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Abstract Mendelian Randomization (MR) studies are threatened by population stratification, batch effects, and horizontal pleiotropy. Although a variety of methods have been proposed to mitigate those problems, residual biases may still remain, leading to highly statistically significant false positives in large databases. Here we describe a suite of sensitivity analysis tools that enables investigators to quantify the robustness of their findings against such validity threats. Specifically, we propose the routine reporting of sensitivity statistics that reveal the minimal strength of violations necessary to explain away the MR results. We further provide intuitive displays of the robustness of the MR estimate to any degree of violation, and formal bounds on the worst-case bias caused by violations multiple times stronger than observed variables. We demonstrate how these tools can aid researchers in distinguishing robust from fragile findings by examining the effect of body mass index on diastolic blood pressure and Townsend deprivation index. 

The ability to predict human phenotypes and identify biomarkers of disease from metagenomic data is crucial for the development of therapeutics for microbiome-associated diseases. However, metagenomic data is commonly affected by technical variables unrelated to the phenotype of interest, such as sequencing protocol, which can make it difficult to predict phenotype and find biomarkers of disease. Supervised methods to correct for background noise, originally designed for gene expression and RNA-seq data, are commonly applied to microbiome data but may be limited because they cannot account for unmeasured sources of variation. Unsupervised approaches address this issue, but current methods are limited because they are ill-equipped to deal with the unique aspects of microbiome data, which is compositional, highly skewed, and sparse. We perform a comparative analysis of the ability of different denoising transformations in combination with supervised correction methods as well as an unsupervised principal component correction approach that is presently used in other domains but has not been applied to microbiome data to date. We find that the unsupervised principal component correction approach has comparable ability in reducing false discovery of biomarkers as the supervised approaches, with the added benefit of not needing to know the sources of variation apriori. However, in prediction tasks, it appears to only improve prediction when technical variables contribute to the majority of variance in the data. As new and larger metagenomic datasets become increasingly available, background noise correction will become essential for generating reproducible microbiome analyses. 

Microbial source tracking analysis has emerged as a widespread technique for characterizing the properties of complex microbial communities. However, this analysis is currently limited to source environments sampled in a specific study. In order to expand the scope beyond one single study and allow the exploration of source environments using large databases and repositories, such as the Earth Microbiome Project, a source selection procedure is required. Such a procedure will allow differentiating between contributing environments and nuisance ones when the number of potential sources considered is high. Here, we introduce STENSL (microbial Source Tracking with ENvironment SeLection), a machine learning method that extends common microbial source tracking analysis by performing an unsupervised source selection and enabling sparse identification of latent source environments. By incorporating sparsity into the estimation of potential source environments, STENSL improves the accuracy of true source contribution, while significantly reducing the noise introduced by noncontributing ones. We therefore anticipate that source selection will augment microbial source tracking analyses, enabling exploration of multiple source environments from publicly available repositories while maintaining high accuracy of the statistical inference. 

The number of variants that have a non-zero effect on a trait ( i.e . polygenicity) is a fundamental parameter in the study of the genetic architecture of a complex trait. Although many previous studies have investigated polygenicity at a genome-wide scale, a detailed understanding of how polygenicity varies across genomic regions is currently lacking. In this work, we propose an accurate and scalable statistical framework to estimate regional polygenicity for a complex trait. We show that our approach yields approximately unbiased estimates of regional polygenicity in simulations across a wide-range of various genetic architectures. We then partition the polygenicity of anthropometric and blood pressure traits across 6-Mb genomic regions ( N = 290K, UK Biobank) and observe that all analyzed traits are highly polygenic: over one-third of regions harbor at least one causal variant for each of the traits analyzed. Additionally, we observe wide variation in regional polygenicity: on average across all traits, 48.9% of regions contain at least 5 causal SNPs, 5.44% of regions contain at least 50 causal SNPs. Finally, we find that heritability is proportional to polygenicity at the regional level, which is consistent with the hypothesis that heritability enrichments are largely driven by the variation in the number of causal SNPs. 

In this paper, we explore connections between interpretable machine learning and learning theory through the lens of local approximation explanations. First, we tackle the traditional problem of performance generalization and bound the test-time accuracy of a model using a notion of how locally explainable it is. Second, we explore the novel problem of explanation generalization which is an important concern for a growing class of finite sample-based local approximation explanations. Finally, we validate our theoretical results empirically and show that they reflect what can be seen in practice. 

Linear mixed models (LMMs) can be applied in the meta-analyses of responses from individuals across multiple contexts, increasing power to detect associations while accounting for confounding effects arising from within-individual variation. However, traditional approaches to fitting these models can be computationally intractable. Here, we describe an efficient and exact method for fitting a multiple-context linear mixed model. Whereas existing exact methods may be cubic in their time complexity with respect to the number of individuals, our approach for multiple-context LMMs (mcLMM) is linear. These improvements allow for large-scale analyses requiring computing time and memory magnitudes of order less than existing methods. As examples, we apply our approach to identify expression quantitative trait loci from large-scale gene expression data measured across multiple tissues as well as joint analyses of multiple phenotypes in genome-wide association studies at biobank scale.