Alzheimer's disease (AD) lacks effective cures and is typically detected after substantial pathological changes have occurred, making intervention challenging. Alzheimer's disease (AD) intervention requires early detection of risk factors and understanding their complex interactions before substantial pathological changes manifest. Current research often examines individual risk factors in isolation, limiting our understanding of their combined effects. We present a novel multivariate analytical framework to simultaneously assess multiple AD risk factors using mouse models expressing human ApoE alleles. Our methodological innovation lies in combining high-resolution magnetic resonance diffusion imaging with a comprehensive multifactorial analysis that integrates genotype, age, sex, diet, and immunity as interacting variables. This approach enables the simultaneous examination of regional brain volume and fractional anisotropy changes across multiple risk factors, providing a more holistic view than traditional univariate analyses. Our proposed method effectively identified how these factors converge on specific brain regions - with genotype influencing the caudate putamen, pons, cingulate cortex, and cerebellum; sex affecting the amygdala and piriform cortex; and immune status impacting association cortices and cerebellar nuclei. Importantly, our integrated approach revealed factor interactions that would remain undetected in single-variable studies, particularly in the amygdala, thalamus, and pons. While many findings align with previous research, our multidimensional framework offers a methodological advancement for studying AD risk factors by modeling their combined effects rather than isolated impacts. This approach creates a template for future studies to investigate mechanisms underlying coordinated changes in brain structure through network analyses of gene expression, metabolism, and structural pathways involved in neurodegeneration.

Chemical risk assessment is evolving from traditional deterministic approaches to embrace proba­bilistic methodologies, where risk of hazard manifestation is understood as a more or less probable event depending on exposure, individual factors, and stochastic processes. This is driven by advancements in human stem cells, complex tissue engineering, high-performance computing, and cheminformatics, and is more recently facilitated by large-scale artificial intelligence models. These innovations enable a more nuanced understanding of chemical hazards, capturing the complexity of biological responses and variability within populations. However, each technology comes with its own uncertainties impacting on the estimation of hazard probabilities. This shift addresses the limitations of point estimates and thresholds that oversimplify hazard assessment, allowing for the integration of kinetic variability and uncertainty metrics into risk models. By leveraging modern technologies and expansive toxicological data, probabilistic approaches offer a comprehensive evaluation of chemical safety. This paper summarizes a workshop held in 2023 and discusses the technological and data-driven enablers, and the challenges faced in their implementation, with particular focus on perturbation of biology as the basis of hazard estimates. The future of toxico­logical risk assessment lies in the successful integration of these probabilistic models, promising more accurate and holistic hazard evaluations.

Batch effects, undesirable sources of variability across multiple experiments, present significant challenges for scientific and clinical discoveries. Batch effects can (i) produce spurious signals and/or (ii) obscure genuine signals, contributing to the ongoing reproducibility crisis. Because batch effects are typically modeled as classical statistical effects, they often cannot differentiate between sources of variability due to confounding biases, which may lead them to erroneously conclude batch effects are present (or not). We formalize batch effects as causal effects, and introduce algorithms leveraging causal machinery, to address these concerns. Simulations illustrate that when non-causal methods provide the wrong answer, our methods either produce more accurate answers or "no answer," meaning they assert the data are inadequate to confidently conclude on the presence of a batch effect. Applying our causal methods to 27 neuroimaging datasets yields qualitatively similar results: in situations where it is unclear whether batch effects are present, non-causal methods confidently identify (or fail to identify) batch effects, whereas our causal methods assert that it is unclear whether there are batch effects or not. In instances where batch effects should be discernable, our techniques produce different results from prior art, each of which produce results more qualitatively similar to not applying any batch effect correction to the data at all. This work, therefore, provides a causal framework for understanding the potential capabilities and limitations of analysis of multi-site data.

Over the past two decades, considerable strides have been made in advancing neuroscientific techniques, yet challenges remain in attributing causality to observed associations. This review addresses a fundamental issue in observational neuroscience studies and advocates for incorporating causal inference frameworks into standard practice. We systematically introduce necessary definitions and concepts, emphasizing how causal assumptions underlie statistical analyses even when not explicitly stated. Through a running example on sleep quality and white matter integrity, we illustrate how persistent challenges, including confounding and selection biases, can be conceptualized and addressed using causal frameworks. We demonstrate practical approaches for making assumption violations transparent through hands-on examples: supplementary case studies using multi-site harmonization and head motion exclusion procedures provide step-by-step diagnostic techniques for checking covariate overlap and identifying selection bias through exclusion pattern analysis. We explore how these causal perspectives can inform both experimental design and analytical choices, particularly for observational studies where traditional randomization is infeasible. Together, we believe this framework offers concrete tools for strengthening causal interpretations and inspiring more robust approaches to problems in neuroscience.

The connectome, a map of the structural and/or functional connections in the brain, provides a complex representation of the neurobiological phenotypes on which it supervenes. This information-rich data modality has the potential to transform our understanding of the relationship between patterns in brain connectivity and neurological processes, disorders, and diseases. However, existing computational techniques used to analyze connectomes are often insufficient for interrogating multi-subject connectomics datasets: many current methods are either solely designed to analyze single connectomes or leverage heuristic graph statistics that are unable to capture the complete topology of multiscale connections between brain regions. To enable more rigorous connectomics analysis, we introduce a set of robust and interpretable statistical hypothesis tests motivated by recent theoretical advances in random graph models. These tests facilitate simultaneous analysis of multiple connectomes across different scales of network topology, enabling the robust and reproducible discovery of hierarchical brain structures that vary in relation to phenotypic profiles. In addition to explaining the theoretical foundations and guarantees of our algorithms, we demonstrate their superiority over current state-of-the-art connectomics methods through extensive simulation studies and real-data experiments. Using a set of high-resolution connectomes obtained from genetically distinct mouse strains (including the BTBR mouse-a standard model of autism-and three behavioral wild-types), we illustrate how our methods successfully uncover latent information in multi-subject connectomics data and yield valuable insights into the connective correlates of neurological phenotypes that other methods do not capture. The data and code necessary to reproduce the analyses, simulations, and figures presented in this work are available athttps://github.com/neurodata/MCC.

The advent of modern data collection and processing techniques has seen the size, scale and complexity of data grow exponentially. A seminal step in leveraging these rich datasets for downstream inference is understanding the characteristics of the data which are repeatable-the aspects of the data that are able to be identified under duplicated analyses. Conflictingly, the utility of traditional repeatability measures, such as the intra-class correlation coefficient, under these settings is limited. In recent work, novel data repeatability measures have been introduced in the context where a set of subjects are measured twice or more, including: fingerprinting, rank sums and generalisations of the intra-class correlation coefficient. However, the relationships between, and the best practices among, these measures remains largely unknown. In this manuscript, we formalise a novel repeatability measure, discriminability. We show that it is deterministically linked with the intra-class correlation coefficients under univariate random effect models and has the desired property of optimal accuracy for inferential tasks using multivariate measurements. Additionally, we overview and systematically compare existing repeatability statistics with discriminability, using both theoretical results and simulations. We show that the rank sum statistic is deterministically linked to a consistent estimator of discriminability. The statistical power of permutation tests derived from these measures are compared numerically under Gaussian and non-Gaussian settings, with and without simulated batch effects. Motivated by both theoretical and empirical results, we provide methodological recommendations for each benchmark setting to serve as a resource for future analyses. We believe these recommendations will play an important role towards improving repeatability in fields such as functional magnetic resonance imaging, genomics, pharmacology and more.

A complete understanding of human behavior and disease depends upon our ability to parse genetic and environmental influences in the human brain. The heritability of a trait quantifies the degree of its variability due to genetic influences. Classical approach for quantifying heritability operate on simple traits, and sometimes do not properly model and control for other potential sources of variation, such as age or sex. We therefore develop Causal Heritability of Networks (CHaiN) to rigorously quantify heritability of human brain networks (i.e., connectomes). We applied CHaiN to 1024 anatomical connectomes derived from the Human Connectome Project. Connectomes appeared to be heritable, but heritability was insignificant once we addressed variability within networks. These results suggest that previous conclusions on connectome heritability may be driven by the shared network structures, and highlights the importance of modeling networks and other sources of variability when studying heritability of connectomes.

Characterizing individual variations is central to interpreting individual differences in neuroscience and clinical studies. While the field has examined multifaceted individual differences in brain functional organization, it is only in recent years that neuroimaging researchers have begun to place a priority on its quantification and optimization. Here, we highlight a potential analytic pitfall that can lead to contaminated estimates of inter-individual differences. We define a two-dimensional individual variation field map to decipher sources of individual variation and their relation to fingerprinting and measures of reliability. We illustrate theoretical gradient flow that represents the most effective direction for optimization when measuring individual differences. We propose to use this general framework for dissecting within- and between-individual variation and provide a supporting online tool for the purposes of guiding optimization efforts in biomarker discovery.

Why do brains have inhibitory connections? Why do deep networks have negative weights? We propose an answer from the perspective of representation capacity. We believe representing functions is the primary role of both (i) the brain in natural intelligence, and (ii) deep networks in artificial intelligence. Our answer to why there are inhibitory/negative weights is: to learn more functions. We prove that, in the absence of negative weights, neural networks with non-decreasing activation functions are not universal approximators. While this may be an intuitive result to some, to the best of our knowledge, there is no formal theory, in either machine learning or neuroscience, that demonstrates why negative weights are crucial in the context of representation capacity. Further, we provide insights on the geometric properties of the representation space that non-negative deep networks cannot represent. We expect these insights will yield a deeper understanding of more sophisticated inductive priors imposed on the distribution of weights that lead to more efficient biological and machine learning.

Natural intelligences (NIs) thrive in a dynamic world - they learn quickly, sometimes with only a few samples. In contrast, artificial intelligences (AIs) typically learn with a prohibitive number of training samples and computational power. What design principle difference between NI and AI could contribute to such a discrepancy? Here, we investigate the role of weight polarity: development processes initialize NIs with advantageous polarity configurations; as NIs grow and learn, synapse magnitudes update, yet polarities are largely kept unchanged. We demonstrate with simulation and image classification tasks that if weight polarities are adequately set a priori, then networks learn with less time and data. We also explicitly illustrate situations in which a priori setting the weight polarities is disadvantageous for networks. Our work illustrates the value of weight polarities from the perspective of statistical and computational efficiency during learning.

Causal inference studies whether the presence of a variable influences an observed outcome. As measured by quantities such as the "average treatment effect," this paradigm is employed across numerous biological fields, from vaccine and drug development to policy interventions. Unfortunately, the majority of these methods are often limited to univariate outcomes. Our work generalizes causal estimands to outcomes with any number of dimensions or any measurable space, and formulates traditional causal estimands for nominal variables as causal discrepancy tests. We propose a simple technique for adjusting universally consistent conditional independence tests and prove that these tests are universally consistent causal discrepancy tests. Numerical experiments illustrate that our method, Causal CDcorr, leads to improvements in both finite sample validity and power when compared to existing strategies. Our methods are all open source and available at github.com/ebridge2/cdcorr.

Comparing connectomes can help explain how neural connectivity is related to genetics, disease, development, learning, and behavior. However, making statistical inferences about the significance and nature of differences between two networks is an open problem, and such analysis has not been extensively applied to nanoscale connectomes. Here, we investigate this problem via a case study on the bilateral symmetry of a larval Drosophila brain connectome. We translate notions of ‘bilateral symmetry’ to generative models of the network structure of the left and right hemispheres, allowing us to test and refine our understanding of symmetry. We find significant differences in connection probabilities both across the entire left and right networks and between specific cell types. By rescaling connection probabilities or removing certain edges based on weight, we also present adjusted definitions of bilateral symmetry exhibited by this connectome. This work shows how statistical inferences from networks can inform the study of connectomes, facilitating future comparisons of neural structures.

Batch effects, undesirable sources of variance across multiple experiments, present a substantial hurdle for scientific and clinical discoveries. Specifically, the presence of batch effects can create both spurious discoveries and hide veridical signals, contributing to the ongoing reproducibility crisis. Typical approaches to dealing with batch effects conceptualize ‘batches’ as an associational effect, rather than a causal effect, despite the fact that the sources of variance that comprise the batch – potentially including experimental design and population demographics – causally impact downstream inferences. We therefore cast batch effects as a causal problem rather than an associational problem. This reformulation enables us to make explicit the assumptions and limitations of existing approaches for dealing with batch effects. We therefore develop causal batch effect strategies—Causal Dcorr for discovery of batch effects and Causal ComBat for mitigating batch effects – which build upon existing statistical associational methods by incorporating modern causal inference techniques. We apply these strategies to a large mega-study of human connectomes assembled by the Consortium for Reliability and Reproducibility, consisting of 24 batches including over 1700 individuals to illustrate that existing approaches create more spurious discoveries (false positives) and miss more veridical signals (true positives) than our proposed approaches. Our work therefore introduces a conceptual framing, as well as open source code, for combining multiple distinct datasets to increase confidence in claims of scientific and clinical discoveries.

Abstract Teaching data analysis by providing students with real-world problems and datasets allows students to integrate a variety of skills in a situation that mirrors how data analysis actually works. However, whole data analyses may obscure the individual skills of data analytic practice that are generalizable across data analyses. One such skill is the ability to diagnose the cause of unexpected results in a data analysis. While experienced analysts can quickly iterate through a series of potential explanations when confronted with unexpected results, novice analysts often struggle to figure out how to move forward. The goal of this article is to describe an approach to teaching students skills in diagnosing data analytic problems. The exercise described here is targeted to allow students to practice this skill and to assess the depth of their knowledge about the statistical tools they have learned. We take a hypothetical case study approach and focus on the students’ reasoning through their diagnoses and suggestions for follow-up action. We found the implementation of this exercise in a small graduate course to provide valuable information about the students’ diagnostic thought processes, but further work is needed regarding structured approaches to implementation and the design of assessments. Supplementary materials for this article are available online.

The alignment strength of a graph matching is a quantity that gives the practitioner a measure of the correlation of the two graphs, and it can also give the practitioner a sense for whether the graph matching algorithm found the true matching. Unfortunately, when a graph matching algorithm fails to find the truth because of weak signal, there may be ``phantom alignment strength'' from meaningless matchings that, by random noise, have fewer disagreements than average (sometimes substantially fewer); this alignment strength may give the misleading appearance of significance. A practitioner needs to know what level of alignment strength may be phantom alignment strength and what level indicates that the graph matching algorithm obtained the true matching and is a meaningful measure of the graph correlation. The {\it Phantom Alignment Strength Conjecture} introduced here provides a principled and practical means to approach this issue. We provide empirical evidence for the conjecture, and explore its consequences.

The alignment strength of a graph matching is a quantity that gives the practitioner a measure of the correlation of the two graphs, and it can also give the practitioner a sense for whether the graph matching algorithm found the true matching. Unfortunately, when a graph matching algorithm fails to find the truth because of weak signal, there may be “phantom alignment strength” from meaningless matchings that, by random noise, have fewer disagreements than average (sometimes substantially fewer); this alignment strength may give the misleading appearance of significance. A practitioner needs to know what level of alignment strength may be phantom alignment strength and what level indicates that the graph matching algorithm obtained the true matching and is a meaningful measure of the graph correlation. The Phantom Alignment Strength Conjecture introduced here provides a principled and practical means to approach this issue. We provide empirical evidence for the conjecture, and explore its consequences.

Replicability, the ability to replicate scientific findings, is a prerequisite for scientific discovery and clinical utility. Troublingly, we are in the midst of a replicability crisis. A key to replicability is that multiple measurements of the same item (e.g., experimental sample or clinical participant) under fixed experimental constraints are relatively similar to one another. Thus, statistics that quantify the relative contributions of accidental deviations—such as measurement error—as compared to systematic deviations—such as individual differences—are critical. We demonstrate that existing replicability statistics, such as intra-class correlation coefficient and fingerprinting, fail to adequately differentiate between accidental and systematic deviations in very simple settings. We therefore propose a novel statistic, discriminability , which quantifies the degree to which an individual’s samples are relatively similar to one another, without restricting the data to be univariate, Gaussian, or even Euclidean. Using this statistic, we introduce the possibility of optimizing experimental design via increasing discriminability and prove that optimizing discriminability improves performance bounds in subsequent inference tasks. In extensive simulated and real datasets (focusing on brain imaging and demonstrating on genomics), only optimizing data discriminability improves performance on all subsequent inference tasks for each dataset. We therefore suggest that designing experiments and analyses to optimize discriminability may be a crucial step in solving the replicability crisis, and more generally, mitigating accidental measurement error.

To solve key biomedical problems, experimentalists now routinely measure millions or billions of features (dimensions) per sample, with the hope that data science techniques will be able to build accurate data-driven inferences. Because sample sizes are typically orders of magnitude smaller than the dimensionality of these data, valid inferences require finding a low-dimensional representation that preserves the discriminating information (e.g., whether the individual suffers from a particular disease). There is a lack of interpretable supervised dimensionality reduction methods that scale to millions of dimensions with strong statistical theoretical guarantees.We introduce an approach, XOX, to extending principal components analysis by incorporating class-conditional moment estimates into the low-dimensional projection. The simplest ver-sion, Linear Optimal Low-rank projection (LOL), incorporates the class-conditional means. We prove, and substantiate with both synthetic and real data benchmarks, that LOL and its generalizations in the XOX framework lead to improved data representations for subsequent classification, while maintaining computational efficiency and scalability. Using multiple brain imaging datasets consisting of >150 million features, and several genomics datasets with>500,000 features, LOL outperforms other scalable linear dimensionality reduction techniques in terms of accuracy, while only requiring a few minutes on a standard desktop computer.

Using brain atlases to localize regions of interest is a requirement for making neuroscientifically valid statistical inferences. These atlases, represented in volumetric or surface coordinate spaces, can describe brain topology from a variety of perspectives. Although many human brain atlases have circulated the field over the past fifty years, limited effort has been devoted to their standardization. Standardization can facilitate consistency and transparency with respect to orientation, resolution, labeling scheme, file storage format, and coordinate space designation. Our group has worked to consolidate an extensive selection of popular human brain atlases into a single, curated, open-source library, where they are stored following a standardized protocol with accompanying metadata, which can serve as the basis for future atlases. The repository containing the atlases, the specification, as well as relevant transformation functions is available in the neuroparc OSF registered repository or https://github.com/neurodata/neuroparc .

The data science of networks is a rapidly developing field with myriad applications. In neuroscience, the brain is commonly modeled as a connectome, a network of nodes connected by edges. While there have been thousands of papers on connectomics, the statistics of networks remains limited and poorly understood. Here, we provide an overview from the perspective of statistical network science of the kinds of models, assumptions, problems, and applications that are theoretically and empirically justified for analysis of connectome data. We hope this review spurs further development and application of statistically grounded methods in connectomics.