide significant associations, harboring the genes CBEP4, SLC9A8, TNFSF4, and SP140, respectively. Our findings highlight the utility of the high-performance DBF test in β diversity GWAS and emphasize the important role of host genetics and immunity in shaping the human intestinal microbiota.

Faster permutation inference in brain imaging

Permutation tests are increasingly being used as a reliable method for inference in neuroimaging analysis. However, they are computationally intensive. For small, non-imaging datasets, recomputing a model thousands of times is seldom a problem, but for large, complex models this can be prohibitively slow, even with the availability of inexpensive computing power. Here we exploit properties of statistics used with the general linear model (GLM) and their distributions to obtain accelerations irrespective of generic software or hardware improvements. We compare the following approaches: (i) performing a small number of permutations; (ii) estimating the p-value as a parameter of a negative binomial distribution; (iii) fitting a generalised Pareto distribution to the tail of the permutation distribution; (iv) computing p-values based on the expected moments of the permutation distribution, approximated from a gamma distribution; (v) direct fitting of a gamma distribution to the empirical permutation distribution; and (vi) permuting a reduced number of voxels, with completion of the remainder using low rank matrix theory. Using synthetic data we assessed the different methods in terms of their error rates, power, agreement with a reference result, and the risk of taking a different decision regarding the rejection of the null hypotheses (known as the resampling risk). We also conducted a re-analysis of a voxel-based morphometry study as a real-data example. All methods yielded exact error rates. Likewise, power was similar across methods. Resampling risk was higher for methods (i), (iii) and (v). For comparable resampling risks, the method in which no permutations are done (iv) was the absolute fastest. All methods produced visually similar maps for the real data, with stronger effects being detected in the family-wise error rate corrected maps by (iii) and (v), and generally similar to the results seen in the reference set. Overall, for uncorrected p-values, method (iv) was found the best as long as symmetric errors can be assumed. In all other settings, including for familywise error corrected p-values, we recommend the tail approximation (iii). The methods considered are freely available in the tool PALM - Permutation Analysis of Linear Models.

Nonlinear association criterion, nonlinear Granger causality and related issues with applications to neuroimage studies

BACKGROUND

Quantifying associations in neuroscience (and many other scientific disciplines) is often challenged by high-dimensionality, nonlinearity and noisy observations. Many classic methods have either poor power or poor scalability on data sets of the same or different scales such as genetical, physiological and image data.

NEW METHOD

Based on the framework of reproducing kernel Hilbert spaces we proposed a new nonlinear association criteria (NAC) with an efficient numerical algorithm and p-value approximation scheme. We also presented mathematical justification that links the proposed method to related methods such as kernel generalized variance, kernel canonical correlation analysis and Hilbert-Schmidt independence criteria. NAC allows the detection of association between arbitrary input domain as long as a characteristic kernel is defined. A MATLAB package was provided to facilitate applications.

RESULTS

Extensive simulation examples and four real world neuroscience examples including functional MRI causality, Calcium imaging and imaging genetic studies on autism [Brain, 138(5):13821393 (2015)] and alcohol addiction [PNAS, 112(30):E4085-E4093 (2015)] are used to benchmark NAC. It demonstrates the superior performance over the existing procedures we tested and also yields biologically significant results for the real world examples.

COMPARISON WITH EXISTING METHOD(S)

NAC beats its linear counterparts when nonlinearity is presented in the data. It also shows more robustness against different experimental setups compared with its nonlinear counterparts.

CONCLUSIONS

In this work we presented a new and robust statistical approach NAC for measuring associations. It could serve as an interesting alternative to the existing methods for datasets where nonlinearity and other confounding factors are present.