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 at https://github.com/neurodata/MCC .

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.